In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language are studied and we give some closure properties of fuzzy local ω-languages. We also establish relationship between deterministic fuzzy local automaton and fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.

The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

A fuzzy context-free K-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol α, the set containing all right-hand sides of rules with left-hand side equal to α forms a fuzzy language that belongs to a given family K of fuzzy languages. In this paper we study the effect of the non-self-embedding restricti...

In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations of the formulas in F) and by a closure operator in the lattice of the fuzzy subsets of F (we call deduction oper...

We study the structure of partially ordered monoids generated by certain operators on families of fuzzy languages. These operators are induced by simple, well-known operations on fuzzy languages, like fuzzy homomorphism, fuzzy finite substitution and intersection with regular fuzzy languages. The structure of these monoids provides better insight in the (in)dependency of closure properties of s...

In this paper we have characterized the epimorphisms in the full subcategory of Hausdorff fuzzy topological spaces (introduced by Srivastava et al.[10]) of the category FTS of fuzzy topological spaces and fuzzy continuous functions using the Salbanytype closure operator.

We give a new version of fuzzy alternating Büchi automata over distributive lattices: weights are putting in every leaf node of run trees rather than along with edges from every node to its children. Such settings are great benefit to obtain complement just by taking dual operation and replacing each final weight with its complement. We prove that L-fuzzy nondeterministic Büchi automata have th...