In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,i] X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule "lira" which to any prefilter on X assigns, a function lira E [0,i] X. We give necessary and sufficient conditions for the function lim in order that it can be derived f...

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...

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen’s fuzzy topology and show that the category of Lowen’s fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

There are many symmetries in intuitionistic fuzzifying topology. In the present paper, notion of topology as an extension and a preliminary research on bi-intuitionistic fuzzy is introduced. A theory with semantic method logic established.

For modeling the topological relations between spatial objects, the concepts of a bound on the intersection of the boundary and interior, and the boundary and exterior are defined in this paper based on the newly developed computational fuzzy topology. Furthermore, the qualitative measures for the intersections are specified based on the a-cut induced fuzzy topology, which are (Aa‘qA)(x),12a an...

The fuzzy concept has invaded all branches of Mathematics ever since the introduction of fuzzy set by Zadeh [10]. Fuzzy sets have applications in many fields such as information [5] and control [8]. The theory of fuzzy topological spaces was introduced and developed by Chang [3] and since then various notions in classical topology have been extended to fuzzy topological spaces. Sostak [6] intro...

A poset model of a topological space X is a poset P together with a homeomorphism φ : X−→Max(P ) (Max(P ) is the subspace of the Scott space ΣP consisting of maximal points of P ). In [11] (also in [2]), it was proved that every T1 space has a bounded complete algebraic poset model. It is, however still unclear whether each T1 space has a dcpo model. In this paper we give a positive answer to t...

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some ...