(5.3)--5.3-ScalarMultiplication.pdf

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1、5.35.3 Scalar MultiplicationScalar Multiplication Theorem 1Theorem 1 Let Let .Then.Then=，=.ProofProof =|=,=.Support and Support and kernelkernel Let Let .is called the support of is called the support of,denoted by denoted by,=.is called the kernel of is called the kernel of,denoted by,denoted by,=.

2、=.1()1(),Scalar Scalar multiplicationmultiplication Let Let ,.The The scalar scalar multiplication multiplication of of and and is a fuzzy set,is a fuzzy set,denoted by denoted by,where,where ()=,.Example 1Example 1 Let Let =,.=+.=+.Example Example 2 2 If If ,then,then =,.Example Example 3 3 If If ,then then =,.Theorem 2Theorem 2 Let Let ,.If.If ,thenthen .Proof Proof Suppose Suppose ,()=().Theorem 3Theorem 3 Let Let,.If.If ,then then .Proof Proof ,()(),.