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...

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of spaces. Dip’s approach helps to rectify deviation some definitions subsets In this paper, further definitions, and theorems fill lack article. Different types are presented such as co-finite, co-countable, right left ray, usual topology. Furthermore, boundary, exterior, isolated points sets investigated illustr...

Following the introduction of fuzzy sets in 1965, a notion of fuzzy topological group was proposed by Foster in 1979: essentially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of fuzzy topological group was introduced by Ma and Yu in 1984 by replacing points by fuzzy points. Recently two of the coauthors have introduced the notion of the topology indu...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

Fuzzy topology based on interior operators is studied in the fully graded framework of Fuzzy Class Theory. Its relation to graded notions of fuzzy topology given by open sets and neighborhoods is shown.

In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new defin...

We introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. In this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. Inparticular, we will prove that ...

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 aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces