The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.

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...

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that...

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...

Closure operators defined on various sets (set of all classical fuzzy sets, set of all semi-cuts, set of all cuts in a Q-set, etc.) are investigated and it is shown how a closure operator defined on one set can be extended to a closure operator defined on another set.

For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

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.