(7.2)--7.2-RepresentationTheoremPart1.pdf

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1、7.27.2 Representation Representation Theorem:Part 1Theorem:Part 1 Representation Representation TheoremTheorem Let Let be the set of nests of sets in be the set of nests of sets in.Let Let be the fuzzy power set of be the fuzzy power set of.DefineDefine :,=,.Prove that Prove that is a mapping from i

2、s a mapping from to to .Suppose Suppose .If If ,.ThenThen ()=,.Prove Prove that that :is a surjection.is a surjection.Suppose Suppose .DefineDefine =,.Prove that Prove that (),.=,=(),=(),There There exists exists ,=,.Prove Prove that that ,.Suppose Suppose =,()=,.Suppose Suppose (,.If If ,then then

3、=.Prove that Prove that ,(,.=,=,=,().(),.,By By resolution principle resolution principle,()=(),).Prove that Prove that:is a is a homomorphic homomorphic mapping.mapping.Let Let .Let.Let be the identifier set,be the identifier set,.Then Then =(),=(),=().Prove that Prove that =().=(),.Proof Proof If

4、If =,then,then =().If If ,),then then()=().=()()=().=(),.By By resolution resolution principle principle ，=().Similarly,Similarly,=(),=().Theorem 1(Representation theorem)Theorem 1(Representation theorem)LetLet :,=,.Then Then is a surjection and a homomorphic is a surjection and a homomorphic mapping from mapping from ,to to ,.()(),.()=(),).