In this article we firstly summarize some notions on L−fuzzy sets, where L denotes a complete lattice. We then study a special case of L−fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is being defined independently from the fuzzy membership function. The latter implies both flexibility and effectiveness in fuzzy inference a...

In this paper basic notions of the rough intuitionistic fuzzy set theory will be given. In fact the paper concerns a relationship between rough intuitionistic fuzzy sets and lattice theory. We shall introduce the notion of rough intuitionistic fuzzy lattice (resp rough intuitionistic fuzzy ideals). We also defined intuitionistic fuzzy rough set corresponding to a rough set and given conditions ...

In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets [36] and a soft sets [30]. Our ivn−soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft se...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the notion of intuitionistic nil radicals of intuitionistic fuzzy ideals in commutative rings some properties of such nil radicals. Mathematics Subject Classification: 03E72

The aim of this paper is to generalise the concept of intuitionistic fuzzy soft set. Relations on generalised intuitionistic fuzzy soft sets and a few of their algebraic properties are studied. Finally, an adjustable approach to generalised intuitionistic fuzzy soft sets based decision making is presented. 2010 AMS Classification: 54A40

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