In this paper, we introduce the concepts of r-closure and r-interior defined by intuitionistic gradation of openness. We also introduce the concepts of r-gp-maps, weakly r-gp-maps, and obtain some characterizations in terms of r-closure and r-interior operators.

Two families of metrics in space of intuitionistic fuzzy numbers are considered. A method of ranking intuitionistic fuzzy numbers based on these metrics is also suggested and invesigated.

The concept of an intuitionistic fuzzy neighbourhood is introduced. This notion turns out to be more sensitive to variations in the different points of the universe compared to the standard neighbourhood definition of metric space. We apply the intuitionistic fuzzy neighbourhood to the extended modal operators, defined over intuitionistic fuzzy sets.

in this paper, we introduce a new class of implicit functions and also common property (e.a) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. we are not aware of any paper dealing with such implicit functions in modified intuit...

and Applied Analysis 3 x ν αx, t ν x, t/|α| for each α/ 0, xi ν x, t ν y, s ≥ ν x y, t s , xii ν x, · : 0,∞ → 0, 1 is continuous, xiii limt→∞ν x, t 0 and limt→ 0ν x, t 1. In this case μ, ν is called an intuitionistic fuzzy norm. Example 1.4 cf. 37 . Let X, ‖·‖ be a normed space, a∗b ab, and a b min a b, 1 for all a, b ∈ 0, 1 . For all x ∈ X and every t > 0 and k 1, 2, consider μk x, t ⎧ ⎨ ⎩ t t...

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced previously, and some its properties were studied. So far, there are two different IFMTSs based on the classical intuitionistic fuzzy operations: “union” (∪) “intersection” (∩). In present paper, new developed. They topological operators from closure interior types, here for first time, standard modal □ ◊. ...

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

Abstract In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new nutrosoph...

The aim of this paper is to introduce the notion of  -chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings in this newly defined space. Our result is intuitionistic fuzzy version of Cho and Jung's [1] and Mukherjee's [9] results in  -chainable fuzzy metric space.