JP2518096B2 - Arithmetic unit - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention relates to an arithmetic device for fuzzy arithmetic operation, and more particularly, to the centroid and centroid of a membership function finally obtained when performing fuzzy inference. The present invention relates to an arithmetic device for obtaining a central variance.

[Conventional technology]

 First, a conventional technique will be described.

The fuzzy inference performs a fuzzy operation on one or a plurality of inputs based on a predetermined fuzzy rule (inference rule, hereinafter referred to as rule), and outputs the result as an inference result.

By the way, the rule above is that the input is x0, x
When the outputs are 1, x2 ..., y1, y2 ..., IF x0 = A and x1 = B and x2 = A ... THEN y1 = P, y2 = Q. Of these, the part of "IF x0 = A and x1 = B and x2 = A ..." is called the antecedent part, and the part of "THEN y1 = P, y2 = Q ..." is called the consequent part. And this rule states that if x0 is the value of A and x1 is the value of B and x2
Is the value of A and ... means the value of P is output as y1, the value of Q is output as y2, and so on.

Here, the values of A, B, P, Q, etc. are called fuzzy variables, but in fuzzy theory, these are not single values, but are triangular or bell-shaped functions that represent the goodness of fit as shown in the graph of FIG. Is defined.

In FIG. 5, the horizontal axis represents the input value or the output value, and the vertical axis represents the fitness.

FIG. 5 shows two fuzzy variables A and B for the variable x1. For example, when the value of x1 is X11, the degrees of fitness for the fuzzy variables A and B are sa1 and sb1, respectively. Also, when the value of x1 is x12, 0, s
It becomes b2. In other words, in the fuzzy theory, the description of x1 = A is evaluated not by two values, that is, true or false, but by continuous values using the fitness.
A function that represents such a degree of conformity is called a membership function.

In addition, in the above rule, the description “x1 = A”, “X2 = B”, “x3 = A” in the antecedent part and the description “y1 = P”, “y1 = Q” in the consequent part are both Any number of 1 or more is acceptable. In the present invention, for simplification of description, a case where the description of the antecedent part is 2 and the description of the consequent part is 1 will be described as an example.

Now, regarding fuzzy inference, several methods are known for this. Of these, here min-max-
The centroid method will be described, but the fuzzy inference is not limited to the min-max-centroid method, and the above rules are operated as they are.

For example, as shown in Fig. 6, IF x1 = A and x2 = B THEN y = P (Rule 1) IF x1 = C and x2 = D THEN y = Q (Rule 2) Done.

First, input the description "x1 = A", which is the antecedent part of rule 1, based on the membership function that defines A.
Goodness of fit s1 showing how well x1 fits A
Ask for 1. Similarly, for the description “x2 = B”, the goodness of fit s12 for B of the input x2 is obtained. And “and”
Select the smaller of the two as s1 and call it s1 (this is called the minimum operation). S1 obtained in this way is the degree of conformity with respect to rule 1.

Similarly, for rule 2, the fitness s21 of x1 for the description “x1 = C” and the fitness s22 of x2 for the description “x2 = D” are obtained, and the smaller of the two is determined by the minimum operation. Select and set to s2. The above is the processing relating to the antecedent part.

 Next, the processing for the consequent part will be described.

In the consequent part, first, a function H1 in which a portion larger than the fitness s1 regarding the membership function G1 defining the fuzzy variable P is cut based on the description of "y1 = P" in Rule 1 is considered. Similarly, regarding the membership function G2 that defines the fuzzy variable Q, consider a function H2 in which a portion larger than s2 is cut.

Then, a function F that selects the larger of the two values of y for both functions H1 and H2 is set as the membership function of the output (such processing is the maximum value calculation: maximum
Calculation).

This function F is a function shown at the lower right of FIG. 6, and is nothing but what expresses the meanings of the rules 1 and 2 by weights of the respective rules. That is, the rule 1 instructs to output the central value p of the function G1 as y, but since the fitness s1 of the rule 1 is considerably large as shown in the figure, the upper part is not much cut. There will be no function H1. On the other hand, the rule 2 instructs to output the center value q of the function G2 as y, but the fitness s2 of the rule 2 is considerably small as shown in FIG. Function H2.

Therefore, it can be easily understood that the final output value of y should be the average value of the functions H1 and H2. However, in this case, in the min-max-centroid method, the arithmetic mean of the functions H1 and H2 is not calculated, and a maximum operation is performed on the functions H1 and H2 to obtain a function F, and the center of gravity of this function F is set to both functions. H
The semantic mean of 1 and H2. That is, the center of gravity r of the function F shown in FIG. 6 is the inference result, and becomes the output value of y.

The above is the fuzzy inference method based on the min-max-centroid method.

By the way, in fuzzy inference, it is also necessary to evaluate the validity of the inference result, that is, the inconsistency of the defined rules. For example, the functions F1 and F shown in FIG.
Various combinations of functions having the same center of gravity value r such as 2 are conceivable, but fuzzy reasoning requires evaluation for this shape.

Here, consider two functions F1 and F2 shown in FIG.

First, in the function F1, the two functions H that are the target of the maximum calculation
The distances of 11, H12 are far apart, and both have large values. This indicates that the rules 11 and 12 for deriving the functions H11 and H12 respectively have mutually contradictory meanings. That is, when the input is in the state shown in FIG. 7, rule 11 strongly instructs to output p1 as output y, and rule 12 strongly instructs to output q1. Even in such a case, it is of course possible to obtain the center of gravity r of the function F1 as the inference result.
Then, it is necessary to say that the intermediate value between the requirements of the two contradictory rules is simply obtained, and the reliability of the value is extremely low.

On the other hand, in the function F2, although the two functions H21 and H22 to be subjected to the maximum operation are slightly apart, the function H21
Has a significantly smaller value than the function H22.
In such a case, rules 21 and 22 for deriving both functions H21 and H22, respectively, instruct to output p2 and q2. However, they do not indicate contradiction because the input conditions that match them are different.
Because the input state shown in FIG. 7 is rule 22
Of the rule 21, but the rule of the rule 22 is largely reflected in the output, and the rule 21 is almost completely reflected. It is not done. That is, there is no problem even if the two rules instruct to output different values.

As described above, in the fuzzy inference, there are cases where the rules are semantically inconsistent. Therefore, it is necessary to detect not only the inference but also the inconsistency of the rule defining the inference.

As an example of a fuzzy reasoning apparatus that detects such a rule inconsistency, Japanese Patent Laid-Open No. 61-264411 is known. The method for detecting the inconsistency of the fuzzy rules disclosed in Japanese Patent Application Laid-Open No. 61-264411 will be briefly described below with reference to FIG.

In the method disclosed in JP-A-61-264411, when the finally obtained membership function has two or more large peaks, it is determined that the rules are inconsistent. As shown in FIG. 8, the detection of the above-mentioned large peak is performed by taking the maximum peak value g _M1 of the membership function, the second largest peak value g _M2 and the minimum value l of the membership function between those peaks. ₁ and g _M1 = g _M2, or when g _M1 ≠ g _M2 , let rg be a constant (usually rg = 1) (g _M2 −l ₁ ) / (g _M1 −g _M2 ) ≧ rg If so, it is performed by considering that there are two or more large peaks.

That is, since the above two expressions are indexes indicating how large the second peak is compared to the first peak, by evaluating these expressions, it is determined whether there are two or more peaks. A determination is made as to whether or not it is.

[Problems to be Solved by the Invention]

However, the method for detecting the inconsistency of rules as disclosed in the above-mentioned Japanese Patent Laid-Open No. 61-264411 is only for evaluating the magnitude relation of the peaks of the membership function. That is, only the vertical axis of the membership function is evaluated, and the horizontal axis is not considered at all. Therefore, if there are two membership functions having peaks of the same height but different distances between them, as shown in FIGS. 9 (a) and 9 (b), for example, It is not possible to distinguish between the case of FIG. That is, in the functions shown in FIGS. 9 (a) and 9 (b), g _M1 , g _M2 , and l ₁ have the same value, and (g _M2 −l ₁ ) / (g _M1 −g _M2 ) ≦ 1.

Therefore, it is determined that there is no inconsistency in the rules in the method disclosed in Japanese Patent Application Laid-Open No. 61-264411. However, in the example shown in FIG. 9 (a), yet in the example shown in FIG. 9 (b), the two rules clearly instruct to output greatly different values. It should be determined that there is.

As described above, in the method for detecting the inconsistency of rules as disclosed in Japanese Patent Laid-Open No. 61-264411, it is impossible to consider it even when it is appropriate to determine that there is an inconsistency. There is a problem that is. In other words, the detection accuracy of the inconsistency of the rule is low.

In view of such circumstances, the inventor of the present application has previously filed Japanese Patent Application No.
-64853 proposes the invention of a "fuzzy inference method" for the purpose of solving the above problems. However, in the invention of Japanese Patent Application No. 2-64853, since the invention of the fuzzy inference method is carried out by utilizing the operation circuit of the conventional general configuration, the operation efficiency is low and it is realized as an actual device. In that case, the problem remains that the amount of hardware increases.

The present invention has been made in view of such circumstances, and an object thereof is to provide an arithmetic device for fuzzy arithmetic capable of detecting rule inconsistency with high accuracy with a simple hardware configuration.

[Means for solving the problem]

The arithmetic device according to the present invention is a statistical device that considers not only the value of the function (vertical axis value) but also the position of the function (horizontal axis value) for the membership function after the maximum arithmetic operation when executing the fuzzy arithmetic operation. It is used to calculate the variance that is a general value and determine the inconsistency of the rule according to this result, and is configured to perform the product-sum calculation required for the variance calculation by three-stage acceleration. That is, the arithmetic unit of the present invention includes a function value generating means for generating each function value corresponding to a plurality of input discrete values, and three storages for respectively storing the first, second and third addition results. Means, adding the function value corresponding to each input discrete value and the first addition result, adding the first addition result and the second addition result, and adding the addition result and the third addition result, respectively. Adding means for executing, counting means for counting the number of discrete values to be inputted, control means for causing the adding means to perform addition processing for each discrete value, and number of discrete values to which the counted value of the counting means is inputted And the calculation means for obtaining the center of gravity of the function and the variance around the center of the function based on the contents of the three storage means.

[Action]

In the arithmetic device of the present invention, the value of the function corresponding to the input discrete value is generated from the function value generating means in order to obtain the center of gravity of the function (membership function) for fuzzy calculation and the variance around the center. The function value corresponding to each input discrete value of the membership function is added to the first addition result, this value is added to the second addition result, and this addition result and the third addition result are added, A process in which each addition result is stored in three storage means is repeatedly executed for all input discrete values, and the last addition result is used to calculate the center of gravity of the membership function and its center Then, the sum of products required for the variance calculation is executed only by the adder using the three-stage addition.

Example of Invention

Hereinafter, the present invention will be described in detail with reference to the drawings showing its embodiments.

First, prior to describing the embodiment of the present invention, a method for obtaining the center of gravity and the variance in fuzzy computation by digital computation will be described.

In the digital operation, as shown in FIG. 2, the function F _(y) is an integer value F ₍₀₎ , F at a discrete value y (y = 0,1,2... N).
₍₁₎ , F ₍₂₎ , F ₍₃₎ … Defined by F _(n-1) , F _(n) .

Here, Q ₀ = F _(n) Q _{i + 1} = Q _i + F _{(n-i + 1)} (1 ≦ i ≦ n) P ₀ = 0 P _{i + 1} = P _i + Q _i (1 ≦ i < n) Q ₀ = 0 Q _{i + 1} = Q _i + P _{i + 1} (1 ≦ i <n) That is, Q _i = F _(n) + F _(n-1) + F _(n-2) + ... + F _{( n-i + 1)} + F _(ni) P _i = Q _n + Q _n-1 + Q _n-2 + ...… + Q _{n-i + 1} V _i = P _n + P _n-1 + P _n-2 +…… + P _{n Assuming -i + 1} + P _n-1 , Q = Q _n P = P _n V = V _n is expressed as follows.

Q = F ₍₀₎ ＋ F ₍₁₎ ＋ F ₍₂₎ ＋ ・ ・ ・… ＋ F _(n-1) ＋ F _(n) P ＝ 1 × F ₍₁₎ ＋ 2 × F ₍₂₎ ＋ ・ ・ ・ ・ ・ ・ ＋ (n-1) × F _(n-1) + n × F _(n) V = 1/2 × {1 × (1 + 1) × F ₍₁₎ +2 × (2 + 1) × F ₍₂₎ + ...… + (n-1) × (N-1 + 1) F _(n-1) + n x (n + 1) F _(n) } = 1/2 x {1 ² xF ₍₁₎ +2 ² xF ₍₂₎ + ... + (n-1) ² x F _(n-1) + n ² x F _(n) +1 x F ₍₁₎ + 2 x F ₍₂₎ + ... + (n-1) x F _(n-1) + n x F _(n) } = 1/2 × {1 ² × F ₍₁₎ +2 ² × F ₍₂₎ + ...… + (n-1) ² × F _(n-1) + n ² × F _(n) + P} By the way, The center r of the function F _(y) is defined by r = P / Q, and the variance s centered on the center r is U = (0-r) ² × F ₍₀₎ + (1-r ) ² x F ₍₁₎ + (2-r) ² x F ₍₂₎ + ... + (n-1-r) ² x F _(n-1) + (nr) ² x F _(n) and Then, s = U / Q is defined. Here, U = 0 ² × F ₍₀₎ +1 ² × F ₍₁₎ +2 ² × F ₍₂₎ ＋ ……… + (n-1) ² × F _(n-1) + n ² × F _(n) -2 × r × {0 × F ₍₀₎ + 1 × F ₍₁₎ + 2 × F ₍₂₎ + ...… + (n-1) × F _(n-1) + n × F _(n) } + r ² × {F ₍₀₎ + F ₍₁₎ + F ₍₂₎ + ... + F _(n-1) + F _(n) } = (2 x V-P) + 2 x r x p + r ² x Q, and s = U / Q = a (2 × V-P) / Q-2 × r × P / Q + r 2 = 2 × V / Q-r-2 × r 2 + r 2 = 2 × V / Q-r 2 -r. Therefore, if Q, P, and V are obtained, the center of gravity r and the variance s can be easily calculated by several divisions, multiplications, and subtractions. Further, Q, P, and V can be obtained by repeating n additions as described above, and multiplication is unnecessary.

Examples of the present invention based on the above method will be described below.

FIG. 1 is a block diagram showing an example of the configuration of a calculation device of the present invention for fuzzy calculation.

In FIG. 1, reference numerals 1, 2 and 3 are all adders,
4, 5 and 6 are accumulators, 7 is a memory, 8 is a detector, 9
Is an address selector, 10 is a counter, 11 is a general-purpose arithmetic unit,
12 is a control circuit and 13 is a bus.

The control circuit 12 controls the entire arithmetic unit shown in FIG. 1, but its control signal is omitted for simplification of description.

The general-purpose arithmetic unit 11 is specifically composed of an arithmetic unit and a register, and mainly executes processing relating to the antecedent part and maximum arithmetic. The input / output of the general-purpose arithmetic unit 11 is connected to the bus 13, and the final arithmetic result is stored in the memory 7 as a membership function F in the state as shown in FIG. That is, the function F ₍₀₎ is at the address 0 of the memory 7 and the address 1
Function F ₍₁₎ is ..., the address n function F _(n) is stored in the.

Note that, in the present invention, the processing of the antecedent part and the means of the maximum calculation may use known methods, and therefore the description thereof will be omitted here.

The adders 1, 2 and 3, the accumulators 4,5 and 6, the detector 8, the address selector 9, and the counter 10 are provided for centroid calculation and variance calculation. As shown in FIG. 1, the adder 1 and the accumulator 4 are in the first stage, the adder 2 and the accumulator 5 are in the second stage, and the adder 3 and the accumulator 6 are in the second stage. And constitute a third stage adder circuit.

The counter 10 counts the value input from the bus 13 and outputs the counted value to the address selector 9 and the flight detector 8.

The address selector 9 selects either the value inputted from the bus 13 or the value given from the counter 10 and outputs it to the memory 7 as the address.

When the count value of the counter 10 becomes "0", the detector 9 detects it and outputs a detection signal to the control circuit 12.

As described above, the memory 7 is associated with each address and the data stored therein. The memory 7 fetches the data from the bus 13 under the control of the control circuit 12, and the value stored in itself is stored in the adder 1. Output to the first input. The address at that time is given from the address selector 9.

As described above, the adder 1 inputs the output of the memory 7 to the first input, and supplies the output to the accumulator 4,
The output of the accumulator 4 is the second input of the adder 1. Then, the adder 1 adds both inputs and outputs the result to the accumulator 4.

The accumulator 4 accumulates the output of the adder 1. Also accumulator 4
Outputs its accumulated value to the bus 13 and the second input of the adder 1 as well as to the first input of the adder 2.

The adder 2 provides its output to the accumulator 5 and the first input of the adder 3, and the output of the accumulator 5 is the second input of the adder 2. Then, the adder 2 adds both inputs and outputs the result to the accumulator 5.

The accumulator 5 accumulates the output of the adder 2 and outputs the output to the bus 13 and the second input of the adder 2.

Further, the adder 3 gives its output to the accumulator 6,
The output of the accumulator 6 is the second input of the adder 2. Then, the adder 2 adds both inputs and outputs the result to the accumulator 6.

The accumulator 6 accumulates the output of the adder 3 and outputs the output to the bus 13 and the second input of the adder 3.

The calculation procedure for obtaining the center of gravity and the variance of the function executed by the arithmetic device of the present invention for the fuzzy calculation configured as described above will be described with reference to the flowchart of FIG.

In this calculation means, the counter 10 holds the value of n-1, the accumulator 4 holds the value of Q _i , the accumulator 5 holds the value of P _i , and the accumulator 6 holds the value of V _i .

Therefore, the control circuit 12 controls the address selector 9 so that the content of the counter 10 is given as the address input of the memory 7 (step S1).

The control circuit 12 then controls the adders 1, 2 and 3 so that they all output 0. Also the control circuit 12
Initializes the accumulators 4, 5 and 6 to "0", and adders 1 and 2
The outputs of 3 and 3 (both are "0") are accumulators 4, 5 and 6, respectively.
To be stored in. Further, the control circuit 12 presets the content of the counter 10 to n via the bus 13 (step S2).

From the above, j = n, Q _i = P _i = V _i = 0.

Thereafter, the control circuit 12 controls the adders 1, 2 and 3 so that the adder 1 outputs the contents of the accumulator 4 and the output of the memory 7, and the adder 2 outputs the contents of the accumulator 5 and the accumulator. 4 is added by the adder 3 to the contents of the accumulator 6 and the output of the adder 2, respectively.

As a result, the adder ₁ outputs the value of Q _i + F _(n-1) , and the adder 2 outputs the value of P _i + Q _i , that is, Q _{i + 1} and P _{i + 1} , respectively.

Further, the adder 3 outputs V _i + P _{i + 1} , that is, V _{i + 1} .

At this time, as described above, as the initial state, the contents of the accumulators 4, 5, and 6 are all 0, that is, Q _i = P _i = V _i = 0, and the content of the counter 10 is n. Adder
The outputs of 1, 2 and 3 are F _(n) , 0, ₀ respectively, that is, Q ₀ , respectively.
It becomes P ₀ , V ₀ .

The control circuit 12 controls the accumulators 4, 5 and 6 to take in the outputs of the respective adders 1, 2 and 3 (step S3). As a result, the contents of the accumulators 4, 5 and 6 become Q ₀ , P ₀ and V ₀ , respectively.

Next, the control circuit 12 subtracts 1 from the content of the counter 10 (step S4). As a result, the outputs of the adders 1, 2 and 3 become Q ₁ , P ₁ and V ₁ , respectively.

Hereinafter, the acquisition of the outputs of the adders 1, 2 and 3 by the accumulators 4, 5 and 6 and the subtraction of the counter 10 will be described below.
Is repeated until the count value of is 0 (steps S3, S4, S
Five). As a result, Q, P, and V are finally obtained as the contents of the accumulators 4, 5, and 6 (step S6). The detector 8 detects that the count value of the counter 10 in step S5 is "0".

Finally, the control circuit 10 transfers the Q, P, V obtained as the contents of the accumulators 4, 5 and 6 to the general-purpose arithmetic unit 11, and the above-mentioned r = P / Q s = 2 × V / Q by causing the calculation of -r ² -r, it obtains the center of gravity r and dispersion s (step S7).

In the above embodiment, the three stages of addition are sequentially performed by independent adders. However, by adopting the configuration shown in FIG. It is also possible to adopt a configuration of dividing and using.

In the configuration shown in FIG. 10, the adder has reference numeral 1
2 is provided, and data selectors 14 and 15 for switching the input to the adder 1 are provided. The data selector 14 selects whether the output of the memory 7 or the contents of the accumulator 5 is input to the first input of the adder 1, and the data selector 15 accumulates to the second input of the adder 1. Select whether to input the contents of the instrument 4 or the accumulator 6. The other structure is similar to that of the embodiment shown in FIG.

The control circuit 12 controls the three-stage addition by the adder 1 and the accumulators 4, 5 and 6 and the subtraction of the counter 10 in the configuration shown in FIG. 10 as follows.

First, by switching the data selector 14 to the accumulator 5 side and the data selector 15 to the accumulator 4 side,
The contents of and are added by the adder 1 and the result is stored in the accumulator 5. Next, by switching the data selector 14 to the memory 7 side and the data selector 15 to the accumulator 4 side, the contents of the memory 7 and the accumulator 4 are added by the adder 1, and the result is added to the accumulator 4 side. Stored in. Then, by switching the data selector 14 to the accumulator 5 side and the data selector 15 to the accumulator 6 side, the contents of the accumulators 5 and 6 are added by the adder 1 and the result is accumulated. It is stored in the calculator 6. Finally, the content of the counter 10 is decremented by "1".

As in the case of the first embodiment, the above processing is performed by the counter.
By repeating until the content of 10 becomes "0", the same result as the first embodiment is obtained.

〔The invention's effect〕

As described above in detail, the arithmetic unit of the present invention obtains the variance of the membership function finally obtained in the fuzzy operation, evaluates the inconsistency of the rules based on the value, and determines the reliability of the inference. The circuit is configured such that the sum of products calculation for obtaining the variance and the center of gravity for use as an index can be performed only by three stages of adder circuits including adders and accumulators and a control circuit for them. Since no multiplier is used, the hardware configuration is simplified and the calculation accuracy is improved.

Further, in the second embodiment, one adder is used in a time division manner so as to have substantially the same configuration as the three-stage adder circuit, so that the amount of hardware can be further reduced. .

[Brief description of drawings]

FIG. 1 is a block diagram showing an example of the configuration of an arithmetic unit for fuzzy arithmetic according to the present invention, FIG. 2 is a schematic diagram showing a method of defining a function in digital arithmetic, and FIG. 3 is shown in FIG. FIG. 4 is a schematic diagram showing the storage state of the membership function obtained by the maximum operation in the fuzzy inference device in the memory, and FIG. 4 shows the procedure for calculating the center of gravity and variance of the membership function by the operation device of the present invention. A flow chart, FIG. 5 is an explanatory diagram of a membership function, FIG. 6 is a schematic diagram showing a general method of fuzzy inference, FIG. 7 is a schematic diagram showing inconsistency that occurs in fuzzy rules, and FIG. 8 is a conventional diagram. FIG. 9 is an explanatory diagram of a method for detecting inconsistency of fuzzy rules, FIG. 9 is a schematic diagram showing the problem, and FIG. 10 is a block diagram showing another embodiment of the present invention. 1,2,3 ... Adder, 4,5,6 ... Accumulator, 7 ... Memory, 8
...... Detector, 9 ...... Address selector, 10 ...... Counter, 11 ...... General-purpose arithmetic unit, 12 ...... Control circuit In the drawings, the same reference numerals indicate the same or corresponding parts.

Claims (1)

(57) [Claims] 1. An arithmetic unit for obtaining a center of gravity and a variance around the center of gravity for a given function, the function value generating generating a value of the function corresponding to a plurality of discrete values as inputs. Means, first, second and third storage means, first addition of the function value generated by the function value generation means and the storage value of the first storage means, and the first storage means of the first storage means Second addition of the stored value and the stored value of the second storage means, and third addition of the second addition result and the stored value of the third storage means
Adding means for performing addition of, and storing the first addition result in the first storage means,
Storing the second addition result in the second storage means,
Control means for sequentially executing processing for storing the third addition result in the third storage means for each of the discrete values, counting means for counting the number of times of processing by the control means, and count value of the counting means When the number of the discrete values reaches the number of the discrete values, the calculating means obtains the centroid of the function and the variance around the centroid based on the contents of the first, second and third storage means. An arithmetic unit characterized by the above.