MATLAB实现模糊逻辑系统详解与应用

需积分: 9 188 浏览量更新于2024-07-18 收藏 9.68MB PDF 举报

本资源深入探讨了"模糊逻辑在MATLAB中的应用"这一主题，它涵盖了模糊系统原理以及与计算过程相关的宝贵信息和实用知识。书中详尽地介绍了模糊系统的各种算法，并针对研究项目、实验室以及高等教育中的模糊系统学习提供了全面且实用的解决方案。《模糊逻辑MATLAB教程》由S. N. Sivanandam, S. Sumathi, 和 S. N. Deepa共同编写，共包含304幅图表和37张表格，旨在帮助读者理解并掌握这一复杂而强大的工具。该书的目的是通过MATLAB这一平台，让读者能够实践和掌握模糊逻辑的基本概念，如模糊集合、模糊推理、模糊控制器设计等核心原理。MATLAB作为一种广泛使用的自动化编程系统，其强大的图形用户界面和内置函数库使得模糊逻辑的理论知识能够转化为实际可操作的代码。书中首先对模糊逻辑的理论基础进行了简要介绍，包括模糊集的概念、模糊度量化、模糊规则的表示和处理等，这些都是理解和应用模糊逻辑的关键步骤。随后，章节逐渐深入，涉及模糊逻辑在控制系统、决策支持系统、模式识别、机器学习等领域的具体应用实例，通过实际案例解析，使读者了解如何将模糊逻辑应用于解决现实生活中的复杂问题。此外，书中还介绍了如何利用MATLAB的fuzzy logic toolbox进行建模、仿真和优化，包括如何设计模糊控制器、创建模糊系统、执行模糊推理以及评估系统性能。读者可以通过阅读和实践书中的示例，提升在MATLAB环境中开发和调试模糊系统的技能。最后，版权信息强调了所有内容受德国版权法保护，复制或使用需遵循相关法律条款，特别是对于Springer公司的出版物，任何未经授权的复制行为都将受到法律追究。该书的印刷质量良好，使用环保纸张，旨在为学习者提供一个长期耐用的学习资源。《模糊逻辑using MATLAB》是一本极具价值的参考书籍，无论是对初学者还是高级研究者，都是理解和应用模糊逻辑技术的绝佳指南，尤其是在MATLAB环境下进行自动化编程和系统设计的过程中。通过阅读本书，读者将能够加深对模糊逻辑的理解，提升在IT领域中的专业技能。

2 1 Introduction

The closer one looks at a real world problem, the fuzzier becomes its

solution (Zadeh 1973)

The Fuzzy Logic tool was introduced in 1965, also by Lotﬁ Zadeh, and is

a mathematical tool for dealing with uncertainty. It oﬀers to a soft computing

partnership the important concept of computing with words’. It provides a

technique to deal with imprecision and information granularity. The fuzzy

theory provides a mechanism for representing linguistic constructs such as

“many,” “low,” “medium,” “often,” “few.” In general, the fuzzy logic provides

an inference structure that enables appropriate human reasoning capabilities.

On the contrary, the traditional binary set theory describes crisp events, events

that either do or do not occur. It uses probability theory to explain if an

event will occur, measuring the chance with which a given event is expected

to occur. The theory of fuzzy logic is based upon the notion of relative graded

membership and so are the functions of mentation and cognitive processes.

The utility of fuzzy sets lies in their ability to model uncertain or ambiguous

data, Fig. 1.1, so often encountered in real life.

It is important to observe that there is an intimate connection between

Fuzziness and Complexity. As the complexity of a task (problem), or of a

system for performing that task, exceeds a certain threshold, the system must

necessarily become fuzzy in nature. Zadeh, originally an engineer and sys-

tems scientist, was concerned with the rapid decline in information aﬀorded

by traditional mathematical models as the complexity of the target system in-

creased. As he stressed, with the increasing of complexity our ability to make

precise and yet signiﬁcant statements about its behavior diminishes. Real-

world problems (situations) are too complex, and the complexity involves the

degree of uncertainty – as uncertainty increases, so does the complexity of the

problem. Traditional system modeling and analysis techniques are too precise

for such problems (systems), and in order to make complexity less daunt-

ing we introduce appropriate simpliﬁcations, assumptions, etc. (i.e., degree of

uncertainty or Fuzziness) to achieve a satisfactory compromise between the

information we have and the amount of uncertainty we are willing to accept.

In this aspect, fuzzy systems theory is similar to other engineering theories,

because almost all of them characterize the real world in an approximate

manner.

Fuzzy

Imprecise

data

Vague

statements

logic

system

Decisions

Fig. 1.1. A fuzzy logic system which accepts imprecise data and vague statements

such as low, medium, high and provides decisions

www.freepdf-books.com

1.1 Fuzzy Logic 3

Fuzzy sets provide means to model the uncertainty associated with vague-

ness, imprecision, and lack of information regarding a problem or a plant, etc.

Consider the meaning of a “short person.” For an individual X, the short per-

son may be one whose height is below 4





. For other individual Y, the short

person may be one whose height is below or equal to 3





. This “short” is

called as a linguistic descriptor. The term “short” informs the same meaning

to the individuals X and Y, but it is found that they both do not provide a

unique deﬁnition. The term “short” would be conveyed eﬀectively, only when

a computer compares the given height value with the preassigned value of

“short.” This variable “short” is called as linguistic variable, which represents

the imprecision existing in the system.

The uncertainty is found to arise from ignorance, from chance and random-

ness, due to lack of knowledge, from vagueness (unclear), like the fuzziness

existing in our natural language. Lotﬁ Zadeh proposed the set membership

idea to make suitable decisions when uncertainty occurs. Consider the “short”

example discussed previously. If we take “short” as a height equal to or less

than 4 feet, then 3





would easily become the member of the set “short”

and 4





will not be a member of the set “short.” The membership value

is “1” if it belongs to the set or “0” if it is not a member of the set. Thus

membership in a set is found to be binary i.e., the element is a member of a

set or not.

It can be indicated as,

(x)=



,x∈ A

,x /∈ A



where χ

(x) is the membership of element x in set A and A is the entire set

on the universe.

This membership was extended to possess various “degree of membership”

on the real continuous interval [0,1]. Zadeh formed fuzzy sets as the sets on the

universe X which can accommodate “degrees of membership.” The concept

of a fuzzy set contrasts with a classical concept of a bivalent set (crisp set),

whose boundary is required to be precise, i.e., a crisp set is a collection of

things for which it is known whether any given thing is inside it or not. Zadeh

generalized the idea of a crisp set by extending a valuation set {1, 0} (deﬁ-

nitely in/deﬁnitely out) to the interval of real values (degrees of membership)

between 1 and 0 denoted as [0,1]. We can say that the degree of membership

of any particular element of a fuzzy set express the degree of compatibility of

the element with a concept represented by fuzzy set. It means that a fuzzy set

A contains an object x to degree a(x), i.e., a(x)=Degree(x ∈ A), and the

map a : X →{M embership Degrees} is called a set function or membership

function. The fuzzy set A canbeexpressedasA = {(x, a(x))}, x ∈ X,andit

imposes an elastic constrain of the possible values of elements x ∈ X called the

possibility distribution. Fuzzy sets tend to capture vagueness exclusively via

membership functions that are mappings from a given universe of discourse

www.freepdf-books.com

4 1 Introduction

X − universe of discourse

Fig. 1.2. Boundary region of a fuzzy set

X to a unit interval containing membership values. It is important to note

that membership can take values between 0 and 1.

Fuzziness describes the ambiguity of an event and randomness describes

the uncertainty in the occurrence of an event. It can be generally seen in

classical sets that there is no uncertainty, hence they have crisp boundaries,

but in the case of a fuzzy set, since uncertainty occurs, the boundaries may

be ambiguously speciﬁed.

From the Fig. 1.2, it can be noted that a is clearly a member of fuzzy set

P , c is clearly not a member of fuzzy set P, but the membership of b is found

to be vague. Hence a can take membership value 1, c can take membership

value 0 and b can take membership value between 0 and 1 [0 to 1], say 0.4,

0.7, etc. This is set to be a partial member ship of fuzzy set P .

The membership function for a set maps each element of the set to a

membership value between 0 and 1 and uniquely describes that set. The val-

ues 0 and 1 describe “not belonging to” and “belonging to” a conventional set

respectively; values in between represent “fuzziness.” Determining the mem-

bership function is subjective to varying degrees depending on the situation.

It depends on an individual’s perception of the data in question and does not

depend on randomness. This is important, and distinguishes fuzzy set theory

from probability theory (Fig. 1.3).

In practice fuzzy logic means computation of words. Since computation

with words is possible, computerized systems can be built by embedding hu-

man expertise articulated in daily language. Also called a fuzzy inference

engine or fuzzy rule-base, such a system can perform approximate reasoning

somewhat similar to but much more primitive than that of the human brain.

Computing with words seems to be a slightly futuristic phrase today since

only certain aspects of natural language can be represented by the calculus of

fuzzy sets, but still fuzzy logic remains one of the most practical ways to mimic

human expertise in a realistic manner. The fuzzy approach uses a premise that

humans do not represent classes of objects (e.g. class of bald men,ortheclass

of numbers which are much greater than 50 ) as fully disjoint but rather as

sets in which there may be grades of membership intermediate between full

www.freepdf-books.com

6 1 Introduction

nonlinear mappings of inputs (stimuli) to outputs (responses), i.e., certain

types of fuzzy systems can be written as compact nonlinear formulas. The

inputs and outputs can be numbers or vectors of numbers. These rule-based

systems in theory model represents any system with arbitrary accuracy, i.e.,

they work as universal approximators.

The Achilles’ heel of a fuzzy system is its rules; smart rules give smart

systems and other rules give smart systems and other rules give less smart or

even dumb systems. The number of rules increases exponentially with the di-

mension of the input space (number of system variables). This rule explosion is

called the principle of dimensionality and is a general problem for mathemat-

ical models. For the last ﬁve years several approaches based on decomposition

(cluster) merging and fusing have been proposed to overcome this problem.

Hence, Fuzzy models are not replacements for probability models. The

fuzzy models sometimes found to work better and sometimes they do not.

But mostly fuzzy is evidently proved that it provides better solutions for

complex problems.

1.2 Mat LAB – An Overview

Dr Cleve Moler, Chief scientist at MathWorks, Inc., originally wrote Matlab,

to provide easy access to matrix software developed in the LINPACK and

EISPACK projects. The very ﬁrst version was written in the late 1970s for

use in courses in matrix theory, linear algebra, and numerical analysis. Matlab

is therefore built upon a foundation of sophisticated matrix software, in which

the basic data element is a matrix that does not require predimensioning.

Matlab is a product of The Math works, Inc. and is an advanced interactive

software package specially designed for scientiﬁc and engineering computation.

The Matlab environment integrates graphic illustrations with precise numer-

ical calculations, and is a powerful, easy-to-use, and comprehensive tool for

performing all kinds of computations and scientiﬁc data visualization. Mat-

lab has proven to be a very ﬂexible and usable tool for solving problems in

many areas. Matlab is a high-performance language for technical computing.

It integrates computation, visualization, and programming in an easy-to-use

environment where problems and solutions are expressed in familiar mathe-

matical notation. Typical use includes:

– Math and computation

– Algorithm development

– Modeling, simulation, and prototyping

– Data analysis, exploration, and visualization

– Scientiﬁc and engineering graphics

– Application development, including graphical user interface building

Matlab is an interactive system whose basic elements are an array that

does not require dimensioning. This allows solving many computing problems,

www.freepdf-books.com

剩余439页未读，继续阅读

m0_37804179

粉丝: 0
资源: 1

MATLAB实现模糊逻辑系统详解与应用

matlab fuzzy logic 使用手册

Fuzzy_Logic_Toolbox

MATLAB 模糊逻辑工具箱Fuzzy Logic Toolbox 用户手册

fuzzy logic matlab不用工具箱

怎么打开Fuzzy Logic Toolbox

使用fuzzy logic toolbox在MATLAB中生成模糊控制表的具体步骤

matlab中fuzzy logic designer与优化算法联立

Fuzzy Logic Toolbox

Fuzzy Logic jar包

matlab中fuzzy logic controller的surface四维表面图怎么生成

最新资源