On ordered categories as a framework for fuzzification of algebraic and topological structures

Authors:
Sergey A. Solovyov
Affiliations:
Department of Mathematics, University of Latvia, Zellu iela 8, LV-1002 Riga, Latvia
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

Using the framework of ordered categories, the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by Rosenfeld as well as provides a new approach to fuzzification of topological structures, which amounts to fuzzifying the underlying ''set'' of a structure in a suitably compatible way, leaving the structure itself crisp. The latter machinery allows the so-called ''double fuzzification'', i.e., a fuzzification of something that is already fuzzified.