Fuzzy system

System Introduction

When studying a quantified precise system that does not participate, there is a series of effective system theories; but in human machine system, management system, economic system, society In systems such as human thinking activities, the system is not completely accurate due to the logic, reasoning, judgment, and decision making of the human brain, this related system has some kind of fuzzy. As the electronic digital computer develops to the direction of the smart machine, there will be more and more fuzzy systems.

In the usual system theory, a system is clearly determined at a certain time state and input, and the status and output of the next moment will be clearly unique. This system is called a deterministic system, otherwise It is called a non-deterministic system. It is assumed that the status and input of a system at a certain moment, although the status and output of the next time cannot be determined, but can determine the probability distribution of the next state, this system is called a random system, which is a class of non-determination. Sexual system. If it is not possible to determine the probability distribution of the next state, it is possible to determine the collection of possible status of the next time, which is another type of non-deterministic system. If the set of possible states in this non-qualitative system is represented by a blurred collection, it is called a fuzzy system.

The fuzzy system is the same as the classic system, its research content also includes energy, can observe, minimal implementation, system identification, prediction, control, and stability.

Fuzzy logic foundation

Fuzzy set

Many of people's thinking have no clear extension, such as "big", "medium", "small" Wait, these fuzzy concepts cannot be described in a classic collection. Professor Zadeh, Professor Zadeh, proposed to describe these fuzzy concepts, defined as follows:

given the domain u, u to [0, 1] closed interval

: u → [0, 1], u →

is called a blurred subset of u,

called a blur subset of subset,
is called U for a membership degree Reflections with U on the degree of from the ostly set A, the fuzzy subset is also known as a blurred collection.

Subjectivity function

There are several types of common membership functions: triangular functions (Figure 1-1), ladder function (Figure 1-2), Gaussian type Function (Figure 2-1), Zhongmoid function (Figure 2-2), Sigmoid type function (Fig. 3-1) and Z-type function (Fig. 3-2).

Triangle function and ladder function are essentially segment linear functions, so it is relatively simple to use and calculate.

Gaussian membership function and the bell membership function curve have good smooth, and the graphics are not zero and have a relatively clear physical significance, which is the most commonly used membership function.

Sigmoid type membership function curve also has a good smooth, different from the Gaussian membership function, and the SigmoID type membership function is suitable for means of asymmetricity. The Z-type membership function is based on spline interpolation.

Basic architecture

Fuzzy system Basic architecture As shown in Figure 4, the main function block includes: ambiguity mechanism, a fuzzy rule base, fuzzy reasoning, and deprive The mechanism.

Fuzzy mechanism

The function of ambitating mechanism is to convert clear external input data into an appropriate language fuzzy information; that is to say, clear data is blurred into blur information.

Fuzzy system

Fuzzy rule library

1, language fuzzy rules (Mamdani fuzzy rules):

: if
and ... and



2, functional fuzzy rules:

: if
and ... Section>




(1) linear fuzzy Rules:

: if
and ... and

(2) single point fuzzy rules:

: if
and ... and



(3) Tsukamoto Fuzzy Rule: Rear Part of this Fuzzy rule

uses ambiguity for monotonic membership functions For a collection, therefore, each fuzzy rule is reasonabated, it is a clear value.

The reasoning engine will be reasonably performed by these fuzzy rules to determine the decision to take in the next step. The main differences in the above three rules are only different in the rear of the fuzzy rules.

Fuzzy inference

Fuzzy reasoning engine is the core of a fuzzy system, which can simulate human thinking decision modes by approximate reasoning or fuzzy reasoning, to achieve solving problems Date.

Defusion mechanism

will pass through the fuzzy reasoning, and the process of converting into a clarity of the numerical value, we call "deprive".

Due to the different fuzzy rules, it will be different, prison, after the fuzzy reasoning, the hypothesis is expressed in a blurred collection (such as a language blur rule), and Some is expressed in a clear value.

For reasoning is a fuzzy set, the commonly used deprive method has the center of gravity, the maximum average method, the maximum average method, the central average method, and the correction center; it is clear after reasoning If the value, the weight averaging method is the most widely used deprive method.


The advantage of a fuzzy system is that it can be integrated into expert experience, and the generalization capacity is subject to data. Because of the use of expert experience in language, the fuzzy reasoning system has been applied in many engineering sectors. However, the current fuzzy logic system input is fully accurate or a full blur collection, which may need to be input at the same time in the application. Accurate value and fuzzy language variables need to be improved on existing fuzzy systems; input, output space division and membership function and its parameters are mainly relying on personal experience, often need repeated trial, Very subjective and uncertainty.

Fuzzy System Type

Pure Fuzzy Logic System

Pure Fuzzy Logic System is only composed of fuzzy rules and fuzzy reinforcing machines, As shown in Figure 5, its input and output is a blurred set. Because the input and output of the pure fuzzy logic system is a blurred collection, the input and output of most engineering systems in the real world are precise, so the pure fuzzy logic system cannot be directly applied to the actual engineering. In order to solve this problem, the scholars propose Mamdani fuzzy logic system with fuzzy generator and blur elimination based on the pure fuzzy logic system, and Japanese scholarous high-wood (sugeno) proposed a fuzzy rule. The latter conclusion is the fuzzy system of the precise value, called high-grade - closing fuzzy logic system.

Gaogu - Guan Yeno type fuzzy logic system

Gao Wume - Guan Yeeno type fuzzy logic system structure Figure 6 shows that it is a class of more special fuzzy logic systems, which differ in the form of a general fuzzy rule. The output of Gaowu-Guanye-type fuzzy logic system is still precise value without blur elimination. Its advantage is that the output can be expressed by the linear combination of input values, because the method can be brought to the parameter estimation to determine the parameters of the system, and can be approximately analyzed and design a fuzzy logic system with a linear control system analysis method. The disadvantage of the system is that the output portion of the rule does not have a fuzzy language value, so it does not take advantage of expert knowledge, and various principles of fuzzy logic are also limited in this system.

Mamdani fuzzy system

In the Mamdani type fuzzy system, the front and rear of the fuzzy rules are fuzzy language values, which is essentially The input and output portions of the pure fuzzy logic system add a fuzzy generator and blur elimination, and the structure is shown in FIG. The input and output of the system are accurate, so they can be applied directly in the actual engineering. Due to its extensive application, it is also known as the standard model of the fuzzy system.

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