On some fuzzy functional equations

In this paper we offer a comprehensive and unified approach to the study of existence theorems for fuzzy functional equations of the form f( x) = h( x, f( s( x))). Though this equation in the classical setting has been studied extensively in the literature there has not been much of a study of fuzzy...

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Bibliographic Details
Published in:Fuzzy sets and systems 1994-06, Vol.64 (3), p.333-338
Main Authors: Subrahmanyam, P.V., Sudarsanam, S.K.
Format: Article
Language:English
Subjects:
analysis
Fuzzy function
fuzzy functional equation
fuzzy numbers
gauge space
Hausdorff metric
pseudometric
Zadeh's extension principle and fuzzy solution
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Summary:In this paper we offer a comprehensive and unified approach to the study of existence theorems for fuzzy functional equations of the form f( x) = h( x, f( s( x))). Though this equation in the classical setting has been studied extensively in the literature there has not been much of a study of fuzzy functional equations. We employ the tools of analysis as available in E n , the space of fuzzy numbers (which are normalized, fuzzy convex, upper semicontinuous and compactly supported).
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(94)90156-2