JP3137996B2 - Neural network using membership function and its learning method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a neural network using a membership function which enables calculation of a membership function in fuzzy control by a neural network, and a learning method thereof. Conventionally, fuzzy control has been applied in fields such as plant control where mathematical models cannot be established. Recently, however, neural network control has attracted attention because of its man-hours, accuracy, and ease of adjustment. However, the neural network needs to be adjusted to a neuron characteristic function that approximates a membership function by learning, and there is a problem that learning takes time. Therefore, improvement in this point is desired.

[0002]

2. Description of the Related Art A neural network is configured by connecting units imitating neurons in a network. In this neural network, input data and desired teacher data for the input data are paired to prepare a learning pattern, and a plurality of patterns are presented to the network for learning. As a learning method, there is a back propagation method that minimizes the sum of squares of the error between the actual output value of the network and the teacher data.

FIG. 21 shows an example of a learning pattern used for learning of a neural network for realizing a membership function. Such an input / output relationship learning pattern is shown in FIG. First as a layer
And a neural network having a four-layer structure of a second layer and an output layer. The number of times of learning in this case is 429
This is one time, and the weights and thresholds of the neurons in the first layer, the second layer, and the output layer after learning are as shown in FIG.

[0004]

However, in the case of a conventional neural network that realizes a membership function, the weight of the connection between the layers is fully connected, and the analysis of the weight of the connection is complicated. In addition, there is a problem that a lot of time is required to complete learning. The present invention has been made in view of such conventional problems, and it is an object of the present invention to provide a neural network using a membership function that is easy to learn and that can easily analyze connection weights, and a learning method thereof. I do.

[0005]

FIG. 1 is a diagram illustrating the principle of the present invention. First, the present invention provides an input layer 10 for branching an input,
A neural network having a hierarchical structure including a hidden layer 12 and an output layer 14 using neurons is targeted. In the present invention, such a neural network is provided between the input layer 10 and the hidden layer 12.
A neuron with a sigmoid function as a nonlinear function
One layer 18 and a second layer 20 of neurons with linear functions
A membership function realizing layer 16 for realizing a membership function by configuring , and a network connection weight W and a neuron threshold value θ of a portion of the membership function realizing layer 16 are set in advance. Neural network using functions.

The membership function realizing layer 16 includes neurons having nonlinear characteristics for realizing a large membership function and neurons having non-linear characteristics for realizing a small membership function. The network for realizing the membership function Medium includes a first neuron having a non-linear characteristic for realizing a small membership function, a second neuron having a non-linear characteristic for realizing a large membership function, and first and second neurons. A third neuron having a linear characteristic that outputs a value obtained by subtracting 1 from the sum of outputs of two neurons. Another network that realizes a membership function medium is a first network having a nonlinear characteristic that realizes a membership function small (or large).
A neuron, a second neuron having a non-linear characteristic for realizing another membership function small (or large), and a third neuron having a linear characteristic for obtaining a difference between outputs of the first and second neurons. Is also good.

[0007] The large membership function consists of an input X and an output Y
Where a and b (where a <b) are constants, when X ≦ a, Y = 0, when a <X <b, Y = (X−a) / (ba) b ≦ At the time of X, there is a relationship of Y = 1, and when approximating this membership function large by a neuron, the characteristic function of the neuron is set so as to minimize the integral of the square of the error from the membership function large.

Specifically, the maximum gradient of the characteristic function of the neuron is set to 1.3253 times 1 / (ba) which is the gradient of the membership function large.

More specifically, when the characteristic function of the neuron is Y = 1 / {1 + exp (−wX + θ)}, the weight w of the connection and the threshold θ are given by: w = 5.3012 / (ba) θ = Set to 2.506 (a + b) / (ba).

When the characteristic function of the neuron is approximated by Y = 0.5 + 0.5 tanh (wX-θ), the weight of the connection and the threshold θ are calculated as follows: w = 2.6506 / (ba) θ = 1. 3253 (a + b) / (ba).

On the other hand, the small membership function is defined as follows: a, b (where a <b) is a constant between input X and output Y, when X ≦ a, Y = 1 when a <X <b , Y = − (X−a) / (ba) When b ≦ X, there is a relation of Y = 0. When approximating this membership function small by a neuron, the absolute value of the characteristic function of the neuron The maximum gradient is 1.3253 times the gradient of the small membership function, −1 / (ba).

More specifically, when the characteristic function of the neuron is Y = 1 / {1 + exp (−wX + θ)}, the connection weight w and the threshold θ are w = −5.3012 / (ba) θ = −2.6506 (a + b) / (ba).

When the characteristic function of the neuron is approximated by Y = 0.5 + 0.5 tanh (wX-θ), the weight of the connection and the threshold value θ are calculated as follows: w = −2.6506 / (ba) θ = − 1.3253 (a + b) / (ba) may be set.

Further, as a learning method of the neural network, the entire network except the membership function realizing layer 16 is learned, or the membership function realizing layer 1
6. Learn the entire network, including 6.

[0015]

According to the neural network using the membership function and the learning method according to the present invention having such a configuration, the input portion of the neural network includes:
Membership function small, m composed of neurons
A layer representing edium and large is provided. The weight and threshold value of the connection of each neuron in the membership function realization layer are obtained by calculation and set in advance so as to minimize the integral of the square of the error with the membership function (pre-wire).

As described above, the weight and the threshold value obtained by calculation are pre-wired to the input portion of the network, so that the learning by the back propagation method does not need to be performed on this portion, so that the learning time of the entire network can be reduced. Also, even if all layers from the input layer to the output layer are learned by back propagation, the connection weights and thresholds at the input portion are pre-wired in advance,
Less learning time.

[0017]

FIG. 2 is a block diagram showing an embodiment of the present invention. In FIG. 2, the neural network is
It has an input layer 10 as a branching unit, an intermediate layer 12 having a two-layer structure using neurons, and an output layer 14. In the present invention, a membership function realizing layer 16 is newly provided between the input layer 10 and the intermediate layer 12. The membership function realizing layer 16 includes a first layer 18 of neurons having a sigmoid function as a nonlinear function and a second layer 20 of neurons having a linear function. The intermediate layer 12 includes a third layer 22 and a fourth layer 24.

Each neuron of the membership function realizing section 16 approximates the membership functions small, medium, and large as shown in FIGS. 3 (a), 3 (b) and 3 (c). FIG. 4 is an explanatory diagram showing a definition of a membership function approximated by the membership function realizing unit 16 of FIG. 2. The four basic membership functions of small medium 1 medium 2 large are the values of the input variable X. Are defined by input variables a, b, and c.

Of these, the membership functions small and large can be approximated by a single neuron. On the other hand, the membership function medium is approximated as shown in FIG. 5 or FIG. FIG.
Is obtained as a value obtained by subtracting 1 from the sum of the membership functions small and large. In the case of FIG. 6, the difference is obtained as the difference between the same type of membership functions small having different characteristics. In the case of FIG. 6, the membership function lar
Ge difference may be.

The embodiment of FIG. 2 takes the case of FIG. 6 as an example, so that the membership functions medium1 and me
two neurons of the first layer realizing the
The weights of the connections to one neuron of the layer are set to +1 and -1. FIG. 7 shows the values of the connection weight w and the threshold value th set to each neuron of the membership function realizing section 16 of FIG. 2. These values are the membership function and the neuron sigmoid shown in FIG. The calculation is performed so as to minimize the integration of the square of the error with the function, specifically, to set the maximum slope of the characteristic function of the neuron to 1.3253 times the slope of the membership function.

The calculation contents for obtaining the result of FIG. 7 are as follows. Now, in the case of the membership function large shown in FIG. 8B, ie, between the input X and the output Y,
a, b (where a <b) is a constant, when X ≦ a, Y = 0, when a <X <b, Y = (X−a) / (ba) (1) When b ≦ X When the membership function having the relationship of Y = 1 is approximated by the neuro unit 30 in FIG. 8A, the maximum value of the slope of the sigmoid function is 1 of the slope 1 / (ba) of the membership function large. .3253 times, the connection weight w and the threshold θ
Determine the value of.

That is, when the sigmoid function of the neuro unit 30 is given by Y = 1 / {1 + exp (−wX + θ)} (2), the weight w of the connection and the threshold θ are w = 5.3012 / (ba). (3) θ = 2.6506 (a + b) / (ba) (4)

The sigmoid function of the neuro unit 30 can be approximately expressed as Y = 0.5 + 0.5 tanh (wX-θ) (5) In this case, the connection weight w and the threshold θ
Is determined as: w = 2.6506 / (ba) (6) θ = 1.253 (a + b) / (ba) (7)

On the other hand, the membership function sm shown in FIG.
all, ie, between input X and output Y, a, b
(Where a <b) is a constant, when X ≦ a, Y = 1 when a <X <b, Y = − (X−a) / (ba) (8) When b ≦ X, The membership function having the relationship of Y = 0 is set to the neuro unit 30.
, The connection weight w and the threshold θ are set so that the absolute value maximum slope of the characteristic function of the neuro unit 30 is 1.3253 times −1 / (ba), which is the slope of the membership function small.
To determine.

That is, when the sigmoid function of the neuro unit 30 is given by Y = 1 / {1 + exp (-wX + θ)} (9), the weight w of the connection and the threshold value θ are w = −5.3012 / (ba) (10) θ = −2.6506 (a + b) / (ba) (11)

The sigmoid function of the neuro unit 30 can be approximately expressed as Y = 0.5 + 0.5 tanh (wX-θ) (12). In this case, the weight w of the connection and the threshold value θ are expressed as w = −2.6506 / (ba) (13) θ = −1.3253 (a + b) / (ba) (14)

Next, the reason why the integral of the square of the error of the sigmoid function with respect to the membership function can be minimized by setting the absolute value maximum slope of the sigmoid function to 1.3253 times the membership function will be described in detail. Now the membership function large

[0028]

(Equation 1)

(15) Let us consider approximation by the sigmoid function: Y = tanh (wX) (16)

FIG. 10 is a graph showing the membership function of equation (15) and the sigmoid function of equation (16).

In FIG. 10, the integral B (w) of the square of the error of the sigmoid function with respect to the membership function is

[0032]

(Equation 2)

(17) Next, half B of the integral of the square of the error of equation (17)
Find the weight w that minimizes (w).

[0034]

(Equation 3)

## EQU1 ## Therefore, when w that satisfies dB (w) / dw = 0 is obtained by an approximate solution with four digits after the decimal point being valid, w = 1.2533 is obtained.

Here, the membership function large in FIG.
Is f (x),

[0037]

(Equation 4)

And the zigmoid function f '(X) is

[0039]

(Equation 5)

Is as follows. Therefore, assuming that both are approximately equal, the membership function f (x) becomes

[0041]

(Equation 6)

(18) Therefore, the connection weight w and the threshold value θ for minimizing the integral of the square of the error of the membership function represented by tanh with respect to the membership function large are: w = 2.6506 / (ba) θ = 1.3253 (a + b) / (ba) may be determined.

Next, when the sigmoid function of the neuro unit 30 is set to Y = 1 / {1 + exp (-wX + θ)} as shown in the above equation (2), the same can be obtained.

[0044]

(Equation 7)

From the result of the above equation (18), the connection weight w and the threshold value for minimizing the integral of the square of the error of the membership function represented by exp with respect to the membership function large θ is

[0046]

(Equation 8)

Is obtained as Therefore, it may be determined that w = 5.3012 / (ba) θ = 2.6506 (a + b) / (ba).

FIG. 11 shows that the membership function “large” is a = 0.3 b = 0.6. In order to approximate this by the neuro unit 30 having the exp sigmoid function of the above equation (2), Based on Equation (4), the membership function large when w = 5.3012 / (ba) = 17.6707 θ = 2.6506 (a + b) / (ba) = 7.952 is set A sigmoid function is shown, and an approximate relationship of the sigmoid function that minimizes the integral of the square of the error with respect to the membership function can be uniquely realized by setting the connection weight w and the threshold value θ.

On the other hand, in the case of the membership function small shown in FIG. 9B, ie, between the input X and the output Y,
When a and b (where a <b) are constants, when X ≦ a, Y = 1 when a <X <b, Y = − (X−a) / (ba) (19) b ≦ X In the following, a case will be described where a membership function having a relationship of Y = 0 is approximated by a neuro unit 30 having a nonlinear characteristic function. The sigmoid function of the threshold processing unit 14 in the neuro unit 30 that approximates the membership function small is f (X) = 1 / {1 + exp (−wX + θ)} (20). To approximate the sigmoid function such that the integral of the square of the error with the membership function is minimized, the slope of the membership function small, −1 / (ba), may be increased to 1.3253 times.

More specifically, as the weight w of the connection and the threshold value θ in the sigmoid function expressed by exp in the equation (21), w = −5.3012 / (ba) (22) θ = −2.6506 (A + b) / (ba) (23)

The membership function small is changed to tan
If the sigmoid function of h is approximately f (X) = 0.5 + 0.5 tanh (wX−θ) (24), then f (X) = 0.5 + 0.5 tanh (wX−θ) = 1 / Using the fact that {1 + exp (−2wX + 2θ)}, 2w = −5.3012 / (ba) 2θ = −2.6506 (a + b) / (ba) Therefore, the weight w and the threshold θ may be set as follows: w = −2.6506 / (ba) (24) θ = −1.3402 (a + b) / (ba) (25)

FIG. 12 shows a membership function lar according to the present invention.
FIG. 9 is a flowchart illustrating a process for obtaining a weight w and a threshold θ when approximation is performed so as to minimize integration of a square of an error of a sigmoid function with respect to “ge” and “small”. In FIG.
First, a coefficient F is determined in step S1. The coefficient F is F = 2, tan when exp is used as a sigmoid function.
To use h, set F = 1. Then step S
In step 2, constants a and b that determine the attribute of the membership function are read. Next, the weight w is calculated in step S3, and the weight θ is calculated in step S4, and the process ends.

Of course, the membership function “medium” can be similarly calculated and set by calculating the membership function “small” and / or “large” as shown in FIGS. 5 and 6. Thus, the first layer 18 and the second layer 18 constituting the membership function realizing section 16 are described.
After the connection weight and the threshold value of the layer 20 have been pre-wired, the learning from the third layer 22 to the output layer 14 is performed by the back propagation method in the learning mode 1 of the present invention.

FIG. 13 shows the result of learning in mode 1, in which the number of times of learning was 471. FIG. 14 shows connection weights and threshold values obtained as learning results. From this result, the number of times of learning of the present invention is about 1 compared to the conventional network.
It can be seen that the number has decreased to / 10. FIG. 15 shows the membership function after learning, and the approximation of the membership function is accurately realized by the neural network after learning.

As learning of mode 2 according to the present invention,
FIG. 16 shows the result of performing a method of learning all the layers from the input layer 10 to the output layer 14 in a state where the first layer 18 and the second layer 20 constituting the membership function realizing layer 16 are pre-wired. In this mode 2, the number of times of learning is 25
Seven times. Figure 1 shows the membership function after learning.
FIG. By the learning in the mode 2, the number of times of learning can be further reduced.

Here, the specific configuration of each neuro unit shown in FIG. 2, the learning of the hierarchical network composed of the neuro units, and the learning of the neural network by the back propagation method will be described as follows. FIG. 18 is an explanatory diagram of functions of the neuro unit used in the present invention. In FIG. 18, reference numeral 30 denotes a neuro unit, taking 5 inputs and 1 output as an example. The neuro unit 30 is provided with a multiplication processing unit 32. The multiplication processing unit 32 multiplies the input signals X1 to X5 by weights W1, W2,.
-1 to 32-5. Numeral 33 denotes an accumulator, and all multiplication results X1W1 to X1W1 output from the multiplication processor 32
X5W5 is added.

Reference numeral 34 denotes a threshold processing unit,
, A non-linear threshold value process is performed using the sigmoid function, for example, as an S-shaped function on the accumulated value from. Note that the threshold processing unit 34 can use another function, for example, a linear function, instead of the sigmoid function depending on the application. The calculation performed by the neuro unit 30 is represented by the following equation. First, assuming that the input signals are X1 to X5, the output Y of the accumulation processing unit 33 is as follows: Y = X1W1 + X2W2 +... + XnWn. Next, the output Z of the threshold value processing unit 34 is as shown in the above equation (2), where θ is the threshold value.

FIG. 19 is a block diagram of a specific embodiment of the neuro unit 30 of FIG. 18, and corresponding portions use the same numbers. In FIG. 19, 32 is a multiplication type D / A
The converter 33 is an accumulation processing unit.
Has an analog adder 33a and a holding circuit 33b.
34 is a threshold processing unit, 35 is an output holding unit, 36 is an output switch unit, 37 is an input switch unit, 38 is a weight holding unit,
9 is a control circuit.

The input switch section 37 has input signals X1 to X5.
Are sequentially input, and are turned on in synchronization with the input timing. Weight signals W1 to W5 are also transmitted in synchronization with the input timings of input signals X1 to X5,
Specifically, the weight input control signal is sequentially output from the control circuit 39 to the receiver 40, and the weight signals W1 to W5 are sequentially transmitted to the weight holding unit 38 via the receiver 40. As a result, the multiplying D / A converter 32, X1W1 to X
5W5 is sequentially calculated.

The accumulation processing unit 33 is initially in the holding circuit 33
Since b has been cleared to zero, the first multiplied value X1W1
And zero are added by the analog adder 33a, and then held in the holding circuit 33b. Next, when the multiplication value X2W2 is input, the analog adder 33a adds the multiplication value X1W1 held in the holding circuit 33b and the newly input multiplication value X2W2, and holds the addition result (X1W1 + X2W2) in the holding circuit 33b. I do.

In this way, the cumulative value Y = X1W1 + X2W2 +... + X5W5 is calculated.

When the arithmetic processing of the arithmetic processing unit 33 is completed,
The control circuit 39 outputs a conversion control signal and an output control signal,
In response to the conversion control signal, the threshold processing unit 34 performs threshold processing on the accumulated value Y, and temporarily holds the output Z obtained from the threshold processing unit 34 in the output holding unit 35. In this state, the control circuit 3
When the output switch 36 is turned on by the output control signal from the switch 9, Z held in the output holding unit 35 is output.

FIG. 20 shows a specific embodiment of a hierarchical network used in the present invention, taking a three-layer network as an example. The neural unit 30 shown in FIG.
Configure using. In FIG. 20, reference numeral 50 denotes an analog bus, which is a neuro unit 30 constituting an input layer.
h, the neuro unit 30i constituting the intermediate layer and the neuro unit 30j constituting the output layer are connected as shown. Reference numeral 51 denotes a weight output circuit for giving a weight value to the weight holding unit 38 in FIG. 19; 52, an input signal holding circuit for holding an input signal to the neuro unit 30h constituting the input layer; A synchronization control signal line 54 for transmitting a signal is a main control unit that comprehensively controls the hierarchical network.

The weight value of the neuro unit 30h in the input layer is 1, and therefore, the numerical value 1 is stored in the weight output circuit 51 of the neuro unit 30h.
Next, the learning process of the weight value and the threshold value will be described using the hierarchical network of FIG. 20 as an example. As an algorithm for this learning process, a back propagation method is usually used. The back propagation method learns by adjusting the weight value and the threshold value of the hierarchical network by feedback of an error.

For example, taking the basic three-layer network of FIG. 20 as an example, the known input signals X1, X
,... Xn are input to the neuro unit 30h of the input layer, and the outputs Z1, Z2,. .. Dn, and an error Δd1 = D1-Z1 Δd2 = D2-Z2... Δdn = Dn−Zn is obtained.

Next, first, each neuro unit 3 in the output layer
The threshold value θ and the weight value Wji to 0j are determined by errors Δd1 and Δd.
,... Δdn are reduced, and then the threshold value θ and the weight value W for the neuro unit 30i of the intermediate layer are adjusted.
Adjust ih similarly. When a series of learning is completed in this manner, the second known input signals X1 ', X2',.
Similarly, the threshold value and the weight value are adjusted so as to minimize the error from the teacher signal by using '.

Hereinafter, similar learning is repeatedly performed based on a learning pattern in which a plurality of input signals and a teacher signal are paired, so that not only the input / output data used for the learning pattern but also the input not used for the learning are input. The data can also be adjusted so that the same output result as at the time of learning or an approximate value thereof can be obtained. Although a linear function is used for the neurons in the second layer 20 in the embodiment of FIG.
This may be a sigmoid function.

[0068]

As described above, according to the present invention, the weights and thresholds determined so far in the learning are calculated from the membership functions in the layer for realizing the membership functions newly provided in the input portion. By learning after pre-wired in the search, the efficiency of learning can be greatly improved,
An accurate approximation result is obtained. Further, since the input part for realizing the membership function is pre-wired, the connection weight can be easily analyzed from the result of learning the whole.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is a configuration diagram of an embodiment of the present invention.

FIG. 3 is a unit configuration diagram of a neuron approximating a membership function used in the present invention.

FIG. 4 is an explanatory diagram showing a definition of a membership function realized by the present invention.

FIG. 5 is a configuration explanatory diagram of a membership function medium of the present invention.

FIG. 6 is an explanatory diagram of another configuration of the membership function medium of the present invention.

FIG. 7 is an explanatory diagram of calculation results of connection weights and thresholds for pre-wiring according to the present invention.

FIG. 8 is an explanatory diagram of a neuron approximating a membership function large according to the present invention.

FIG. 9 is an explanatory diagram of a neuron approximating a membership function small according to the present invention.

FIG. 10 is an explanatory diagram for proving an approximate relationship between a membership function and a sigmoid function according to the present invention.

FIG. 11 is an explanatory diagram of an approximation result of a sigmoid function and a membership function of a neuron of the present invention.

FIG. 12 is a processing flowchart showing a calculation process of a weight and a threshold according to the present invention;

FIG. 13 is an explanatory diagram of a learning result according to mode 1 of the present invention.

FIG. 14 is an explanatory diagram of connection weights and threshold values after learning in FIG. 13;

FIG. 15 is an approximate characteristic diagram of a membership function obtained from the learning result of FIG.

FIG. 16 is an explanatory diagram of a learning result according to mode 2 of the present invention.

FIG. 17 is an approximate characteristic diagram of a membership function realized based on the learning result of FIG. 16;

FIG. 18 is a configuration diagram of an embodiment of a neuro unit of the present invention.

FIG. 19 is a configuration diagram of a specific embodiment of the neuro unit of FIG. 18;

FIG. 20 is a configuration diagram of an embodiment of a hierarchical network used in the present invention.

FIG. 21 is an explanatory diagram of a conventional learning pattern.

FIG. 22 is an explanatory diagram of a conventional neural network.

FIG. 23 is an explanatory diagram of a conventional learning result.

[Explanation of symbols]

 10: input layer 12: intermediate layer 14: output layer 16: membership function realization layer 18: first layer 20: second layer 22: third layer 24: fourth layer 30: neuro unit

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Asahi Kawamura 1015 Uedanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Inside Fujitsu Limited (72) Inventor Ryusuke Masuoka 1015 Kamikodanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Fujitsu Limited ( 72) Inventor Kazuo Asakawa 1015 Uedanaka, Nakahara-ku, Kawasaki City, Kanagawa Prefecture Within Fujitsu Limited (72) Inventor Shigenori Matsuoka 1 Fujimachi, Hino-shi, Tokyo Fuji Facom Control Co., Ltd. (72) Inventor Hiroyuki Okada Tokyo No. 1, Fuji-cho, Hino-shi, Tokyo (56) References JP-A-4-64132 (JP, A) JP-A-4-275629 (JP, A) JP-A-4-275634 (JP, A) A) (58) Field surveyed (Int. Cl. ⁷ , DB name) G06G 7/60 G06F 15/18 G06N 3/00 540

Claims (15)

(57) [Claims] In a neural network having a hierarchical structure including an input layer (10) for branching an input, an intermediate layer (12) using neurons, and an output layer (14), the input layer (10) ) nonlinear function between the intermediate layer (12)
The first layer of neurons with sigmoid functions as numbers (1
8) and the second layer (20) of neurons with a linear function
A membership function realization layer (16) that realizes a membership function by being configured is added, and the weight (W) of the network connection and the threshold value (θ) of the neuron of the portion of the membership function realization layer (16) are preset. A neural network using a membership function characterized by the following. 2. A neural network using a membership function according to claim 1, wherein said membership function realizing layer (16) comprises a neuron having a non-linear characteristic for realizing a membership function large. Neural network using the membership function that is the feature. 3. A neural network using a membership function according to claim 1, wherein said membership function realizing layer (16) includes a neuron having a non-linear characteristic for realizing a small membership function. Neural network using the membership function that is the feature. 4. A neural network using a membership function according to claim 1, wherein said membership function realizing layer (16) includes a first neuron having a non-linear characteristic for realizing a small membership function, and a member. A membership function medium consisting of a second neuron having a non-linear characteristic for realizing a large ship function and a third neuron having a linear characteristic for outputting a value obtained by subtracting 1 from the sum of outputs of the first and second neurons is represented by A neural network using a membership function, characterized in that the neural network includes a realizing network. 5. A neural network using a membership function according to claim 1, wherein said membership function realizing layer (16) includes a first neuron having a non-linear characteristic for realizing a small membership function, and another. With a non-linear characteristic that realizes a small membership function of
A neural network using a membership function, comprising a network for realizing a membership function medium consisting of a neuron and a third neuron having a linear characteristic for obtaining a difference between outputs of the first and second neurons. . 6. A neural network according to claim 1, wherein said membership function realizing layer (16) comprises a first neuron having a non-linear characteristic for realizing a membership function large, and a second neuron. And a network for realizing a membership function medium consisting of a second neuron having a non-linear characteristic for realizing a large membership function and a third neuron having a linear characteristic for obtaining a difference between outputs of the first and second neurons. A neural network using a membership function. 7. A neural network using a membership function according to claim 2, 4 or 6, wherein a and b (where a <b) are constants between an input X and an output Y. When ≦ a, Y = 0 When a <X <b, Y = (X−a) / (ba) When b ≦ X, a membership function large having a relationship of Y = 1 is applied to the neuron. A neural network using a membership function, wherein a characteristic function of the neuron is set so as to minimize integration of a square of an error with the membership function large when approximation is performed. 8. A neural network using a membership function according to claim 7, wherein the maximum gradient of the characteristic function of the neuron is 1.3253 of 1 / (ba) which is the gradient of the membership function large. A neural network using a membership function characterized by being doubled. 9. A neural network using a membership function according to claim 8 , wherein when the characteristic function of the neuron is Y = 1 / {1 + exp (−wX + θ)}, a connection weight w and a threshold value are set. A neural network using a membership function, wherein θ is set to w = 5.3012 / (ba) θ = 2.6506 (a + b) / (ba). 10. A neural network using a membership function according to claim 8 , wherein when the characteristic function of the neuron is Y = 0.5 + 0.5 tanh (wX-θ), the weight of the connection and the threshold value A neural network using a membership function, wherein θ is set to w = 2.6506 / (ba) θ = 1.253 (a + b) / (ba). 11. A neural network using a membership function according to claim 3, 4 or 5, wherein the input X
Where a and b (where a <b) are constants between Y and Y, when X ≦ a, Y = 1, when a <X <b, Y = − (X−a) / (b− a) When b ≦ X, when approximating the membership function small having the relationship of Y = 0 by a neuron, the absolute value maximum slope of the characteristic function of the neuron is the slope of the membership function small. A neural network using a membership function, which is 1.3253 times as large as (ba). 12. In a neural network using a membership function according to claim 11, when the characteristic function of the neuron is Y = 1 / {1 + exp (−wX + θ)}, the weight w of the connection and the threshold value are set. A neural network using a membership function, wherein θ is set to w = −5.3012 / (ba) θ = −2.6506 (a + b) / (ba) 13. A neural network using a membership function according to claim 11, wherein when the characteristic function of the neuron is Y = 0.5 + 0.5 tanh (wX-θ), the weight of the connection and the threshold value A neural network using a membership function, wherein θ is set as follows: w = −2.6506 / (ba) θ = −1.3253 (a + b) / (ba) 14. A neural network using a membership function according to claim 1, wherein the entire network except for the membership function realizing layer (16) is learned. Network learning method. 15. A neural network using a membership function according to claim 1, wherein the membership function realizing layer (16) is used to learn the entire network including the membership function. Learning method for neural networks.