Continuity of Fuzzy-Valued Operations

Qihao CHEN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.9   pp.2184-2189
Publication Date: 2002/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: General Fundamentals and Boundaries
fuzzy value,  operation,  continuity,  metric space,  

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Fuzzy value is a fuzzy set on interval [0,1], whose α-cuts are all closed intervals for α [0,1], i.e., fuzzy value is a fuzzy number on [0,1]. In this note, we introduce three kinds of metrics di (i=1,2,3) into fuzzy-valued space m[0,1] and consider continuity of fuzzy-valued operations on metric spaces (m[0,1], di) (i=1,2,3). The obtained results will provide some theoretical bases for numeral calculation of fuzzy-valued operations.