The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorm...

Research on soft set based decision making has received much attention in recent years. Feng et al. presented an adjustable approach to fuzzy soft sets based decision making by using level soft set, and subsequently extended the approach to interval-valued fuzzy soft set based decision making. Jiang et al. generalize the approach to solve intuitionistic fuzzy soft sets based decision making. In...

Intuitionistic fuzzy sets gained attention of many researchers and are employed in many axes of research. Thus, different operators are given to deal with intuitionistic fuzzy sets, among them similarity measures. The latter are the object of many propositions and discussions. Our aim is to present several studies on similarity measures between intuitionistic fuzzy sets. Such presentation is ve...

In this paper, we propose a new entropy measure with geometrical interpretation of intuitionistic fuzzy sets. Compared with the entropy measure provided by Szmidt and Kacprzyk, the new entropy formula in this paper can measure both fuzziness and intuitionism for intuitionistic fuzzy sets. According to the relationship between entropy and similarity measure, we construct a new similarity measure...

In this article, the concept of similarity measure for intuitionistic fuzzy soft sets based on distance between two intuitionistic fuzzy soft sets, some examples and basic properties are also studied. An algorithm is developed in intuitionistic fuzzy soft set and an example is given to illustrate possible application in a medical diagnosis problem

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied. Index Terms — Second Zadeh‟s implication, Second Zadeh‟s conjunction, Second Zadeh‟s disjunctio...

Classical sets, fuzzy intuitionistic and other sets are all generalized into the neutrosophic sets. A set is a mathematical approach that helps with challenges involving data inconsistent, indeterminate, or imprecise. The goal of this manuscript to present notion 2-metric spaces. In situation, we prove various fixed point theorems. findings support previous methodologies in literature backed up...

In this paper, we study modal operator F α,β in intuitionistic fuzzy subgroup of a group and derive some results. 1. Introduction The idea of intuitionistic fuzzy sets (IFSs) was given by [1, 2] to generalize the notion of fuzzy sets (FSs). Intuitionistic fuzzy modal operator was defined by Atanassov in [3]. The modal operators have been known to be important tools for IFSs where the operators ...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...