JP2553725B2 - Reasoning device - Google Patents

Description

TECHNICAL FIELD The present invention controls equipment based on input data,
The present invention relates to an inference device for performing inference by an expert system or pattern recognition.

2. Description of the Related Art In describing conventional technology, first, a basic outline of fuzzy inference will be described by taking fuzzy control used in device control or the like as an example.

In a control system involving human evaluation, variables that the operator subjectively and sensorily judge, such as "large,""medium,""very,""little" variables (called fuzzy variables) ) May be used to determine the final control manipulated variable. In this case, the operator determines the operation amount from the input variable based on the control experience obtained from his own experience. In the inference device using fuzzy control, “IF… THEN
Applying a fuzzy variable of an input variable to the IF part of an inference rule according to an inference rule of the form "..." and showing how much the inference rule is satisfied (membership value), TH
The fuzzy number of the output in the EN section is determined. The actual manipulated variable can be obtained by taking the barycentric value of the fuzzy numbers output by a plurality of rules.

Now, one of the conventional control methods using this fuzzy inference is fuzzy modeling. For example, Kanezawa, Michio Sugano, "Fuzzy Modeling", Transactions of the Society of Instrument and Control Engineers vol.23, no.6, pp. .650-652, 1987.
In the control rules that make up fuzzy modeling, the IF
The part consists of fuzzy propositions, and the THEN part consists of ordinary linear relations of input and output. Now, for example, considering a first-order lag tank model, the control deviation e and its change rate de
And the control rule between the control output (operation amount) u is as follows.

If e is Zero and de is Positive Medium Then u = 0.25e + 1.5de A plurality of inference rules as described above are prepared, and the whole is called a control rule. Zero, Positive Medium, etc. are labels that represent the fuzzy number of inputs used to describe rules,
It is a fuzzy variable. FIG. 1 shows an example thereof. In Figure 1, NB is Negative Big, NM is Negative Medium, N
S is Negative Small, Z0 is Zero, PS is Positive Small, P
M means Positive Medium, PB means Positive Big. Here, the function expressing the fuzzy number F on X is called a membership function μ _F (), and the function value of each x ⁰ is called a membership value μ _F (x ⁰ ). The general form of the above control rule is as follows.

Here, R ^s indicates the sth rule, x _j is an input variable, A _j ^s is a fuzzy set, y ^s is an output from the sth rule, and c ^s is a THEN part parameter. Some input (x ₁ ⁰ , x ₂ ⁰ ,
,, x _m ⁰ ), the inference result y is obtained by the following equation.

Where n is the number of rules and W ^s is the input (x ₁ ⁰ , x ₂ ⁰ , ..., x _m ⁰ ).
Is the ratio that applies to the IF part of the sth rule. The membership value at x ⁰ of the fuzzy set A ^s W ^s is expressed by the following equation.

The fuzzy model identification consists of two steps: structure identification of the IF and THEN parts and parameter identification of the IF and THEN parts. In the conventional identification method, (1) the fuzzy proposition of the IF part is set to an appropriate proposition, (2) W ^s is changed constantly,
(3) Search for only really needed input variables in the THEN part by the variable reduction method, (4) Obtain parameters in the THEN part by the least squares method, (5) and above (2) to (4) Repeatedly, the optimum parameters were determined, (6) changing the fuzzy proposition in the IF section, returning to (7) (2), and repeatedly searching for the optimum parameters under the conditions of the new fuzzy proposition. In other words, it can be said that this is a heuristic identification algorithm.

As a conventional inference device, for example, there is a fuzzy inference device as shown in block 25 of FIG. In FIG. 2, 1a is a data (including measurement value and human evaluation value) input unit, 2a is a display instruction unit, 3a is a fuzzy inference operation unit, 4a is an inference result output unit, and 5a is a display unit. Display
2a is composed of a keyboard, and the fuzzy inference operation unit 3a is composed of a digital computer. The data input to the data input unit 1a is subjected to the inference operation in the fuzzy inference operation unit 3a, and the inference result is output. At the same time, the display unit 5a uses the inference rule list, the fuzzy variable list and various inference rules. The status is displayed. In the conventional inference apparatus as shown in FIG. 2, the inference rules of the fuzzy inference rules and the fuzzy variables as input data are fixed at the fuzzy inference operation unit 3a, and there is no function to change the fuzzy variables.

Not only in the above fuzzy modeling but also in the conventional inference rule determination method, the membership function determination algorithm is based on the heuristic solution method, so it is complicated and the number of parameters to be determined is very large. Therefore, the optimum inference rule cannot be obtained quickly and easily.

Further, in the inference apparatus of FIG. 2 as described above, since there is no learning function of the inference rule, the characteristic of the input variable changes with time, and it is possible to cope with the problem that the inference precision becomes worse with the initially set inference rule. There wasn't. For example, "If it's hot, ○
There must be an inference rule that "controls to ○". Since the vague concept of "hot" varies depending on the person and the season, satisfactory control cannot be performed unless the inference device has a learning function and can adaptively change the inference rule according to the usage situation. Further, in reality, non-linear inference is often required, and the method of performing linear approximation as described in the description of the conventional example has a limit in improving inference accuracy.

DISCLOSURE OF THE INVENTION In order to solve the conventional problems, it is an object of the present invention to provide an inference apparatus that can cope with a high speed even when the inference apparatus is nonlinear by utilizing the nonlinearity of a neural network model. Another object of the present invention is to provide an inference device that can deal with inference problems at high speed by utilizing the nonlinearity of a neural network model. In this reasoning device,
The membership value decision unit, which has a neural network structure, estimates the membership value corresponding to the IF part of each inference rule from the input variable. Moreover, the individual inference amount determination unit of this inference device estimates the inference amount corresponding to the THEN part of the inference rule from the input variable. Then, the final inference amount determination unit comprehensively judges from the membership value and the inference amount estimated for each rule for the input variable to obtain the final inference amount. The present invention is an inference device that operates in this way.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory diagram of fuzzy variables, FIG. 2 is a block diagram of a conventional inference apparatus, and FIGS. 3 and 4 are nerves constituting a membership value determination unit and an individual inference amount determination unit. FIG. 5 is a configuration diagram of a circuit network model, FIG. 5 is a configuration diagram of a linear signal processing unit, and FIG.
Fig. 7 is a block diagram of the non-linear signal processing unit, Fig. 7 is an input / output characteristic diagram of the threshold value processing unit, Fig. 8 is an explanatory diagram of an automatic determination method of a membership function using a neural network model, and Fig. 9 is a book. FIG. 10 is a configuration diagram of an inference apparatus according to an embodiment of the invention, FIG. 10 is an input / output data configuration diagram for explaining the operation of the first embodiment, and
FIG. 12 is a diagram for explaining the membership value of each learning data in the IF section of the first embodiment, FIG. 12 is an inference error diagram when the input variables are reduced, and FIG. 13 is a result diagram for estimating the inference amount of the first embodiment. FIG. 14 is an estimation result diagram when the present invention is applied to the COD concentration estimation problem in Osaka Bay.

BEST MODE FOR CARRYING OUT THE INVENTION A feature of the inference rule determination method used here is that the learning function sequentially determines the membership function. There are various methods for realizing the learning function, but as an example here, a learning algorithm of a neural network model is used. Therefore, the description of the neural network model and the learning algorithm of the neural network model will be described before the description of the embodiment.

The neural network model is a mathematical network inspired by the connection of brain neurons. By determining the connection strength between the units forming the network by sequential learning, it is possible to determine the inference rule without empirical learning.

The network of FIG. 3 is one type of neural network model.
In FIG. 3, reference numeral 100 represents a multi-input / single-output signal processing unit, and 101 represents an input unit of the neural network model.
FIG. 4 shows a specific configuration example. FIG. 4 is an example of a neural network model with a three-stage configuration in which four input variables are input and one output value is estimated. There is no mutual connection in each stage and the signal propagates only to the upper layer. To be done. Of the multi-input one-output signal processing unit 100 that constitutes such a neural network model,
FIG. 5 specifically shows the configuration of the linear signal processing unit based only on the linear operation. In FIG. 5, 1001
Is the input section of the multi-input / single-output signal processing section 100, and 1002 is the input section 1
A memory that stores a weighting coefficient for weighting a plurality of inputs from 001, 1003 is a multiplier that multiplies the weighting coefficient of the memory 1002 and the input from the input unit 1001, respectively, and 1004 is an adder that adds the outputs of the multipliers 1003. is there. That is, in the multi-input one-output signal processing unit 100 shown in FIG. 5, if the input value to the input unit 1001 is x ₁ and the weighting coefficient stored in the memory 1002 is c ₁ , then y = Σc ₁ x ₁ It is calculated. Further, FIG. 6 concretely shows the configuration of the non-linear signal processing unit which also performs non-linear operation in the multi-input one-output signal processing unit 100 constituting the neural network model. In FIG. 6, 1000 is the linear signal processing unit described in FIG. 5, and 2000 is a threshold processing unit that limits the output of the linear signal processing unit to a value within a certain range. FIG. 7 shows an example of the input / output characteristics of the threshold processing unit 2000. For example, the input / output characteristic of the threshold processing unit 2000 that limits the output to the range of (0,1) can be expressed mathematically as OUT = 1 / (1 + exp (−IN)). Here, IN and OUT are threshold processing units 2
000 inputs and outputs.

The input / output relationship of the above neural network is expressed by equation (1).

y = NH (x) (1) In the description of the embodiment, the scale of the model is k layers [u ₀ ×
u ₁ × ... × u _k ]. u ₁ is the number of nerve cell models in the input layer, the intermediate layer, and the output layer, respectively. The above is a general description of the neural network model.

Next, the learning algorithm of the neural network model will be described. Various learning algorithms have been proposed, part 1
Backpropagation (DERumelhart, GEHinton an
d RJWilliams, “Learning Representations by Back
-Propagating Errors, "Nature, vol.323, pp.533-536, O
ct.9, 1986). The mathematical proof / formulation is given in the reference, but basically it is as follows. First, a large number of input variables and a belonging ratio value to each inference rule estimated by another means are prepared as a set as learning data. Input data into the neural network model. Initially, an appropriate value, for example, a random number value is stored in the memory 1002. The error between the output value of the neural network model at that time and the belonging ratio value to the inference rule is calculated. Since this error is a function of the weighting coefficient of the memory 1002, the weighting coefficient is modified in the weight differential direction of the error. That is, learning is performed by minimizing the error by sequentially correcting the weight according to the steepest decent method. This is an outline of the learning method using the Backpropagation algorithm.

An inference rule determination method and an inference amount calculation method will be described using the above neural network model and learning algorithm.

[Step 1] Select only input variables that have a high correlation with the inferred value, and remove unnecessary input variables. For example, when making this determination using a neural network model, first, each input variable x _j , j = 1,
Input 2, ..., k to the neural network model and learn so that the inference value becomes y _i . Next, the input variable is decreased by one and the same learning is performed. Similarly, the variable reduction method is repeated thereafter. The difference between the output of each neural network model after completion of these learnings and the inference value y _i is compared using the error sum of squares as an evaluation index, and the input variable x _j of the neural network model when the smallest error is obtained, j = 1,2,
, M, m ≦ k only is selected.

[Step 2] Input / output data (x _i , y _i ) is data for structure identification of inference rules (hereinafter referred to as TRD. N _t pieces) and evaluation data for inference rules (hereinafter referred to as CHD. N _o pieces) ) And split. n = n _t + n _o
Is.

[Step 3] TRD is subjected to optimum r division using a normal clustering method. R ^s , s = 1,2,
…, R, R ^s learning data And However, (n _t ) ^s indicates the number of TRD data at each R ^s . Here, dividing the m-dimensional space into r means making the number of inference rules r.

[Step 4] Identify the IF structure. Let x _{i be} the input value of the input layer of the neural network model, and the output value of the output layer be And Then, the neural network model is learned so as to estimate the proportion w _i ^s of each learning data (x _i , y _i ) belonging to each R ^s .
The value output by the learned neural network model is the membership value of the IF section.

That is, the membership function is And

The learning data that becomes And

[Step 5] The structure of the THEN part is identified. The THEN part structural model of each inference rule is expressed by the input / output relation (1) of the neural network model, and the input value of TRD And output value y _i ^s . A neural network model that estimates the inference amount by learning is identified. Next, input the value of CHD to the obtained neural network model. To obtain the error sum of squares Θ ^s .

[Step 6] Using the variable reduction method, only the input variables that contribute to the inference amount estimation formula in the THEN part of each inference rule are selected. An arbitrary one input variable is removed from the m input variables, and the TRD is used to identify the neural network model for each THEN portion as in step 5. Next, the estimation error sum of squares Θ _m-1 ^sp of the inference amount when CHD is used is calculated.

From the above equation, we can see how important the removed input variables are in determining the THEN part. That is, If so, the input variable x ^p removed is considered to be of low importance, so x ^p is discarded.

[Step 7] The same operation as in step 5 is performed with the number of remaining input variables set to m. Hereinafter, steps 5 to 6 are repeated, and when the expression (2) is not satisfied for all input variables, the calculation is stopped. The model with the smallest Θ ^s is the optimal neural network model.

Through steps 1 to 7, the IF part and THEN part for each inference rule are determined, and the structural identification of the fuzzy inference rule is completed.

[Step 8] The inference amount y _i ^* is obtained by the following equation.

y ^s is the CH in the optimal neural network model obtained in step 7.
The estimated value with D substituted is shown.

If the neural network model is a collection of nonlinear characteristics as shown in FIG. 7, it is naturally possible to infer a nonlinear object automatically by this learning.

In this way, if the inference rule is determined by the above inference rule determination method, the inference rule is sequentially determined using the learning function even if the inference target is a non-linear relation or ambiguous input / output relation. It is possible to easily and accurately obtain the inference rules without using a specific method.

Next, the method of determining the above-mentioned inference rules will be explained in an easy-to-understand manner using concrete experimental numerical values. Here, Tadashi Kondo, “Improved GMDH for estimating model order”, A simple numerical example shown in the Society of Instrument and Control Engineers, vol.22, no.9, pp.928-934, 1986. The inference rule was determined by using this and the inference amount was determined. The inference rule decision process is described below.

[Steps 1 and 2] Figure 10 shows the input and output data. The data numbers 1-20 are structure determination data (TRD) of the inference rules used for learning, and the data numbers 21-40 are evaluation data (CHD).
Therefore, n _t = n _o = 20, m = 2. 3 layers [3x3x
As a result of learning the 3 × 1] neural network model 15,000 times and selecting input variables, the results shown in Table 1 were obtained.

There is not much difference in the sum of squared errors when the input variable x ₄ is added or removed. Therefore, it is determined that the membership function determination is hardly affected, and will not be used in the following examples.

[Step 3] The TRD is divided using a normal clustering method.
As a result of clustering, each learning data is 2 as shown in Table 2.
It can be divided.

[Step 4] Proportion of learning data (x _i , y _i ), i = 1,2, ..., 20 belonging to A ^s To estimate w _i ^s [0,1] with three layers [3 × 3 × 3 ×
2] the neural network model to learn 5000 times to obtain a fuzzy number A ^s of the IF section. Figure 11 shows the fuzzy number A ¹ in the IF part for the inference rule R ¹ at this time. The learning data is The input data shown in Table 2 below was used.

Similarly, the fuzzy number of the IF part is obtained for R ² .

[Step 5] Obtain the inference amount estimation formula of the THEN part in each inference rule.
Θ ₄ ^s after learning the three-layer [3 × 8 × 8 × 1] neural network model 20000 times was obtained as shown in Table 3.

[Steps 6 and 7] Θ ^s is obtained when an arbitrary one input variable is removed from the structural model of the THEN part of the inference rule R ^s . 3 layers [2 × 8
× 8 × 1] As a result of learning the neural network model 10000 to 20000 times, the error sum of squares of FIG. 12 was obtained for the inference rules R ¹ and R ² . If you compare step 5 and step 6 for each inference rule, with x ₁ removed Therefore, for the inference rule 1, the neural network model of step 5 is used as the THEN part model. The calculation is further continued for the inference rule 2, and the second iteration calculation is completed. Let the neural network model of (x ₂ , x ₃ ) input be the THEN model. The obtained fuzzy model is R ¹ : FI x = (x ₁ , x ₂ , x ₃ ) is A ¹ THEN y ¹ ＝ NH ₁ (x ₁ , x ₂ , x ₃ ) R ² : IF x = (x ₁ , x ₂ , x ₃ ) is A ² THEN y ² = NN ₂ (x ₂ , x ₃ ). FIG. 13 shows y ^* obtained by the equation (3) using the inference device that executes the rule thus obtained.

In this embodiment, the weighted center of gravity based on the equation (3) is adopted as the inference amount obtained as a result of the fuzzy inference, but a method of taking a central value or a maximum value may be used. Further, in the present embodiment, algebraic products are used in the arithmetic expression of W ^s , but fuzzy logic operations such as mini arithmetic may be used instead of algebraic products.

In the procedure of the inference rule determination method described above, the procedure for automatically determining the nonlinear membership function will be described more specifically.

It is natural to think that the same inference rule applies to similar input data. Therefore, in step 3, the learning data is subjected to the crustraling (FIG. 8 (a)). These classes correspond to each inference rule. For example,
It is an inference rule such as "if IF x ₁ is small and x ₂ is large, then ...". In the case of FIG. 8 (a), there are _three inference rules R _{1 to} R ₃ . The typical point of these classes (input data set) is to follow each inference rule almost 100%, but as it approaches the boundary, it will be influenced by multiple inference rules. The function of this ratio is a membership function, and its shape is, for example, FIG. 8 (c). This is a diagram of the membership function seen from above, and the shaded area is the region where the membership functions intersect.

The procedure for creating such a membership function is steps 3 and 4. That is, the neural network model of FIG. 8 (b) is prepared, and the variable values of the IF section are input (x ₁ and x _{2 in the} figure).
To the rule number to which the input value belongs to the output,
In addition, 0 is assigned and learned. One of the important features of the neural network model is that similar inputs correspond to similar inputs. Although only the point x in FIG. 8 (a) was used for learning, if it is in the vicinity, the same output, that is, the fact that the same inference rule is followed, is output. Further, the learned neural network model outputs the optimum balance value of the proportions belonging to the respective inference rules with respect to the input data near the boundary of each inference rule. This is the membership value,
In other words, it can be said that this neural network model internally includes all membership functions of each inference rule.

Although the membership function of the fuzzy inference rule is determined by using the learning algorithm of the neural network in the embodiment of the method of determining the inference rule, other learning algorithms may be used. As can be easily imagined from the fact that the Backpropagation algorithm described in the neural network algorithm is based on the classical steepest descent method, other learning methods include nonlinear minimization such as Newton method and conjugate gradient method. Many learning algorithms used in the problem domain are easily conceivable. Further, in the field of pattern recognition, it is common knowledge to use a learning method in which a standard pattern used for recognition is sequentially brought close to an input pattern, and such a successive learning method may be used.

Further, in the step 5 of the embodiment, the case where the THEN part is also constituted by the neural network has been described, but the THEN part may be expressed by another method. For example, if the fuzzy modeling as described in the conventional method is used, it is different from the first embodiment in the point of nonlinear expression, but if a learning function such as a neural network model is incorporated in the IF part, The essence of sequentially and automatically determining the fuzzy number of the inference rule by the learning function is not impaired.

Further, in the above embodiment, the expression of automatically forming the membership function of the fuzzy inference rule is used. This special case is the case of production rules used in classical expert systems. In this case, it may be easier to understand the expression of automatically forming the reliability of the inference rule. However, this is also only a special case of the embodiment in the method of determining the inference rule.

Next, an embodiment of the present invention that performs inference based on the inference rule obtained by the above inference rule determination method will be described.
FIG. 9 shows a block diagram of a first embodiment of the inference apparatus of the present invention. In FIG. 1, 1 is a membership value determination unit that determines the membership value of the IF portion of each inference rule, 2 is an individual inference amount determination unit that determines the inference amount that should be obtained in the THEN portion of each inference rule, and 3 is an individual It is a final inference amount determination unit that determines the final inference amount from the output from the inference amount determination unit 2 and the output from the membership value determination unit 1. 21 to 2r are internal configurations of the individual inference amount determination unit 21 which determines the inference amount based on each of the inference rules 1 to r. Here, the membership value determination unit 1 and the individual inference amount determination units 21 to 2r
Has a multistage circuit network structure as shown in FIG.

When the input values x _{i to} x _m are input to the inference apparatus of the present invention, the membership value determination unit 1 outputs the ratio of these input values satisfying each inference rule. The membership value determining unit 1 has already learned in accordance with the procedure described in the inference rule determining method. Further, the individual inference amount determination unit 21 outputs the inference amount when these input values follow the inference rule 1. Similarly, the individual inference amount determining units 21 to 2r output the inference amount when the inference rules 2 to r are followed. The final inference amount determination unit 3 outputs the final inference result from the membership value determination unit 1 and the individual inference amount determination unit 2. For the determination method, for example, equation (3) is used.

As is clear from FIGS. 6 and 7, the input / output relationship of the multi-input / output signal processing unit 100 forming the neural network model is non-linear. Therefore, the neural network model itself can also perform non-linear inference. Therefore, the inference apparatus of the present invention can realize high inference accuracy that cannot be achieved by linear approximation.

A concrete application example demonstrates this high inference accuracy of the present invention. Application example was measured in Osaka Bay from April 1976 to March 1979. 5
COD (Chemical oxygen demand: Chemic
al Oxygen Demond) This is a problem of estimating the concentration.

The five measurement parameters are (1) water temperature (° C), (2)
It is transparency (m), (3) DO concentration (ppm), (4) salt concentration (%), and (5) filtered COD concentration (ppm). Of these data, 32 sets of data from April 1976 to December 1978 were used for learning, and the remaining 12 were used as evaluation data after learning. Results estimated by the present invention (solid line) and actual CO
The measured D concentration (dotted line) is shown in FIG. This is a very good estimation result.

As described above, according to the first embodiment of the inference apparatus of the present invention, the membership value determination unit including at least a plurality of network-connected multiple-input / one-output signal processing units, and at least the network-connected plurality of membership value determination units. By providing the individual inference amount determination unit composed of the multi-input / one-output signal processing unit, the inference amount having a learning function and capable of nonlinearly corresponding to the input variable can be determined.

As a second embodiment of the inference apparatus of the present invention, the input / output relationship of the neural network model obtained in advance is held in the memory, and the memory is referred to instead of directly executing the neural network model each time. But approximate reasoning is possible. In the first embodiment, the membership value deciding unit and the individual inference amount deciding unit are configured as the neural network model. However, when the input variables are known in advance or some approximation may be made. Then, the input / output correspondence table can be created in advance from the neural network model determined by the learning algorithm. In the second embodiment, which substitutes the membership value deciding unit or the individual inference amount deciding unit by referring to this correspondence table at the time of executing the inference rule, it becomes impossible to incorporate the above-mentioned inference rule deciding method to have a learning function. However, since the circuit configuration as shown in FIG. 5 is unnecessary, it is possible to realize an inexpensive and small inference device. Further, the inference corresponding to the non-linearity can be performed in the same manner as in the first embodiment of the inference apparatus of the present invention.

As described above, according to the second embodiment, at least the membership value determining unit or the individual inference amount determining unit includes at least the input / output characteristics of the inference unit including a plurality of network-connected multiple input / output signal processing units. By including the memory that holds in advance and the memory reference unit, it is possible to determine the inference amount that nonlinearly corresponds to the input variable with a simple circuit configuration.

INDUSTRIAL APPLICABILITY As described above, according to the inference apparatus of the present invention, inference can be performed accurately even if the inference target is nonlinear.
The practical value of these is enormous.

Continuation of the front page (56) References Maeda, Murakami "Self-adjusting Fuzzy Controller" Proceedings of the Society of Instrument and Control Engineers, Vol. Fuzzy Reasoning Formulation "4th Fuzzy System Symposium, PP. 50-60 (1988) H.M. Takagi NN-drive Fuzzy Reasoning, "Int'l J. of Approximate Reasoning (Special Issue of IIZUKA'88) Vol. 5, No. 3, 991-212.

Claims (4)

(57) [Claims] 1. A membership value deciding unit for deciding a value of a membership function corresponding to an IF part of a fuzzy inference rule from an input value, and an individual estimator for obtaining an operation amount corresponding to an output of a THEN part of the fuzzy inference rule. And a final estimation amount determination unit that integrates the output of the membership value determination unit and the output of the individual estimated amount determination unit to determine a final control operation amount, the membership value determination unit Is a neural network composed of a plurality of multi-input / single-output signal processing units having network connections learned based on desired input / output functions. 2. A membership value deciding unit for deciding a value of a membership function corresponding to an IF part of a fuzzy inference rule from an input value, and an individual estimator for obtaining an operation amount corresponding to an output of a THEN part of the fuzzy inference rule. A final estimation amount determination unit that integrates the output of the membership value determination unit and the output of the individual estimation amount determination unit to determine the final control operation amount, and the individual estimation amount determination unit Is a neural network composed of a plurality of multi-input / single-output signal processing units having network connections learned based on desired input / output functions. 3. A membership value deciding unit for deciding a membership function value corresponding to the IF part of the fuzzy inference rule from an input value, and an individual estimator for obtaining an operation amount corresponding to the output of the THEN part of the fuzzy inference rule. And a final estimation amount determination unit that integrates the output of the membership value determination unit and the output of the individual estimated amount determination unit to determine a final control operation amount, the membership value determination unit And the individual estimation amount determining unit is a neural network composed of a plurality of multi-input / single-output signal processing units having network connections learned based on a desired input / output function. 4. A neural network composed of a plurality of multi-input / single-output signal processing units, each of which has a network connection learned based on a desired input / output function. The inference apparatus according to any one of claims 1 to 3, wherein a memory in which the input / output relation of is calculated and stored in advance is referred to.