JP2913782B2 - A learning device for approximate inference - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION Summary of the Invention Expert knowledge of the relationship between events and conclusions is stored in advance. When a learner enters data on the events that give rise to a conclusion when given a conclusion, the relevance and reliability of the data entered by the learner is determined based on the stored expert knowledge. Calculate and output.

TECHNICAL FIELD The present invention relates to a learning device for approximate inference.

2. Description of the Related Art There is known an approximate inference apparatus which stores in advance the knowledge of many experts regarding the relationship between a plurality of events and a conclusion and calculates the possibility of a conclusion given data representing the event. (For example, Zhang Hongmin “AN E
XPERT SYSTEM WITH THINKING IN IMAGES ", Preprints of
Second IFSA Congress, Tokyo, July 20-25,1987, P.76
Five).

Such an approximate inference device can be used for professional education, but is not necessarily designed for learning.
Becoming a seasoned expert requires a lot of real experience, but it takes a lot of time and money.

SUMMARY OF THE INVENTION Object of the Invention The present invention provides an apparatus capable of performing learning by utilizing abundant expert knowledge accumulated in an approximate inference apparatus in order to efficiently perform expert education. It is.

Structure and effect of the invention A learning device for approximate inference according to the present invention is a storage means for preliminarily storing expert's knowledge on the relationship between an event and a conclusion, and an event for generating a conclusion when a conclusion is given. Means for the learner to input data relating to the learner, and the degree to which the data for a predetermined conclusion input by the learner through the input means matches the expert's knowledge stored in the storage means for the same conclusion. Fitness calculating means for each event, calculating the reliability of data for a predetermined conclusion inputted by the learner through the input means with reference to the expert knowledge stored in the storage means for the same conclusion Means for calculating the reliability, the conformity calculation means and the fitness and reliability calculated by the reliability calculation means A display means for displaying at least one of them is provided.

According to the present invention, learning can be performed using abundant knowledge of experts accumulated in the approximate inference apparatus. Using the data input by the learner and the knowledge of the expert,
The evaluation can be made from the viewpoint of the degree of conformity and reliability, and the education of experts can be performed efficiently.

1. Description of Embodiment (1) Overall Configuration of Learning Apparatus FIG. 1 shows an example of the overall configuration of a learning apparatus.
The learning devices are a knowledge storage device 11, a knowledge synthesis device 12, a synthesized knowledge storage device 13, a learner knowledge input device 14, and a fitness calculation device 1.
5. It is composed of a reliability calculation device 16 and a display device 17. A part of the configuration of this learning device, for example, devices 11, 12, 13
Can also be used as those of the approximation inference device,
The knowledge of many experts stored in the knowledge storage device 13 after synthesis of the approximate inference device can be used in the form of a file, a memory, or the like.

 Hereinafter, these devices will be described in detail.

(2) Knowledge storage device The knowledge storage device 11 is a device that stores knowledge input by an expert or the like in a format indicating a relationship between an event and a conclusion. This device can store the knowledge of several experts.

The two experts ex1 and ex stored in the knowledge storage device 11
An example of knowledge of 2 is shown below in the form of rules.

Expert ex1: if 20 ≦ f1 ≦ 60, 0 ≦ f2 ≦ 40, then c1… (1) if 40 ≦ f1 ≦ 80, 60 ≦ f2 ≦ 100, then c2… (2) Expert ex2: if 30 ≦ f1 ≦ 50,10 ≦ f2 ≦ 30, then c1 ... (3) if 50 ≦ f1 ≦ 70,70 ≦ f2 ≦ 90, then c2 ... (4) f1 and f2 are events.
It may be called. c1 and c2 are conclusions, and these may be called conclusions 1 and 2, respectively.

Also, a and b expressed as a ≦ f1 ≦ b are called a minimum value and a maximum value, respectively.

The above rules are expressed in the form of a table for each expert as follows.

(3) Knowledge Synthesizing Device The knowledge synthesizing device 12 is a device that synthesizes knowledge of a plurality of specialists stored in the knowledge storage device 11 and combines them into one knowledge.

Although there are various methods for synthesizing knowledge, here, the average value and standard deviation of multiple experts are calculated for the maximum value and the minimum value of each event involved in each conclusion.

The knowledge synthesizing process will be described below by taking as an example the knowledge that leads to the conclusion c1 from the event f1 of the two experts described above.

From the above rules (Equations (1) and (3)), event 1
Extracting the rule for obtaining the conclusion 1 (c1) from (f1) is expressed as follows.

Expert ex1: if 20 ≦ f1 ≦ 60 then c1 (5) Expert ex2: if 30 ≦ f1 ≦ 50 then c1 (6) The average value m _{min of the} minimum value and the average value m _{max of the} maximum value are calculated. You.

Standard deviation σ _{min of} minimum value and standard deviation σ of maximum value
_max is calculated.

When such a synthesis operation of expert knowledge is performed for all of the minimum and maximum values of each event involved in each conclusion with respect to the above-described rules (Equations (1) to (4)) , The following table is obtained.

In general, in approximate inference, a membership function is given to an event. Here, as an example, a method of obtaining a membership function by a Gaussian distribution using the expert's knowledge synthesized as described above will be described.

Using the average value m _min of the minimum value, the average value m _{max of} the maximum value, the standard deviation σ _{min of} the minimum value, and the living difference σ _max of the maximum value, the membership function is expressed by the following equation.

Here, x: value of input data to the event Φ (x): degree to which the input data x matches the event (fitness) Gauss (x): value of Gaussian distribution at the input x.

FIG. 2 shows an example of a Gaussian distribution. In this Gaussian distribution, only the left half is used to create the membership function. Position of x in Φ (x) = 0.5 is determined by m _min or m _max, the slope is determined by the sigma _min or sigma _max.

As an example, a membership function for obtaining the conclusion c1 from the event f1 is created as shown in FIGS. 3a to 3c using the values calculated from the equations (7) to (10). In this case, equation (11) becomes as follows.

FIG. 3a shows the first term on the right side of equation (11) or (12), FIG. 3b shows the second term on the right side of equation (11) or (12), and FIG. It represents the result of subtracting the second term from the first term, that is, the membership function represented by equation (11) or (12).

4a and 4b show examples of membership functions for obtaining the conclusions c1 and c2 for each of the events f1 and f2 created based on the combined knowledge shown in Table 3.

(4) Post-synthesis knowledge storage device The post-synthesis knowledge storage device 13 stores the average value and the standard deviation calculated by the knowledge synthesis device 12 in a format as shown in Table 3. Since the synthesis of knowledge does not need to be performed each time inference or learning, the result calculated in advance in this way is stored. By reading and using the value in the storage device 13 each time inference or learning is performed, inference processing is performed.
The learning process can be sped up.

(5) Learner knowledge input device The learner knowledge input device 14 is a device for a learner to input data on an event that causes a conclusion when a certain conclusion is given. For example, it is assumed that the approximate inference device is a device failure diagnosis device, and the knowledge of a specialist represents the relationship between the status of the device or various measured values (events) and the type of failure (conclusion). Assuming that a certain failure has occurred, the learner estimates and inputs the state of the device at the time of the failure.

The knowledge input by the learner is expressed in the same format as the knowledge given by the expert. An example is shown below.

Knowledge input by learner Le1: if 35 ≦ f1 ≦ 50, 15 ≦ f2 ≦ 25, then c1… (13) if 48 ≦ f1 ≦ 90, 50 ≦ f2 ≦ 100, then c2… (14) , A keyboard, a communication interface device, a memory, a file, and the like, and stored in the device 14.

(6) Fitness calculation device The fitness calculation device 15 stores the knowledge of the learner input from the learner knowledge input device 14 and the combined knowledge (membership) of a plurality of specialists stored in the storage device 13. This is a device that calculates the degree of conformity to each function for each event.

The following table summarizes the knowledge input by the learner Le1 expressed by Expressions (13) and (14) in the form of a table.

When the knowledge of the learner Le1 shown in Table 4 is expressed by a crisp set (expressed as an interval), it becomes as shown in FIGS. 5A and 5B.

As an example, the fitness for the event f1 leading to the conclusion c1 will be described with reference to FIG. The membership function represented in FIG. 6 is a membership function for obtaining a conclusion c1 from an event f1 obtained by synthesizing expert knowledge. FIG. 6 shows the range (section) of the event f1 leading to the conclusion c1 input by the learner Le1 over the membership function.

 There are several ways to determine the degree of goodness.

(Part 1) The maximum value C _max and the minimum value C _min of the overlapping portion between the membership function of the expert and the section of the event input by the learner are obtained. The fitness m _x is defined as the average of these maximum and minimum values.

m _x = (C _max + C _min ) / 2 (15) (2) The maximum value C _max is defined as the fitness.

m _x = C _max ‥ (16) (Part 3) The average height of the overlapping portion between the expert's membership function and the section of the event input by the learner is defined as the fitness.

Φ (x) represents the expert membership function. x ₁
~x ₂ is a section of events that learner input.

The conformity may be determined according to any of the above definitions. Further, the degree of conformity can be obtained by MIN-MAX operation or the like.

Goodness of fit is determined for each event for each and every conclusion.

(7) Reliability Calculation Device The reliability calculation device 16 calculates the presence or absence or the degree of the reliability of the learner's knowledge based on the knowledge obtained after the synthesis by the expert. There are several possible algorithms for reliability.

(Part 1) For each conclusion, in the expert's knowledge stored in the knowledge storage device 13 after synthesis, the average value of the minimum value and the average value of the maximum value for each event and the same conclusion input by the learner are derived. The minimum and maximum values of the same event are compared, respectively.

As an example, the minimum value of the event f1 (conclusion c1) will be described.

Referring to Table 3, the average of the minimum values of the knowledge of the multiple experts regarding the event f1 that led to the conclusion c1 is 25. It is assumed that the minimum value given to the event f1 (conclusion c1) by a plurality of experts follows a normal distribution (Gaussian distribution) as shown in FIG. An allowable section is provided in this normal distribution (non-permissible rate = α, allowable degree = 1−α).

If the minimum value μ of the event f1 (conclusion c1) input by the learner satisfies the following equation, the reliability is determined. If not, the reliability is determined to be unreliable.

Here, σ is a standard deviation, and n is a parameter.

Tolerance (1-α) = 95% tolerance interval, and conclude c1 f
When the minimum value of 1 is obtained by using the data in Table 3, σ = 5, n = 2, = 25, α = 0.05, l _{α / 2} = l _0.025 = 1.96
Into the expression (18) to obtain the following expression.

That is, 181 <μ <31.9 (20) The minimum value of the event f1 for the conclusion c1 given by the learner is
Referring to Table 4, it is 35, which means no reliability.

The reliability of the maximum value of the event f1 leading to the conclusion c1 is checked in the same manner.

In addition, other events f2 for conclusion c1, and conclusion c2
With regard to the events f1 and f2 for, whether the minimum value and the maximum value input by the learner are reliable is similarly examined.

The t distribution may be used instead of the normal distribution. In the case of the t-distribution, since _{lα / 2} = _l0.025 = 4.3 in the above example, the following equation is obtained corresponding to equations (19) and (20).

That is, 9.8 <μ <40.2 (22) Since the t distribution is gentler than the normal distribution, the allowable interval is widened. The minimum value 35 for f1 (c1) given by the learner falls within this allowable section. Of course, the allowable interval may be increased or decreased by changing the value of α.

(Part 2) The above-mentioned operation related to reliability is for finally outputting the presence or absence of reliability. On the other hand, data representing the degree of reliability can be obtained as follows.

As in (1) above, the distribution of the minimum value of event f1 input by the expert for conclusion c1 is regarded as a normal distribution,
The degree to which the minimum value x of the section of the event f1 for the conclusion c1 input by the learner matches the normal distribution is defined as the reliability.
That is, the reliability is given by the following equation.

Similarly, the event about the conclusion c1 input by the learner
The reliability of the maximum value of f1 can be obtained. In addition, the minimum and maximum values of other events f2 for conclusion c1
The reliability of the minimum and maximum values of the events f1 and f2 for the other conclusion c2 is obtained.

(8) Display device The display device 17 is a device for calculating the fitness of each event in each conclusion calculated by the fitness calculation device 15 and the reliability calculation device 16.
The presence or absence and / or the reliability of the maximum value and the minimum value for each event in each conclusion calculated in the above are displayed and notified to the human. It is also possible to display only the degree of conformity equal to or higher than a predetermined value, the reliability equal to or higher than a predetermined value, and the reliability. Data on the degree of conformity and data on reliability may be transmitted by communication, or may be stored in a memory or a file.

As described above, the difference between the expert's knowledge of individual phenomena and conclusions and the learner's knowledge can be learned by evaluating the fitness and reliability of the knowledge input by the learner. . Education can be realized efficiently and at low cost.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an example of the overall configuration of the learning device. FIG. 2 is a graph showing a Gaussian distribution. FIGS. 3a to 3c are graphs showing how a membership function is formed. FIGS. 4a and 4b are graphs showing membership functions obtained for each event. FIGS. 5a and 5b are graphs showing the range of events input by the learner. FIG. 6 is a graph showing the calculation of the fitness. FIG. 7 and FIG. 8 are graphs showing operations relating to reliability. 11 ... Knowledge storage device, 12 ... Knowledge synthesis device, 13 ... Knowledge storage device after synthesis, 14 ... Learner knowledge input device, 15 ... Compatibility calculation device, 16 ... Reliability calculation device, 17 ... ... display device.

Claims (1)

(57) [Claims] 1. A storage means for preliminarily storing expert's knowledge about a relationship between an event and a conclusion, and an input means for a learner to input data on an event which gives a conclusion when a conclusion is given. A fitness calculating means for calculating, for each event, a degree to which data for a predetermined conclusion input by the learner through the input means matches the expert's knowledge stored in the storage means for the same conclusion; Reliability calculating means for calculating the reliability of data for a predetermined conclusion input by the learner through the means with reference to the expert knowledge stored in the storage means for the same conclusion, and the fitness calculating means And display means for displaying at least one of the fitness and the reliability calculated by the reliability calculation means. Learning device for approximate reasoning.