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直觉模糊集.ppt

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    “ Add your company slogan ” Atanassov’s intuitionistic fuzzy sets Wang Yanyan LOGO
    Outline 1 2 3 4 Introduction Description Improvement Application
    Chapter 1-Background § There is no doubt that the human brain is the world's most complex , intelligent highest system . § The subtleties of it is to be able to handle information uncertainty , imprecision , incompleteness , fuzziness, randomness and non - monotonic , resulting in incorrect or satisfactory conclusion to provide strong support for people to make decisions.
    Chapter 1--Background time description disadvantage presenter presenter presenter Professor German L.A. Zadeh the mathematician at the Bulgarian Cantor University scholar of Atanassov California in Bokely, the United States of America Late 19th century time description time description 1965 First, fuzzy set theory provides a Cantor set theory , in any one very effective tool to describe and 1986 Atanassov’s intutionistic fuzzy handle fuzziness and uncertainty (A-IF) programming method of domain objects ( elements) , for the simulation system, the aims to solving heterogeneous the relationship between it and fuzzy thinking and decision- multiattribute group decision making and reasoning. making (MAGDM)problems with the collection can only belong A-IF truth degrees in which there or not belong to the Second, in Fuzzy, an object Fuzzy sets are several types of attribute (element) is a characteristic values such as A-IF sets (A- relationship . Namely, .an function of a set can be in the IFSs), trapezoidal fuzzy numbers, object ( element) is a range [0, 1] value, which breaks intervals and real numbers. through the traditional two value characteristic function of a set logic. value is limited to 0 and 1. disadvantage advantage Fuzzy set theory to express Cantor Set theory in uncertainty while using the Intuitionistic fuzzy set contains membership function, it also the membership, non representation and brought some problems, membership and hesitancy processing of namely how to define degree three aspects of Intuitionistic anappropriate membership information, being more various fuzzy sexual fuzzy sets function, which has a certain flexible than the traditional matters have shown degree of subjectivity to some fuzzy set in dealing with extent, it also affected the vagueness and uncertainty. a variety of problems, overall promotion of the theory. but this fuzziness is universal. Set Theory
    Chapter 2—Description § Atanassov’s intuitionistic fuzzy set (AIFS) was characterized with both membership and nonmembership considered at the same time, which provides more choices when describing the properties of things and stronger expression capabilities when dealing with uncertain information. Therefore, intuitionistic fuzzy set has aroused widespread interest in the academics and the engineering technology fields. § Some calculation methods of the past did not take into account the hesitancy degree influence on the results, then we will consider hesitancy degree. Hence, the method I will involve is of the flexibility and universality. § Intuitionistic fuzzy sets contain their own complement which make the system be Intuitionistic fuzzy sets is bound to be more realistic and closer to the smart effect. more complete. § Intuitionistic fuzzy entropy of intuitionistic fuzzy set is an important concept in the theory of intuitionistic fuzzy sets, is a reflection of the degree and uncertainty quantification index. B urlliou and Bustince first gives the definition of it.
    Chapter 3--Improvement § The basic concept of intuitionistic fuzzy sets ( ) x Definition 1. An AIFS A on X is defined as A = Where and are the degrees of membership and nonmembership of x in A, which satisfy ( ), x v A , x u A ( ) x Au Av {  ), ( x ) u 0 ( A  x u A |   x X v A ( x ( ) x  )  v A [0,1] ( x  ) and 1 We stipulate:  1) A B={} 2)AB={} 3) {    A u ,1 (1   u ) , v }  A A A
    Chapter 3-Improvement Definition 2. The Score and Accuracy of an AIFV A are defined by ) ( score A  ( A ccuracy A u   ( S A )  , v A Assume that   ) v u  A A ( ) u H A andB  A A  A   v A u , v B B  are two AIFS , Let S(A),S(B) ,H(A) and H(B) be their score and accuracy function ,respectively . Then : (i) If S(A)
    Chapter 3-Development Definition 3. The hesitancy degrees of A is 1 (    A u A  v ) A A  [ 0 , 1 ] Definition 4. The fuzzy degree of A is 1 |    A u A  v A | A  [ 0 , 1] while the intuitionistic fuzzy numbers equal(0,0), ( ) 1 x  ( ) 1, x  A  A the hesitancy degree and fuzzy degree get maximum value ; while the intuitionistic fuzzy numbers equal(0.5,0.5), x   0 , x ( ) ( ) A A  1 the hesitancy degree gets min value but fuzzy degree gets maximum value; while the intuitionistic fuzzy 0 numbers equal(1,0), ( x A  0 ,   x ( ) ) A
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