Isomorphic continuous connectives in fuzzy logic

Authors:
K. Maes;B. De Baets
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Dedicated to the 60th birthday of Etienne E. Kerre
Year:
2005

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Abstract

Introducing rescaling functions in the definition of an ordinal sum enables us to use ordinal sums for constructing De Morgan triplets. We investigate under which conditions continuous connectives in fuzzy logic are isomorphic to one another and present necessary and sufficient conditions such that a triplet (T,S,N), consisting of a continuous t-norm T, a continuous t-conorm S and a strict negator N, is isomorphic to a given De Morgan triplet.