智能控制智能控制智能控制 (19).pdf

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1、SubsetDefinition:A fuzzy set A is a subset of fuzzy set B if,and only if,for all x,or()()ABABxx ()()ABxx EqualDefinition:Two fuzzy sets,and B,are equal if and only if for all x,or()=()ABABxx A()=()BxxComplementDefinition:The complement of a fuzzy set is denoted by and defined byA()=1-()AxxUnionDefin

2、ition:The union of two fuzzy sets A and B is the third fuzzy set C,written as,with the membership function()max(),(),CABxxxxXor in abbreviated form written by disjunction:()()()CABxxx IntersectionDefinition:The intersection of two fuzzy sets A and B is the third fuzzy set C,written as,with the membe

3、rship function given by or in abbreviated form written by conjunction:()()()CABxxx()min(),(),CABxxxxXOperation RulesAssociative Laws:DeMorgans Laws:()ABCABC（）()ABCABC（）Distributive Laws:()()()()CABCACBCABCACB（）（）ABAB（）ABAB（）More Definitions Support Crossover points Normality Core-cut,strong-cut Conv

4、exity Symmetricity Bandwidth Fuzzy numbers Open left or right,closedMF TerminologyMFX0.510CoreCrossover pointsSupporta-cutaThese expressions are all defined in terms of xConvexity of Fuzzy SetsA fuzzy set A is convex if for any l in 0,1,llAAAxxxx()m in(),()12121A is convex iff all its-cuts are convex.(How do you measure the convexity of an-cut?)convexmf.mSummary Fuzzy Set Operation Equal Subset Complement Union Intersection Convexity of Fuzzy Sets