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Algorithms to extend crisp functions and their inverse functions to fuzzy numbers
Author(s) -
Duarte O. G.,
Delgado M.,
Requena I.
Publication year - 2003
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.10121
Subject(s) - extension (predicate logic) , monotonic function , inverse , mathematics , fuzzy logic , measure (data warehouse) , fuzzy number , discrete mathematics , algebra over a field , algorithm , computer science , calculus (dental) , fuzzy set , pure mathematics , artificial intelligence , data mining , mathematical analysis , medicine , geometry , dentistry , programming language
In this article we present an algorithm to extend continuous crisp functions to fuzzy numbers using the extension principle; the functions must be monotonically increasing in some of the arguments and monotonically decreasing in the others. Then, we present two different solutions to the problem of extending inverse functions that we have called possible extension and necessary extension. Finally, using these solutions we have generated a family of intermediate extensions that let us define a parameter to measure the existence of the extended inverse functions. © 2003 Wiley Periodicals, Inc.