JPH0682397B2 - Fuzzy member-ship function circuits applicable to crisp sets - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION A main part circuit of a Z function circuit or an S function circuit, which is one of fuzzy membership function circuits, is provided with a predetermined grade controlled according to a current comparison circuit and its comparison result. A fuzzy membership function circuit applicable to a crisp set, characterized in that an input / output characteristic having an almost vertical rise is added by providing a circuit for turning on / off a current to be expressed.

The embodiment is shown in FIGS. 34 and 35, and the application example is shown in FIG.

Contents (1) Background of the invention (1.1) Technical field (1.2) New fuzzy logic circuit that operates in the limit and current mode of digital computer (1.3) Concept of membership function circuit and fuzzy control system (Fig. 1, Fig. 1) (Fig. 2) (1.4) Concept of fuzzy system with learning function (Fig. 3) (2) Outline of invention (2.1) Purpose of invention (2.2) Structure and effect of invention (3) Description of embodiments (3.1) ) Membership functions of various types and their definitions (Fig. 4) (3.2) Z-function circuit (Figs. 5, 6, 7, 8) (3.3) S-function circuit (Figs. 9, 10, 11, 12) ) (3.4) Arbitrary setting of gradient during use (Figs. 14, 15) (3.5) Gradient switching control (Figs. 15, 16, 17, 18) (3.6) Programmable multi-membership function circuit (Fig. 19) , 20,21) (3.7) MIN circuit and MAX circuit (22,23,24,25,26,27,28
(Fig.) (3.8) Simplified programmable multi-membership function circuit (Fig. 29, 30) (3.9) Expanded programmable multi-membership function circuit (Fig. 31, 32, 33) (3.10) S-function circuit applicable to crisp sets (34th, 3rd
(Fig. 5) (3.11) Upslope function circuit applicable to crisp sets (Figs. 36, 37) (3.12) Programmable multi-membership function circuit applicable to crisp sets (Fig. 38) (1) BACKGROUND (1.1) Technical field The present invention relates to a membership function circuit that is indispensable for constructing a new fuzzy control system, and more particularly to a fuzzy membership function circuit applicable to a crisp set.

(1.2) New fuzzy logic circuit that operates in the limit and current mode of digital computer Fuzzy logic is a logic that deals with fuzzyness or "ambiguity". There is ambiguity in human thoughts and actions. Therefore, if such ambiguity can be quantified or theorized, it should be applicable to the design of traffic control, emergency, social systems such as applied medical systems, robots imitating human beings, and the like. LA Zadeh in 1965
Since the concept of fuzzy sets was proposed by, fuzzy logic has been studied as one means to deal with "ambiguity" from this point of view. However, most of this research is currently applied to software systems using digital computers. A digital computer performs an operation based on a binary logic consisting of 0 and 1, and its operation processing is extremely strict, but it is necessary to add an A / D conversion circuit to the input of an analog quantity. Therefore, when trying to process a huge amount of information, there is a problem that it takes a long time to obtain a final result. In addition, the program for applying fuzzy logic must be extremely complicated, and a large-scale digital computer is required for complicated processing, which is not economical.

In the first place, fuzzy logic is a logic that handles continuous values (0,1) in the interval from 0 to 1, so it has the aspect that it does not fit into a digital computer based on binary logic. Fuzzy logic handles a wide range of ambiguous quantities, so it is not required to be as rigorous as a digital computer. This is why it is desirable to realize a new circuit suitable for dealing with fuzzy logic.

In order to meet such a demand, the inventor has already proposed a number of fuzzy logic circuits which operate in a current mode (for example, Japanese Patent Application No. 59-57121). The fuzzy logic circuit proposed by the inventor includes a limit difference circuit, a logical complement circuit, a limit sum circuit, a limit product circuit, a logical sum (MAX) circuit, a logical product (MIN) circuit, an absolute difference circuit, an implication circuit, a peer circuit. Etc., and all of these circuits operate in current mode. All of the above fuzzy logic circuits are characterized by being composed of a combination of one or more limit difference circuits and addition (subtraction) circuits. In current mode, since addition and subtraction can be realized by simple wiring (wired sum or wired subtract), all the above fuzzy logic circuits basically have a fuzzy limit difference circuit as their only unit. You can Therefore, a fuzzy logic circuit that operates in current mode is advantageous in many respects both in its circuit design and in the manufacture of ICs.

(1.3) Concept of membership function circuit and fuzzy control system (Figs. 1 and 2) The fuzzy set A is characterized by the membership function µ _A (x). The membership function μ _A (x) represents the degree to which the variable x belongs to the fuzzy set A. This degree is represented by continuous values [0,1] in the interval from 0 to 1. . Membership function μ
An example of _A (x) is shown in FIG.

The membership function circuit is a circuit that outputs a value μ _A (x) representing the degree to which x belongs to the fuzzy set A when a variable x having a certain value is given as an input.

An example of the concept of the fuzzy control system using the fuzzy logic circuit and the membership function circuit as described above is shown in FIG.

As an example of the application of fuzzy control, it has been considered to automate the control of a system that has been operated or controlled by humans based on a wealth of experience and feelings. The system of human control is extremely complicated, but if it is simplified, it can be understood as a combination of some or many empirical rules. This rule of thumb is "○○
(State, etc.) ”is XX, then △△ (state, etc.)
Can be expressed in a straightforward way. It becomes more general if this rule of thumb is made a little more complicated and is expanded to “If XX is XX and (or) XX is XX, then △△ is □□”. The propositional form of this general rule of thumb is called control law in fuzzy control systems.

According to the usage of the feedback control system, the output e of the controlled system and its deviation Δe are used as control inputs, and the control output given to the controlled system is Δu.

In FIG. 2, as an example of the control law, if control law 1 "e is a small negative value and Δe is a small positive value, then Δu
Be a small positive value. " This control rule 1 is expressed as e = NSandΔe = PS → ΔuPS. Here, NS is a negative small value.
l), PS means a positive small value, and and means “and”.

As the control law 2, “if e is a small positive value and Δe is a small negative value, let Δu be a small negative value”. This is expressed as follows.

e = PSandΔe = NS → ΔuNS In addition, some or many control rules are set.

Membership is the answer to the question of how much the given control input e = e ₀ can be said to be a small negative value in judging "e is a small negative value" in Control Law 1. Function 1 _A <MS function 1 _A > The membership function 1 _A is obtained from a membership function circuit (not shown), and represents the degree to which the control input e belongs to “a set of small negative values”. In Fig. 2, a triangular function having a peak at a certain negative value of e is given as the membership function 1 _A. According to this function 1 _A ,
The degree to which a control input e = e ₀ = -0.2 belongs to this set
0.8.

Similarly, FIG. 2 shows the membership function 1 _B <MS function 1 _B > which represents the degree of belonging to the control input Δe “set of small positive values”. This function 1 _B also has a triangular shape that peaks when Δe has a positive value. According to this membership function 1 _B output from a membership function circuit (not shown), a certain control input Δe = Δe ₀ =
The degree to which +0.1 belongs to this set is 0.6.

The condition "and" of "e is a small negative value and Δe is a small positive value" in the control rule 1 is generally calculated by fuzzy logical product (MIN). This operation MIN specifically selects the smaller of the two variables.
Therefore, the value of membership function 1 _A above is 0.8
_From the value of _B of 0.6, the value 0.6
Is obtained.

The command "Set Δu to a small positive value" in Control Law 1 is also given by the membership function <original command 1>. The function represented by the original command 1 is also shown as an example of a triangular shape having a peak value of 1 when Δu has a certain positive value. The function representing the original command 1 is generated from a membership function generating circuit (not shown).

It is executed by "if" in the control law 1, for example, multiplication. A value of 0.6 is obtained by the MIN operation described above. Multiplying the function of original command 1 by 0.6, the peak value is
A triangular function <command 1> of 0.6 is created.

The calculation of “if” may be performed by MIN. In this case, a trapezoidal function as shown by the broken line will be obtained as the command 1.

Similarly in the control law 2, the applied control input e
By applying this control law 2 to and Δe, <command 2> is created. The application of other control laws could create other directives as well.

Generally, a plurality of control rules are set for one controlled system as described above. The respective commands derived from these control laws are used to finally obtain the control output Δu. Therefore, the fuzzy logical sum (MAX) operation is performed on the commands derived from each control law. Second
The graph of <inference result> shown in the figure shows <command 1> and <command 1>.
The MAX calculation result of command 2> is shown. Among them, the solid line graph shows that multiplication was used as the “if” condition of each control law, and the broken line graph shows the “if” condition.
Each shows the result of MIN calculation.

Finally, the control output Δu is determined using such inference result. This is the defuzzific
ation). The above-mentioned operations including the generation of the membership function are performed in a state in which "ambiguity" is included according to the fuzzy logic, but at this stage, the control output Δu having one fixed value is determined. There must be.

The defuzzification can be performed, for example, by taking the weighted average of the function indicating the <inference result>, that is, by obtaining the position of the center of gravity. In this embodiment, the control output is finally determined as Δu = Δu ₀ = + 0.1. Almost the same result will be obtained when MIN is performed as an operation of “if”.

The position of the center of gravity of <command 1> and the position of the center of gravity of <command 2> may be obtained first, and the weighted average of these two positions may be taken to perform the defuzzification.

Membership functions 1 _A , 1 _B, etc. are preferably variable. That is, the control output Δ determined as described above
In the process of continuing the control of the controlled system by u, it is monitored whether the control is properly performed. If the optimal control is not performed, the membership function (its value or the shape of the graph) is changed to pursue the membership function that enables the optimal control. This is generally called "learning function".

(1.4) Concept of fuzzy system with learning function (Fig. 3) Fig. 3 shows fuzzy system with learning function as described above.
1 schematically shows an example of a system.

Any physical input, such as the above-mentioned control input or key-in data, is normalized by the input conversion circuit 11 as necessary, or converted into a signal of an appropriate form. This conversion circuit 11 may be unnecessary in some cases.

The membership function circuit group 12 is provided with many membership function circuits with variable parameters.
One or more predetermined ones are selected according to the input signal from 11, and a signal representing the membership function according to the input signal is output.

On the other hand, circuits that generate one or more membership functions
15 are provided. Membership function outputs from these circuits 12 and 15 are input to a fuzzy logic network 13, where an operation according to a predetermined fuzzy logic is performed and the operation result is output. The logic of this network 13 and the parameters of the membership function function generating circuit 15 are also preferably changeable as required.

The fuzzy information output from the fuzzy logic circuit network 13 may be output as it is, but in some cases, the defuzzification circuit 14 makes some decision and outputs it.

This output may be displayed, used as the control output Δu described above, or used for various purposes.

The output of the fuzzy logic network 13 or the defuzzification circuit 14 is compared to the reference (standard, standard) input.
This reference input represents the correct answer for learning, and may be given by, for example, a skilled expert, digital computer simulation, or the like.

The control / memory circuit 16 changes the shape and parameters of each membership function of the membership function circuit group 12 and the membership function generation circuit 15 so that the deviation becomes zero according to the comparison result, Fuzzy logic network
Change the type and connection of the logical function in 13.

In this way, this fuzzy system is adjusted and modified so that the correct output (correct answer) is always generated by learning.

(2) Outline of the invention (2.1) Object of the invention The object of the invention is to obtain a membership function used in the system described in (1,3) and (1,4) above. It is to provide a fuzzy membership function circuit applicable to a crisp set.

(2.2) Structure and effect of the invention The main part of a circuit that generates a basic fuzzy membership function called a Z-function or S-function performs subtraction between an input signal and a reference signal representing a value related to a breakpoint. The first subtraction circuit to perform, and if the input signal is larger than the reference signal, outputs the subtraction result of the first subtraction circuit,
In other cases, the output signal of the limit difference circuit is subtracted from the signal representing the predetermined grade, and the limit difference circuit consisting of a circuit that outputs a signal representing zero, and the signal representing the positive subtraction result is output and subtracted. It is composed of a second subtraction circuit which outputs a signal representing zero when the result is negative.

According to the present invention, the fuzzy membership function circuit can be applied to the control system using the logic of the crisp set, that is, the binary logic of 1 and 0. Circuit elements are added. That is, the first switching element is provided at a proper position between the first subtraction circuit and the second subtraction circuit, and is provided between the second subtraction circuit and the input terminal of the signal representing the predetermined grade. , Turn on at the same time as the first switching element,
A second switching element that is controlled to be turned off, a third switching element that is connected in parallel to the second switching element, and an input signal and a reference signal are compared, and the third switching element is switched according to the comparison result. It is a comparison circuit for controlling.

0 when the first and second switching elements are turned on
The circuit outputs a membership function for fuzzy logic that handles continuous values of ~ 1. When these switching elements are turned off, the circuit outputs a function for binary logic of 1 and 0.

In the membership function circuit operating in the current mode, the limit difference circuit performs the subtraction between the input current and the reference current representing the value relating to the break point.
And a current mirror connected to the output side of this subtraction circuit. The second subtraction circuit subtracts the output current of the limit difference circuit from the current representing the predetermined grade, and the diode acting element is connected to the output side thereof. The comparison circuit is composed of a current comparison circuit.

When the current mirror of the limit difference circuit is composed of a multi-output current mirror in which a plurality of output lines are connected in parallel and a fourth switching element provided in at least one of the plurality of output lines, It becomes possible to obtain a fuzzy membership function that can be switched.

As will be apparent from the description of the embodiments, the membership function circuit according to the present invention is a basic circuit for generating various fuzzy membership functions, particularly fuzzy membership function generation applicable to crisp sets. It is a basic circuit for and is extremely useful.

Examples of the present invention will be described in detail below.

In the following description of the embodiments, first, various types of membership functions will be clarified (FIG. 4), and circuits that generate basic Z and S functions will be described (FIGS. 5 to 12). After expanding the developments of the Z-function circuit and the S-function circuit and their applications, the S-function circuit applicable to the crisp set which is an embodiment of the present invention will be described with reference to FIGS. 34 and 35, and further, The application example will be described in detail (Fig. 38).

(3) Description of Examples (3, 1) Membership functions of various types and their definitions (Fig. 4) An example of the membership function is generally shown in Fig. 1 (A). It is often expressed as a curve. However, whether or not it should be represented by a curve is not an essential point depending on the membership function. The more important feature of the membership function is that it takes continuous values from 0 to 1.

On the other hand, from a circuit design point of view, it is easier to handle the membership function with a straight broken line, as shown in FIG. Can be characterized and the design is simple. Moreover, even if the membership function is expressed by a broken line, the above characteristics are not lost.

Therefore, in the following description, all memberships will be represented by straight lines or their broken lines.

The membership function shown in FIG. 1 (B) is only an example. There are many other types of membership. The definitions will be described below.

In Figure 4, ten kinds of membership functions are shown.

The first is a function that always takes a value of 0 regardless of the value of the variable x, and this is defined as the φ function.

The second one is defined as one function that always takes the value of one.

The third one takes a value of 1 in the region where the variable x is small,
When it reaches a certain value Z _B , it decreases with a constant gradient and finally reaches 0, and it is a function that always takes a value of 0 in the region where x is larger than that. That is, it has one downward slope on the variable X axis.
This is named the Z function. We call x = Z _B a breakpoint. The gradient can take any value. The X-function can be defined by the breakpoint Z _B and the slope. Even if Z _B = 0 and Z _B <0, this is included in the Z function.

The fourth one is an inverted version of the Z function, which is defined as the S function. That is, it has one upward slope on the X axis. The S function is also defined by the breakpoint S _B and the slope.

The fifth one is called the π function, and takes a value of 1 when the variable x is in a certain area, and x is a break point S.
_When it is smaller than _B2 or larger than ZB2, it decreases with a constant gradient, and finally takes a value of 0, and is a function that is always 0 in a region where x is smaller and larger than that. It can also be called a trapezoidal function. The π function is characterized by two break points S _B2 , Z _B2 and a gradient.

In a special case, S _B2 = Z _B2 , which is a triangle as shown by the chain line.

The sixth one is defined as a U function which is the inverted π function. It can be said that it is a function with one valley. U
The function is defined by two breakpoints Z _B1 , S _B1 and a gradient. In special cases, the shape is indicated by the chain line (Z _B1 = S _B1 ).

The form of the membership function becomes more complicated.

The seventh one is a combination of a trapezoidal function (π function) and an up-slope function (S function) in a region where x is larger than that, and is defined as an N function. From a different point of view, this can be said to be a combination of a function having a valley (U function) and a function of an upslope (S function) in a region where x is smaller than that. In any case, this N-function is defined by three break points S _B2 , Z _B2 , S _B1 and a slope.

The eighth one is the inverse of the N function and is defined as the И function. This is also three break points Z
It is defined by _B1 , S _B2 , Z _B2 and the slope.

The ninth one is called the W function, which can be a combination of two valleys (U function),
A trapezoidal function (π function) with a downward slope (Z function)
And a function having an upward slope (S function) can be combined, and further, it can be said that N function is combined with Z function or И function is combined with S function. In any case, the W function is defined by four break points Z _B1 , S _B2 , Z _B2 , S _B1 and a gradient.

The last is the inverse of the W function and is defined as the M function. This is also four break points S _B1 , B _B2 , S _B2 ,
Defined by B _B1 and slope.

Furthermore, by properly combining the above two or more functions,
It will be readily appreciated that more complex membership functions can be defined.

In FIG. 4, only the positive region of the variable x is shown, but it goes without saying that it can be extended to the negative region of x. In this case, the above-mentioned break point can also generally take a negative value.

It is possible to take any gradient, such as an upslope, a downslope, a trapezoid, or a valley, but in terms of circuit design, the slope is 1 (or -1).
Is the simplest. The slope is 1 as described later
Even when the circuit is used, an arbitrary slope can be obtained by changing the range of the vertical axis and the horizontal axis. If the gradient is defined beforehand, the above-mentioned 10 functions can be uniquely defined by only one or a plurality of break points.

(3,2) Z-function circuit (Figs. 5, 6, 7 and 8)
FIG. 5 shows an example of a membership function circuit that outputs a Z function. Here, the input variable is represented by Z, and the Z function is represented by f _Z. Also, this circuit operates in current mode,
It is a circuit for suction input and discharge output. Suction input is a form in which the input current flows into the circuit, and discharge output is a form in which the output current flows out from the circuit. In the current mode, the positive and negative of variables and functions are represented by the direction of the current, and their absolute values are represented by the current value.

The membership Z-function circuit shown in FIG. 5 provides a current source (which gives the input current to the circuit) 23 which gives a current representing the break point Z _B , a current mirror (CM) 25, and a current having a value of 1. It is composed of a current source (which applies a sinking input current to the circuit) 26 and a diode 28. The current mirror 25 is composed of two N-MOS FETs. A graph showing the current flowing through each part of the circuit of FIG. 5 is shown corresponding to the arrow indicating the direction of the current. The graph of output current f _Z is shown in FIG.

A current representing the value of an input variable (Z ≧ 0) is flowing into the input terminal 21. A current source 23 is connected by a wired OR 24 between the input terminal 21 and the input side of the current mirror 25, and a current of value Z _B (Z _B ≧ 0) flows out from this wired OR. Therefore, a current representing the difference (Z−Z _B ) between Z and Z _B flows from the wired OR 24 toward the current mirror 25, but actually the current mirror 25 acts as a current blocking diode against the reverse current. Therefore, the marginal difference (Z
Z _B ) current will flow (see graph). Here, the calculation of the fuzzy marginal difference is represented, and the marginal difference has the following contents.

From the output side of the current mirror 25, a sink current of the same value is output. A current source 26 is connected by a wired OR 27 between the output side of the current mirror 25 and the output terminal 22.
Accordingly, operation of the 1-in wired OR27 (ZZ _B) is carried out, about to be or sucked current of this value is discharged from the output terminal 22 (see graph). However, since the diode 28 which is in the forward direction with respect to the discharge output is connected between the wired OR 27 and the output terminal 22, the sink output current which is about to appear at the terminal 22 becomes zero. This is equivalent to the operation of 1 (ZZ _B ).

The above operation is summarized as follows.

This operation is graphically represented in FIG. The down slope of this Z-function is -1.

The diode 28 can be replaced with a diode-connected MOS FET.

When the input current Z is negative (however, Z _B ≧ 0), the current (Z + Z _B ) tries to flow from the current mirror 25 toward the wired OR 24, but the current mirror 25 blocks the outflow of this current. Therefore, the current flowing between the current mirror 25 and the wired OR24 is zero. Therefore, the output current of the current mirror is also 0, and the current of the value 1 of the current source 26 is discharged to the output terminal 22 as it is.

When the break point Z _B is negative (where Z ≧ 0), the current (Z + | Z _B |) flows from the wired OR 24 into the current mirror 24, so the output current of the current mirror 25 is also (Z +). | Z _B |). Therefore, the output is represented as:

Expression (3) represents an operation in which the graph of FIG. 6 is left-shifted as it is so that Z _B is on the negative side.

When both the break point Z _B and the input current Z are negative, a current of (| Z _B || Z |) flows from the wired OR 24 toward the current mirror 25. Therefore, the suction output current of the current mirror 25 is also given by (| Z _B || Z |), and the discharge output current is expressed by the following equation.

Expression (4) also expresses the state where the graph of FIG. 6 is shifted to the left.

Thus, the circuit of FIG. 5 has all Z values and
Applicable to Z _B values.

FIG. 7 shows a Z-function circuit realized by using a bipolar transistor array (RO78 TA78). Circuits corresponding to the current sources, current mirrors, etc. in FIG. 5 are designated by the same reference numerals. Further, an input circuit 21A is provided in place of the input terminal 21 in FIG. 5, and an output circuit 22A is provided in place of the output terminal 22. As the diode 28, a base-emitter diode of an NPN transistor (one of TA78) is used.

FIG. 8 shows the experimental results measured using the circuit of FIG. Experiments were performed for three different Z _B (parameters). Input current Z, Break point current Z _B , 1
The current at the value of and the output current f _Z were measured as the voltage drop of the resistor in each circuit. f _Z = 10 μA is μ =
1 and f _Z = 0 μA correspond to μ = 0.

As can be seen from this graph, the circuit of FIG. 7 has a very good linearity and the circuit configuration is simple. Such excellent linearity cannot be realized by a simple voltage mode circuit, and this is also a major reason why a membership function circuit is realized by a current mode circuit. In addition, the circuit of FIG. 7 has a characteristic that it has good temperature stability because it uses a current mirror and is suitable for integration because it does not use a resistor except for a current source.

Further, as can be seen from FIGS. 7 and 8, the Z function circuit can be realized with extremely high practicality not only by the MOS FET but also by the bipolar element.

(3,3) S-function circuit (Figs. 9, 10, 11 and 12)
FIG. 9 shows an example of the membership S-function circuit. The input variable (input current) is shown by S, and the S function output (output current) is shown by f _S. The current S _B representing the break point is provided by the current source 33 and the current representing the value 1 is provided by the current source 36.

The basic difference between the S-function circuit and the Z-function circuit is the direction of the current input to the wired OR34 (corresponding to the wired OR24 in FIG. 5). The input current S is supplied to the wired OR 34 as a discharge input, and the break point current S _B is supplied to the wired OR 34 as a suction input. Therefore, the direction of the sinking input current given to the input terminal 31 is reversed by the current mirror 39. In addition, the break point current source 33 is designed to give a suction input to the circuit (compare the current source 23 in FIG. 5).

Calculation of S _B S is performed by the wired OR34 and current mirror 35. In addition, 1- (S _B
S) is calculated. Since the diode-connected MOS FET38 acting as a diode blocks the current in the sink output direction, the output current is f _S = 1.
A discharge output current representing (S _B S) is obtained. A graph of this output current is shown in FIG.

In this S-function circuit, it is possible to set the break point S _B to a negative value, but if S _B <0, S
In the region of ≧ 0, the output current f _S always takes the value of 1, so S _B
No special significance can be found for setting to negative. S _B = 0 is sufficient.

An S-function circuit implemented using bipolar transistors is shown in FIG. In this figure as well, circuits having the same functions as those shown in FIG. 9 are designated by the same reference numerals. Reference numeral 31A is an input circuit corresponding to the input terminal 31, and reference numeral 32A is an output circuit corresponding to the output terminal 32. The measured characteristics (parameterized by S _B ) of the circuit of FIG. 11 are shown in FIG. It can be seen that this S-function circuit also has an excellent straight line.

(3, 4) Arbitrary setting of slope during use (Figs. 13 and 14)
As shown in the conversion circuit 11 in FIG. 3, generally in the discussion of membership functions, the input value of the physical quantity is normalized using its maximum value (or the allowable value of the circuit), and The normalized value is used as the input value.
For example, when the height H is handled, the maximum value (for example, 2 m) Hmax is used to normalize the height input by H / Hmax.

As an example, the membership function μ _SH of the set “tall person” is shown in FIG. 13 (A) as the S function, and the membership function μ _ZH of the set “short person” is shown in FIG. 13 (B) as Z. Each is shown as a function. The horizontal axis (variable) of these membership functions is expressed as S = H / Hmax and Z = H / Hmax.

Therefore, on the circuit, the effective slope of the membership function, that is, S, depends on how many μA the maximum value Hmax corresponds to and how many μA the grade 1 of the function corresponds.
It is possible to set the upward slope of the function and the downward slope of the Z function to arbitrary values. In the Z function circuit and the S function circuit using the current mirror described above, the gradient of (output current) / (input current) is always -1 or 1, but an arbitrary gradient can be obtained depending on the usage. It is possible.

An example of substantially changing the slope is shown in FIG. 14 using the Z function. FIG. 14 (A) shows the membership function of the set “short person” when Hmax corresponds to 100 μA and Grade 1 corresponds to 10 μA. When it is desired to reduce the slope of the membership function by half, Hmax should be set to 50 μA as shown in FIG. 14 (B). Further, when it is desired to make the gradient 1/4, Hmax should be set to 25 μA as shown in FIG. 14 (C).

As described above, even if the gradient of the membership function generating circuit is fixed to +1 or -1,
It turns out that an arbitrary gradient can be set depending on how it is used.

(3,5) Gradient switching control (Figs. 15, 16, 17 and 1)
(Fig. 8) It is possible to change the slope of the membership function on the circuit structure, which will be described below.

Fig. 15 shows the current source in the Z-function circuit shown in Fig. 5.
23, the wired OR 24 and the current mirror 25 are taken out, and the current mirror 25 is modified to form a current mirror 25A.

The current mirror 25A is composed of a current mirror 41 having two output drains having the same area and an N-MOS FET 42 for switching the parallel connection of these two output drains. The FET 42 is on / off controlled by a control signal V _C given to the control terminal 43.

A graph of the output signal ZZ _B of this current mirror 25A is shown in FIG. When the control signal V _{C is set} to L level, FET42
Is off, the slope of the output current of the current mirror 25A is 1. In this case, the current mirror 25A has the same function as the current mirror 25 shown in FIG. Control signal V _C to H
When the level is turned on, the FET 42 is turned on, the current flows through the two output drains, and as a result, the doubled output current flows, so that the gradient becomes 2.

Therefore, if such a current mirror 25A is used in place of the current mirror 25 shown in FIG. 5, a Z function circuit capable of switching the gradient according to the level of the control signal V _C is realized.
The input / output characteristics of the Z-function circuit when the gradient becomes 2 are shown by the broken line in FIG.

It is possible to switch any number of gradients without being limited to two types of gradients. FIG. 17 shows a part of the S-function circuit, in which the current mirror 35 of FIG. 9 is replaced by a current mirror 35A. In the current mirror 35A,
The current mirror 44 has three output drains, these output drains are connected in parallel, and two of them are connected to FETs 45 and 46 as switching elements. The FETs 45 and 46 are on / off controlled by control signals V _C1 and V _C2 applied to their control terminals 47 and 48.

As shown in Figure 18, both FETs 45 and 46 are both off (V _C1
= V _C2 = L), the output current slope is -1,
When one of them turns on (V _C1 = H, V _C2 = L or V
_C1 = L, V _C2 = H) Gradient is -2, when both are on (V _C1 =
V _C2 = H) The slope will be -3.

(3,6) Programmable multi-membership function circuit (Figs. 19, 20, and 21) Of the above 10 fuzzy membership functions, M
A multi-membership function circuit in which nine functions, excluding functions, can be freely programmed (or externally controlled) is shown in FIG. This functional circuit is
Fan-out circuit 50, first Z-function circuit (No.1) 51, second
Z function circuit (No. 2) 52, first S function circuit (No. 1) 53,
It comprises a second S-function circuit (No. 2) 54, a MIN (fuzzy logical product) circuit 55 and a MAX (fuzzy logical sum) circuit 56. Variable (input) by x, the finally obtained function (output) is given by f _X.

The multi fan-out circuit 50 is
A plurality of (in this case, four) electric currents x having the same value and the same direction are generated, and an example of a concrete configuration thereof is shown in FIG. This circuit is connected to a current mirror 58 for reversing the direction of the input current, and is connected to the output side of this current mirror 58, and generates a plurality (4) of output currents having the same value as the input current but opposite directions. It is composed of a multi-output (multi-drain) current mirror 59.

The four output currents x of the multi fan-out circuit 50 are input to Z function circuits 51 and 52 and S function circuits 53 and 54, respectively.
The Z function circuits 51 and 52 are the same as those shown in FIG. 5, their break points are represented by Z _B1 and Z _B2 , and the output currents are represented by f _ZX1 and f _ZX2 , respectively. The S function circuits 53 and 54 are the same as those shown in FIG. 9, respectively, and their break points are S _B1 and S _B2 , and the output current is f
Represented by _SX1 and f _SX2 respectively. Therefore, the gradient is 1, -1 here.

Output f _{ZX2 of} second Z-function circuit 52 and second S-function circuit
The output f _SX2 of 54 is given to the MIN circuit 55. Figure 21 (A)
As shown in, if the break points of these circuits 52, 54 satisfy the condition of S _B2 ≤ Z _B2 , the MIN operation result of the outputs of these circuits 52, 54 is a trapezoidal function, that is, π It becomes a function. This π function (output of the MIN circuit 55) is represented by f _π x. This is because the MIN operation is an operation for selecting the smallest value (smaller value) of a plurality of input values (here, two input values).

The output f _π x of the MIN circuit 55, the output f _ZX1 of the first Z-function circuit 51 and the output f _SX1 of the first S-function circuit 53 are given to the MAX circuit 56. MAX is an operation for selecting the largest value of a plurality of input values. The current value corresponding to the grade 1 of the function is I ₀ . Referring again to FIG. 21 (A), Z _B1 + 2I
_If these break points are selected so as to satisfy the condition of ₀ ≤ S _B2 , Z _B2 ≤ S _B1 -2I ₀ , the output of the MAX circuit 56 is W
Represents a function.

It is possible to replace the current mirror (reference numeral 25 in FIG. 5 and reference numeral 35 in FIG. 9) in these function circuits 51 to 54 with a current mirror whose gradient can be switched (current mirror 25A in FIG. 15, etc.). is there. The control signals given to the control terminals in this case are given by V _Z1 , V _Z2 , V _S1 , and V _S2 in FIG. By setting the levels of these control signals, it is possible to independently set any of the four gradients of the W function to a value other than 1 as shown in FIG. 21 (B).
FIG. 21B shows a state in which V _Z1 = V _S2 = H and V _Z2 = V _S2 = L are set. It goes without saying that the gradient can be switched by any function described below.

Next, it is shown that the circuit in Fig. 19 can realize nine fuzzy membership functions according to the setting of break point values. The discussion will proceed with reference to FIGS. 4 and 21 (A).

In the following explanation, H _I is the maximum value of input current
Value obtained by adding ₀ (for example, 10 μA) ([maximum input current value]
+ I ₀ ), which means that L _I is −I
_This means that the value is set to ₀ or less. DC is not
Indicates that the value is Don't Care, that is, any value.

The conditions under which the circuit of FIG. 19 realizes each of the nine function circuits are as follows.

φ function Z _B1 = L _I , S _B1 = H _I , S _B2 = H _I , Z _B2 = DC or Z _B1 = L _I , S _B1 = H _I , Z _B2 = H _I , S _B2 = DC 1 function Z _B1 = H _I, other (i.e. _{Z B2, S B1, S B2} ) is DC (Z _B1 is here, may be greater than the maximum input current value, in order not to increase the types of control signals As a sufficient condition, Z _B1 = H _I. ) Or S _B1 = L _I , others DC (S _B1 may be 0 A or less, but S _B1 = L _{I in} order to suppress increase in control signal types) Or S _B2 = L _I , Z _B2 = H _I , others DC (S _B2 should be 0A or less, and Z _B2 should be more than the maximum input current as above. ) Z function S _B1 = H _I , S _B2 = H _I , Z _B2 = DC (In this case, Z _B1 is the break point.) Or S _B1 = H _I , Z _B2 = L _I , S _B2 = DC (Again Z _B1 becomes breakpoint.) _{or, S B1 = H I, S} B2 = L I, Z B1 = L I ( in this case, Z _B2 A break point. In addition, S _B2
Should be 0A or less. ) S function Z _B1 = L _I , Z _B2 = L _I , S _B2 = DC (In this case, S _B1 becomes a break point.) Or Z _B1 = L _I , S _B2 = H _I , Z _B2 = DC (S _B1 is also a break point in this case) or Z _B1 = L _I , S _B1 = H _I , Z _B2 = H _I (In this case, S _B2 is a break point. S _B2 is It should be a value larger than the maximum input current value.) Π function Z _B1 = L _I , S _B1 = H _I , S _B2 ≤Z _B2 (break points are S _B2 and Z _B2 . S _B2 = Z in the case of _B2 is a fourth triangular shape as shown by a chain line in FIG.) U function S _B2 = H _I, and _{Z B2 = DCZ B1 + I 0} ≦ S B1 -I 0 ( breakpoints Z _B1 S _B1 Z _B1 + I ₀ ≦ S _B1
In the case of −I ₀ , the shape is shown by the chain line in FIG. ) Or Z _B2 = L _I , S _B2 = DCZ _B1 + I ₀ ≤S _B1 -I ₀ N function Z _B2 = L _I , S _B2 ≤Z _B2 ≤S _B1 -2I ₀ (break point is S _B2 , Z _B2 , S _B1 .) И function S _B1 = H _I , Z _B1 + 2I ₀ ≤S _B2 ≤Z _B2 (break points are Z _B1 , S _B2 , Z _B2 .) W function Z _B1 + 2I ₀ ≤ S _B2 ≤ Z _B2 ≤ S _B1 -2I ₀ (as described above.) In Fig. 19, the circuit indicated by reference numeral 55 is the MAX circuit,
It can be easily understood that 9 functions except the W function among the 10 functions in FIG. 4 can be realized by replacing the 56 with the MIN circuit.

(3,7) MIN circuit and MAX circuit (Figure 22, Figure 23, Figure 24,
(Figures 25, 26, 27, 28) Details of the MIN (fuzzy AND) circuit and MAX (fuzzy OR) circuit used in the programmable multi-membership function circuit of Figure 19 Is described in the application filed by the applicant (for example, Japanese Patent Application No. 59-57121), which will be briefly described here.

The MIN operation is defined as follows.

Here, μ _X and μ _Y represent membership functions, respectively.

Figure 22 shows a circuit that implements the MIN circuit with a MOS FET. For convenience, the input current is represented by μ _X and μ _Y , and the output current (result of MIN calculation) is given by μ _Z.

The direction of the input current μ _X is inverted by the current mirror 61.
The input current μ _Y is input to the multi-fanout circuit consisting of the current mirrors 66 and 67, which produces two currents μ _Y of equal value.

The wired OR 62 is supplied with a discharge input current μ _X and a suction input current μ _Y, and this wired OR 62 is connected to the current mirror 63. The current mirror 63 also functions as a diode, and the wired OR 62 and the current mirror 63 form a fuzzy limit difference circuit. Therefore,
The sinking output current of the current mirror 63 is given by the following equation.

Similarly, the wired OR 64 and the diode 65 form a limit difference circuit, and the discharge output current of this MIN circuit is given by the following equation.

Expression (7) is the same as Expression (5).

An example in which the MIN circuit is composed of bipolar transistors is shown in FIG. From the comparison with the circuit of FIG. 22, it can be easily understood that the circuit MIN operation of FIG. 23 is performed.

FIG. 24 shows the measurement result of the input / output characteristics of the circuit of FIG. One input μ _Y is used as a parameter. In the circuit shown in Fig. 23, TA is used as the PNP transistor.
57 was used, and TA78 was used as the NPN transistor.

In FIG. 19, the MAX circuit 56 has three inputs. Generally, the 2-input MAX circuit can be easily constructed. To construct a 3-input MAX circuit, as shown in FIG. 25, 2-input MAX circuits 56A, 56B may be connected in two stages.

FIG. 26 shows an example in which a 2-input MAX circuit (56A or 56B) is configured by using a MOS FET. The fuzzy MAX operation is defined by the following equation.

The input current μ _Y is input to the two-output power mirror 71, which produces two currents μ _Y whose directions are opposite to those of the input current,
One is input to the wired OR72, and the other is inverted in direction by the current mirror 75 and is given to the wired OR74.

The input current μ _X is also input to the wired OR72. A limit difference circuit is configured by the wired OR 72 and the diode 73, and the current given by the following equation is output from the diode 73 and flows into the wired OR 74.

In wired OR74, this current μ _X μ _{Y
Since Y} is added, the output current μ _Z is as follows.

Expression (10) represents the same contents as Expression (8).

FIG. 27 shows an example in which the MAX circuit is composed of bipolar transistors. In FIG. 27, those corresponding to those shown in FIG. 26 are designated by the same reference numerals with A added.
The circuit of FIG. 27 does not fully correspond to the circuit of FIG. The two current mirrors 71, 75 in FIG. 26 have been replaced in FIG. 27 by three current mirrors 76, 77, 78.

When a multi-output current mirror is composed of bipolar transistors with multiple collectors, if at least one of the output collectors is opened, saturation occurs in that collector and the output currents of the other output collectors have an error. Occurs. In order to prevent saturation of the collector of the multi-output current mirror in any case, it is necessary to secure a certain collector-emitter voltage.
The circuit of FIG. 27 prevents the saturation of the collector by connecting a circuit having a small input resistance such as the current mirror 78 to the collector of the multi-output current mirror 77. The measures for avoiding saturation of the collector in the multi-output current mirror are described in detail in the applicant's patent application, Japanese Patent Application No. 59-263386.

FIG. 28 shows an example of the measurement result of the input characteristic of the MAX circuit of FIG. 27 with μ _Y as a parameter.

(3.8) Simplified programmable multi-membership function circuit (Figs. 29 and 30) Fig. 29 shows a simplified programmable multi-membership function circuit based on the S function circuit. There is. Here, P-MOS FET is used. Therefore, the direction of current flow is opposite to that of the S-function circuit shown in FIG. The input current is shown by xi and the output current is shown by Z.

The multi-output current mirror 81 generates three currents xi having the same value and opposite directions from one input current xi. These currents xi become the input currents of the three circuits described below.

The first S-function circuit is composed of a wired OR84, a current mirror 85, a wired OR87 and a diode-connected MOS FET88. In comparison with FIG. 9, these elements correspond to the wired OR34, the current mirror 35, the wired OR37 and the diode-connected MOS FET38, respectively. Wired OR84
Is supplied with a x ₁ +1 source input current as a break point. The operation of the first S-function circuit can be easily understood from the comparison with FIG. 9 and the graph shown in FIG. 29 corresponding to the arrow indicating the direction of the current.

The second S-function circuit is composed of a wired OR94, a current mirror 95, a wired OR97 and a current mirror 98.
The current mirror 98 has the function of inverting the direction of the current together with the diode function. The break point is x ₂ , and for the convenience of explanation, it is assumed that the condition of x ₂ −1 ≧ x ₁ +1 is satisfied.

Further, a circuit for generating a function (hereinafter, referred to as an upslope function) having a value of an upslope (slope is 1) from a break point x ₃ (x ₃ ≧ x ₂ ) is provided. It is composed of an OR92 and a diode-connected MOS FET93. Wired OR92 is being provided with a x ₃ value of source input current.

The output current of the up-slope function circuit is input to the second S-function circuit in the wired OR96. In this wired OR96, the output current of the up-slope function circuit is subtracted,
Moreover, since the reverse current is blocked by the current mirror 98, the output current of the current mirror 98 represents a π function (break points x ₂ and x ₃ ).

The current representing the π function is input to the first S-function circuit in the wired OR86 and subtracted from the current flowing there. Therefore, the output current Z is as if the π function is subtracted from the S function, which represents the N function.

In the circuit shown in Fig. 29, diode-connected MOS FETs 99 and 89 are added. These FETs work as follows. That is, the current mirror 81 and the diode-connected MOS FET9
A threshold voltage between the source and gate of the current mirror 98 and the diode-connected MOS FET 99 is added between the source and drain of 3 to enable normal operation of these. Also,
The voltage between the source and drain of two diode-connected MOS FETs 88 and 89 (that is, the sum of these thresholds) is added between the source and drain of the diode-connected MOS FET 99 and the current mirror 98, and normal operation is possible. I have to.

The circuit shown in FIG. 29 can realize the seven functions except the И function, the W function and the M function among the ten functions described above as follows.

φ function x ₁ = H _I , x ₂ , x ₃ = DC (H _I means setting to [maximum input current] + I _0. I ₀ is the current value corresponding to grade 1. φ function in the case of, may be a x ₁ ≧ [maximum input current.) _{or, x 2 = L I, x} 3 = H I, X 1 = DC (L 1 has means to set the -I ₀ In the case of φ function, x ₂ ≦ 0 is required, and x ₃ ≧ [maximum input current] is required.) 1 function x ₁ ＝ L _I , x ₂ ＝ H _I , x ₃ ＝ DC Alternatively, x ₁ = L _I , x ₃ = L _I , x ₂ = DC Z function x ₁ = L _I , x ₃ = H _I (If x ₃ ≧ [maximum input current]. X ₂ −1 is It becomes a break point.) S function x ₂ = H _I , x ₃ = DC (x ₁ +1 becomes a break point) or x ₁ = L _I , x ₂ = H _I (when x ₂ ≤0 X ₃ +1 is the break point.) Π function x ₃ = H _I (If x ₃ ≧ [maximum input current]. X ₁ + 1, x ₂ -1 is a break point.) U function x ₁ = L _I (x ₂ , x ₃ is a break point.) N function The above condition, that is, x ₁ +2 ≤x ₂ ≤x ₃ +2 The circuit of FIG. 29 Is based on the S-function circuit. A simplified programmable multi-membership function circuit can also be realized by using the Z function circuit as the keynote. That is, a Z function circuit having a value as shown in FIG. 30A and having a break point at x ₁ is provided in place of the first S function circuit described above. And this Z
If the π function as shown in FIG. 30 (B) is subtracted from the function, the И function output is obtained as shown in FIG. 30 (C).
However, the condition is x ₂ ≤x ₃ ≤x ₁ -1.

In such a circuit, it is easy to understand that by changing the conditions of x ₁ , x ₂ and x ₃ , 7 kinds of functions except the N function, W function and M function of the above 10 functions can be realized. See.

(3.9) Expanded programmable multi-membership function circuit (Figs. 31, 32, and 33) Fig. 31 is an expansion of the membership function circuit of Fig. 29. Expansion has two meanings. One of them is the provision of two types of grades α and β. In all the circuits described above, the maximum grade was always fixed at 1, but variable values α and β between 1 and 0 are prepared as new grade parameters. The other is that, as can be seen from the graph of the output current Z in FIG. 31, with the introduction of new grade parameters, a new membership function form called M-type deformation was created.

In FIG. 31, the same elements as those shown in FIG. 29 are designated by the same reference numerals with A added. Only the points different from those shown in FIG. 29 will be described below.

The multi-output current mirror 81A is designed to generate four input currents xi.

In the first S-function circuit, the wired OR84A has a value x ₁
The discharge input current of is supplied. Wired OR87
The discharge input current with the value of α is given to A.

A wired OR89 is newly provided between the two wired OR87A and 86A of the first S function circuit, and a newly provided upslope function circuit (first upslope function circuit) is provided there.
The output current of is flowing in. This first up-slope function circuit consists of a wired OR 82 and a diode-connected MOS FET 83, and its break point is x ₄ .

Therefore, by the first S-function circuit and the first up-slope function circuit, the first π-function (break points x ₁ , x
₄ , grade α) is generated.

In the second S-function circuit, the wired OR94A has x
₂ + β discharge input current is applied, and wired OR97A
Is supplied with a β discharge current.

The wired input OR92A of the up-slope function circuit (second up-slope function circuit) attached to this S-function circuit is supplied with a discharge input current of x ₃ -β. The current mirror 99 is for sucking in the discharge input of β and inverting the input.

3 of β value given to wired OR94A, 97A and 92A
It goes without saying that one input current can be generated by a multi-output current mirror (not shown).

By the second S-function circuit and the second up-slope circuit, x
_{A second} π-function with break points at ₂ + β and x ₃ -β and grade β is generated.

The above-mentioned first π function to the second π function is wired OR86.
As a result of subtraction at A, an M function with a maximum grade of α and a dent of β at the center is obtained. Where α ≧ β, x ₁ ≦ x
_{The condition of 2} , x ₂ + 2β ≦ x ₃ ≦ x ₄ is required.

The circuit shown in FIG. 31 can be controlled so as to generate 9 functions excluding the W function out of the 10 functions described above, and also can be modified by setting α and β. .

As a reminder, I will show enough conditions for generating 6 functions except φ function and 1 function from 9 functions.

Z function x ₁ = x ₂ = x ₃ = L _I , α = 1, β = DC (x ₄ is a break point) or x ₁ = L _I , α = 1, β = 1, x ₃ = X ₄ = H _I (x ₂ becomes a break point) S function x ₂ = x ₃ = x ₄ = H _I , α = 1, β = DC (x ₁ becomes a break point) or , x ₁ ＝ x ₂ ＝ L _I , α ＝ β ＝ 1, x ₄ ＝ H _I (x ₃ becomes a break point) π function α ＝ 1, α ＝ 0, x ₂ , x ₃ ＝ DC ( x _1, x ₄ is the breakpoint.) _{or, x 3 = x 4 = H} I, α = β = 1 (x 1, x 2 is the breakpoint.) or x ₁ = x ₂ = L _I , α = β = 1 (x ₃ , x ₄ are break points.) U function x ₁ = L _I , x ₄ = H _I , α = β = 1 (x ₂ , x ₃ are break points the point.) N function _{x 4 = H I, α =} β = 1 (x 1, x 2, x 3 is the breakpoint.) И function _{x 1 = L I, α =} β = 1 (x ₂ , x ₃ , x ₄ is the break point M function α ≦ x ₁ ≦ x ₂ , x ₂ +2 β ≦ x ₃ ≦ x ₄ , α = β = 1 (x ₁ , x ₂ , x ₃ , x ₄ are break points.) 31st Although the circuit in the figure is also based on the S function, it goes without saying that an extended programmable multi-membership function circuit can also be realized by using the Z function as the basis.

FIG. 32 shows a modification of the circuit shown in FIG. 31 so that the gradient can be switched between 1 and 2. The current mirrors 85A and 95A shown in Fig. 31 are slope-switchable current mirrors 85B and 9A.
Replaced by 5B respectively. These current mirrors 85B,
95B is the same as the current mirror 25A in FIG. 15 and the current mirror 35A in FIG.

The diode-connected FETs 83, 93A are also replaced by gradient-switchable current mirrors 83B, 93B and current mirrors 83C, 93C are provided in front of them to correct the direction of the current.

For wired OR94A and 92A, current x
₂ and x ₃ are given.

Since the current mirrors 85B, 83B, 95B, 93B are composed of P-MOS FETs, when their control voltage signals V _{C1 to} V _C4 become L level, the switching FET turns on and the slope becomes 2 or -2. The output current Z has the form shown by the broken line in FIG. Of course, it goes without saying that the control voltages V _{C1 to} V _C4 can be adjusted independently of each other.

(3.10) S-function circuit applicable to crisp sets (34th, 3rd
(Figure 5) The circuit in Figure 34 is an improvement of the S-function circuit (Figure 9 or Figure 32) so that it can be applied to crisp sets.
Further, here, a gradient switching circuit is provided. 9th
In comparison with Figure (or Figure 32), wired OR10
4 to 34 (or 84A), switchable current mirror 105 to current mirror 35 (or 85B), wired OR107 to 37.
(Or 87A), diode 108 is diode-connected FET3
It corresponds to 8 (or 88) respectively. The gradient is switched by the control signal V _C1 .

Therefore, the P-MOS FET 106 as a switching element connected between the wired OR 104 and the current mirror 105,
And N-MO as a switching element connected in parallel between the wired OR107 and a current source (not shown) of value α
S FET 101 and P-MOS FET 102 are newly provided. FET1
02 and 106 are on / off controlled by a control signal V _C2 . F
The ET 101 is controlled by the potential of the node 109. The node 109 is provided between the wired OR 104 and a current source (not shown) having a value x ₁ , and its level changes to H or L level depending on the magnitude of the current flowing in or out of the node.

In a fuzzy set, whether or not something belongs to the fuzzy set is represented by the degree of belonging, that is, a continuous value of 1 to 0. Therefore, the membership function indicating this degree has a sloped portion as described above. On the other hand, in the crisp set,
1 or 0 if something belongs to the crisp set
Is clearly represented by. The membership function of the crisp set has a portion that changes discontinuously from 1 to 0 or 0 to 1 (a portion having an infinite gradient).

Now, in FIG. 34, when the control voltage V _C2 is at L level, the two FETs 102 and 106 are on. Since FET 101 is connected in parallel to FET 102, whether they are on or off, the circuit of Figure 34 acts as a fuzzy set membership S-function circuit. When the control voltage V _C1 is H, the gradient is 1, and when it is L, the gradient is 2. The input / output characteristics at this time are shown in FIG. 35 by a solid line and a broken line, respectively.

When the control voltage V _C2 becomes H level, both FETs 106 and 102 are turned off. Therefore, when the FET 106 is off, the input current xi does not flow into the current mirror 105 but flows from the wired OR 104 toward the node 109. When the FET 102 is off, whether or not the discharge input current α is given to the wired OR 107 depends on the state of the FET 101.

When xi <x ₁ , the potential of the node 109 is at L level and the FET 101 is off. Therefore, the output current Z is O
Is. When xi ≧ x ₁ , the node 109 becomes H level,
FET101 turns on. Current α is from wired OR107 to FET
Flowing through 101. Since the output current of the current mirror 105 is 0, the output current Z eventually becomes equal to α. Thus, as shown by the chain line in Fig. 5, 0 at xi = x ₁
An output Z that is inverted from 1 to 1 is obtained. Control voltage V _C2 is H
At the level, the level of the control voltage V _C1 may be H or L.

The difference between the S-function circuit and the Z-function circuit is that the direction of the current that defines the break point is different as described above. Therefore, the Z-function circuit applicable to the crisp set can be similarly configured by applying the concept of the circuit of FIG. 34 as it is and appropriately selecting the MOS FET as the constituent element to the P type or the N type. it can.

Since the circuit 100 shown by the chain line excluding the diode 108 is used later in FIG. 40, it will be referred to as a main part of the S-function circuit for convenience sake.

(3.11) Up-slope function circuit applicable to crisp sets (Figs. 36 and 37) The circuit in Fig. 36 is an up-slope function circuit (wired OR82, with a slope switching function shown in Fig. 32). Current mirror 83C
And a circuit including a gradient-switchable current mirror 83B, or a wired OR 92A, a current mirror 93C, and a gradient-switchable current mirror 93B) are improved to be applicable to a crisp set.

In comparison with FIG. 32, the wired OR102 has the same 82 (or 92A) and the current mirror 103C has the same 83C (or 93C).
In addition, the gradient switchable current mirror 103B is connected to the same 83B (or 93B).
It corresponds to B) respectively. However, the connection order of the current mirror 103C and the gradient-switchable current mirror 103B is as follows: the current mirror 83C (or 93C) and the gradient-switchable current mirror 83B.
(Or 93B) connection order is reversed. Further, the P type and N type of the FETs forming these current mirrors are exchanged. Then, the gradient switchable current mirror 103B is composed of a current mirror 108 having two output drains and a FET 109 for switching one of the output drains. The FET 109 is on / off controlled by the control signal V _C3 . In addition, an N-MOS F for opening the gate connection drain of the current mirror 108
ET107 is newly added. This FET 107 has a control signal V
Controlled by _C4 .

The structure of the circuit in FIG. 36 is clearly understood when compared with that in FIG. In the circuit shown in Fig. 15, the FET 107 and current mirror 1
Only 03C is added.

When the control signal V _C4 is at the H level, this circuit functions the same as the upslope circuit for the fuzzy set shown in FIG. That is, when V _C4 is H, the FET 107 is turned on.
At this time, the slope of the output current Z is determined by the control signal V _C3 , and the output current Z exhibits the input / output characteristics shown by the solid line and the broken line in FIG.

When the control voltage V _C4 becomes L level, the FET 107 is turned off. F
With the ET107 turned off, the FET 108 no longer acts as a current mirror, but just an amplifier.

When xi <x ₁ , the current flowing into the gate of FET 108 is 0
Therefore, the output current Z is naturally 0.

If xi ≧ x ₁ , and there is a current that is about to flow into the FET 108 even with a small value, this is amplified by the FET 108, and a sharply increasing current flows on the output side thereof. Therefore,
As shown by the chain line in Fig. 37, the input / output characteristic of the output current Z rising almost vertically at xi = x ₁ is obtained.

Since the circuit of FIG. 36 is used in FIG. 38, it is specifically labeled 110.

(3.12) Programmable multi-membership function circuit applicable to crisp sets (Fig. 38) Fig. 38 shows main parts 100 and 36 of the S function circuit applicable to crisp sets shown in Fig. 34. A crisp set obtained by applying the up-gradient function circuit 110 applicable to the crisp set shown in the figure to the extended programmable multi-membership function circuit shown in FIG. 32 and improving it. 2 shows a programmable multi-membership function circuit applicable to.

38, the same parts as those shown in FIG. 32 are designated by the same reference numerals. Also, since two circuits 100 in FIG. 34 are used, these are indicated by 100A and 100B, and similarly, the third circuit is shown.
Two of the circuits 110 shown in Fig. 6 are also used, so this is 110
A, shown at 110B.

From the graphs corresponding to the arrows indicating the current flowing in the circuit, the parameters x _{1 to} x ₄ ,
It can be easily understood that the output current Z representing many types of fuzzy membership functions including the M function can be obtained by changing α and β. The gradient can be changed by switching the levels of the control voltages V _{C11 to} V _C14 and V _{C21 to} V _C24 , and many types of crisp membership functions can be generated.

[Brief description of drawings]

FIG. 1 (A) shows a general membership function, and FIG. 1 (B) shows a practical membership function approximated by a straight line. FIG. 2 shows the concept of the fuzzy control system. FIG. 3 is a block diagram showing the concept of a fuzzy system having a learning function. FIG. 4 is a graph showing various types of membership functions. FIG. 5 is a circuit diagram showing a Z-function circuit constructed using MOS FETs, and FIG. 6 is a graph showing its input / output characteristics. FIG. 7 is a circuit diagram showing a Z-function circuit configured by using bipolar transistors for measuring the input / output characteristics, and FIG. 8 is a graph showing the measured input / output characteristics. FIG. 9 is a circuit diagram showing an S-function circuit constructed using MOS FETs, and FIG. 10 is a graph showing its input / output characteristics. FIG. 11 shows an S-function circuit constructed by using bipolar transistors for measuring the input / output characteristics, and FIG. 12 is a graph showing the measured input / output characteristics. FIG. 13 is a graph showing a practical example of the membership function. FIG. 14 is a graph showing how the slope can be arbitrarily set by the correspondence between the membership function and its variable and the input / output current of the circuit. FIG. 15 is a circuit diagram showing a part of a Z-function circuit capable of switching the gradient to two, and FIG. 16 is a graph showing its input / output characteristics. FIG. 17 is a circuit diagram showing a part of an S-function circuit capable of switching the gradient to three, and FIG. 18 is a graph showing its input / output characteristics. FIG. 19 is a block diagram showing an example of a programmable multi-membership function circuit. FIG. 20 is a circuit diagram showing an example of a multi-fanout circuit. FIG. 21 (A) shows how the W function is generated by the fuzzy MIN operation and fuzzy MAX operation of the Z function and the S function, and FIG. 21 (B) shows the W function with the gradient switched. It is a graph. FIG. 22 is a circuit diagram showing a MIN circuit configured using MOS FETs. FIG. 23 shows a MIN circuit composed of bipolar transistors for measuring input / output characteristics.
FIG. 24 is a graph showing the measured input / output characteristics. FIG. 25 is a block diagram showing a 3-input MAX circuit configured by combining two 2-input MAX circuits. FIG. 26 is a circuit diagram showing a MAX circuit configured using MOS FETs. FIG. 27 shows a MAX circuit configured by using bipolar transistors for measuring the input / output characteristics.
FIG. 28 is a graph showing the measured input / output characteristics. FIG. 29 is a circuit diagram showing an example of a simplified programmable multi-membership function circuit based on the S function circuit. FIG. 30 is a graph showing that a similarly simplified programmable multi-membership function circuit can be created based on the Z function. FIG. 31 is a circuit diagram showing an extended programmable multi-membership function circuit. FIG. 32 is a circuit diagram showing an extended programmable multi-membership function circuit having a gradient switching function, and FIG. 33 is a graph showing its input / output characteristics. FIG. 34 is a circuit diagram showing an S-function circuit applicable to the crisp set, and FIG. 35 is a graph showing its input / output characteristics. FIG. 36 is a circuit diagram showing an upslope function circuit applicable to the crisp set, and FIG. 37 is a graph showing its input / output characteristics. Figure 38 shows a programmable program applicable to crisp sets.
It is a circuit diagram which shows a multi-membership function circuit. 101 ... MOS FET (third switching element), 102 ... MOS FET (second switching element), 104 ... Wired OR (first subtraction circuit), 105 ... current mirror, 106 ... MOS FET (First switching element), 107 ... Wired OR (second subtraction circuit), 109 ... Wired OR (current comparison circuit).

Claims (3)

[Claims] 1. A first subtraction circuit for performing a subtraction between an input signal and a reference signal representing a value relating to a breakpoint, and a subtraction result of the first subtraction circuit if the input signal is larger than the reference signal. In other cases, a limit difference circuit consisting of a circuit that outputs a signal that represents zero, subtracts the output signal of the limit difference circuit from a signal that represents a predetermined grade, and outputs a signal that represents the positive subtraction result. A second subtraction circuit that outputs a signal representing zero when the subtraction result is negative, a first switching element provided at a proper position between the first subtraction circuit and the second subtraction circuit, and a predetermined grade A second switching element, which is provided between the input terminal of the signal representing the signal and the second subtraction circuit and is controlled to be turned on and off at the same time as the first switching element; Switch of 3 A fuzzy membership function circuit applicable to a crisp set consisting of a ching element and a comparison circuit that compares an input signal with a reference signal and controls the third switching element according to the comparison result. 2. The limit difference circuit comprises an input current and a break circuit.
The second subtraction circuit is composed of a first subtraction circuit for performing subtraction with a reference current representing a value related to a point, and a current mirror connected to the output side of the subtraction circuit. The output current of the limit difference circuit is subtracted from the represented current, and the diode action element is connected to the output side, and the comparison circuit is a current comparison circuit. A fuzzy membership function circuit applicable to a crisp set operating in the described current mode. 3. A current mirror of a limit difference circuit comprises a multi-output current mirror in which a plurality of output lines are connected in parallel, and a fourth switching element provided in at least one of the plurality of output lines. A fuzzy membership function circuit applicable to the crisp set according to claim (2).