(2.2)--2.2-OperationsonFuzzySets.pdf

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1、2.22.2 Operations on Fuzzy SetsOperations on Fuzzy Sets Operations on Fuzzy SetsOperations on Fuzzy Sets UnionUnion IntersectionIntersection ComplementationComplementation Operations on Crisp SetsOperations on Crisp Sets Let Let,.UnionUnion .IntersectionIntersection ,.ComplementationComplementation

2、=.Let Let ,=,then then =,=.Let Let ,=,then then =,=.Let Let be the be the identifier identifier set,set,then then =,suchsuch thatthat ,=,.Let Let,and and are their are their characteristic functions respectively,wherecharacteristic functions respectively,where =，,，,=，,，.1 0 0 1 ComplementationComple

3、mentation =,._ 1 1 1 1 0 1 0 1 1 0 0 0 UnionUnion =,._ 1 1 1 1 0 0 0 1 0 0 0 0 IntersectionIntersection =,._ Theorem 1Theorem 1 Let Let,.Then Then ,=,=,=,=,=.Theorem Theorem 2 2 Suppose Suppose is an identifier set,is an identifier set,ThenThen =|=|=,=|=|=.Operations on Fuzzy SetsOperations on Fuzzy

4、 Sets Let Let,.UnionUnion The The union of union of and and is denoted by is denoted by ,where where =，=,.IntersectionIntersection The The intersection of intersection of and and is denoted by is denoted by ,where,where =，=,.ComplementationComplementation The The complement of complement of is denot

5、ed by is denoted by ,where,where =,.Let Let be an be an identifier identifier set,set,.The union The union of the fuzzy setsof the fuzzy sets for for is is denoted by denoted by,where,where =,.The The intersection of the fuzzy setsintersection of the fuzzy sets for for is is denoted by denoted by,where,where =,.