A study on compactness in intuitionistic fuzzy topological spaces

The purpose of this paper is to introduce and study the compactness in intuitionistic fuzzy topological spaces. Here we define two new notions of intuitionistic fuzzy compactness in intuitionistic fuzzy topological space and find their relation. Also we find the relationship between intuitionistic general compactness and intuitionistic fuzzy compactness. Here we see that our notions satisfy hereditary and productive property.

Continuous Maps Via ι-fuzzy θ*-semiopen Sets in Ŝtostak’s Fuzzy Topological Spaces

We introduce fuzzy θ*-semicontinuous mappings and relate with fuzzy continuity, fuzzy θ-continuity, fuzzy a-continuity, fuzzy semicontinuity, fuzzy θ-semicontinuity, fuzzy Y-continuity, fuzzy Z-continuity and fuzzy γ-continuity in Ŝostak sense.

A View on Pythagorean Fuzzy Contra 𝓖∗ Continuous Function

The new dimension of non-standard fuzzy sets called Pythagorean fuzzy sets which can handle the inaccurate data very strongly has been established in recent days. Even though intuitionistic fuzzy sets were generously used in decision making to handle the imprecise data the novelty and the voluminous of Pythagorean fuzzy environment gives motivation to use it in decision making process. The Pythagorean fuzzy topological spaces are the novel generalization of fuzzy topological spaces. Herein the concept of Pythagorean fuzzy contra 𝒢∗ continuous functions are explored. Interrelations have been studied elaborately for the defined functions using various examples.

Zα Open and Closed Mappings in Double Fuzzy Topological Spaces

We introduce and investigate some new class of mappings called double fuzzy Zα-open map and double fuzzy Zα-closed map in double fuzzy topological spaces. Also, some of their fundamental properties are studied. Moreover, we investigate the relationships between double fuzzy Z α-open and other existing mappings. AMS (2000) subject classification: 54A40.

Convergence Classes of L -Filters in L , M -Fuzzy Topological Spaces

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

On а study on intuitionistic fuzzy r-normal spaces

The purpose of this paper is to give some new inferences of intuitionistic fuzzy normal spaces based on the concept of the most studied topics as fuzzy topological spaces. After that, the authors embed an implication among these notions and show that all these conceptions are good extensions of normal spaces. Moreover, the image and the pre-image of intuitionistic fuzzy normal space are also intuitionistic fuzzy normal space.

More on Fuzzy Topological Spaces on Fuzzy Space

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

On induced map f# in fuzzy set theory and its applications to fuzzy continuity

In this paper, we introduce # image of a fuzzy set which gives a induced map f # corresponding to any function f : X → Y , where X and Y are crisp sets. With this, we present a new vision of studying fuzzy continuous mappings in fuzzy topological spaces where fuzzy continuity explains the term of closeness in the mathematical models. We also define the concept of fuzzy saturated sets which helps us to prove some new characterizations of fuzzy continuous mappings in terms of interior operator rather than closure operator.