Paper Info
Title
Fuzzification of Rational and Recognizable Sets
Abstract
In this paper we present a different framework for the study of fuzzy finite machines and their fuzzy languages. Unlike the previous work on fuzzy languages, characterized by fuzzification at the level of their acceptors/generators, here we follow a top-down approach by starting our fuzzification with more abstract entities: monoids and particular families in monoids. Moreover, we replace the unit interval (in fact, a finite subset of the unit interval) as support for fuzzy values with the more general structure of a lattice. We have found that completely distributive complete lattices allow the fuzzification at the highest level, that of recognizable and rational sets. Quite surprisingly, the fuzzification process has not followed thoroughly the classical (crisp) theory. Unlike the case of rational sets, the fuzzification of recognizable sets has revealed a few remarkable exceptions from the crisp theory: for example the difficulty of proving closure properties with respect to complement, meet and inverse morphisms. Nevertheless, we succeeded to prove the McKnight and Kleene theorems for fuzzy sets by making the link between fuzzy rational/recognizable sets on the one hand and fuzzy regular languages and FT-NFA languages (languages defined by NFA with fuzzy transitions) on the other. Finally, we have drawn the attention to fuzzy rational transductions, which have not been studied extensively and which bring in a strong note of applicability.
Year
Venue
Keywords
2007
Fundam. Inform.
unit interval,recognizable set,fuzzy set,fuzzy language,fuzzy transition,rational set,fuzzy finite machine,fuzzy value,fuzzy rational transductions,recognizable sets,fuzzy regular language,lattice
Field
DocType
Volume
Discrete mathematics,Combinatorics,Defuzzification,Fuzzy classification,Algebra,Fuzzy set operations,Rational set,Fuzzy set,Type-2 fuzzy sets and systems,Fuzzy number,Membership function,Mathematics
Journal
76
Issue
ISSN
Citations 
4
0169-2968
8
PageRank 
References 
Authors
0.46
15
3
Name
Order
Citations
PageRank
Stavros Konstantinidis128331.10
Nicolae Santean210913.05
Sheng Yu369777.85