We describe the formal equivalence between interval valued and intuitionistic fuzzy subsets. We then discuss the role of fuzzy set methods in multi-criteria decision-making. We note that when an application involves non-standard, interval valued or intuitionistic fuzzy subsets, a problem arises in choosing a best alternative. This problem is a result of the fact that the membership grades of th...

Abstract: In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0,1]. Some properties of GIVIFMs are studied using the definition of comparability of ...

In this paper, we present the concept of relations in intuitionistic fuzzy soft set and study some of their properties and also discuss symmetric, transitive and reflexive intuitionistic fuzzy soft relations.

* Correspondence author. Abstract The fuzzy multi-attribute decision making problems are investigated, in which the attribute values are given as intervalvalued intuitionistic fuzzy numbers and the attribute weight information is incomplete. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers...

The concept of soft set is one of the recent topics developed for dealing with the uncertainties present in most of our real life situations. The parametrization tool of soft set theory enhance the flexibility of its applications. In this paper, we define intuitionistic fuzzy soft matrices and their operations which are more functional to make theoretical studies in the intuitionistic fuzzy sof...

In this paper we have introduced the concept of intuitionistic fuzzy soft matrix and defined different types of matrices along with some new operations in the parlance of intuitionistic fuzzy soft set theory. Then based on some of these new matrix operations a new efficient methodology named as IFSM -Algorithm has been developed to solve intuitionistic fuzzy soft set based group decision making...

in this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. afterwards, the a...

Interval-valued intuitionistic fuzzy number uses membership degree and non-member ship degree to express a decision-maker’s hesitation, which make decision-maker express his/her opinion in uncertainty decision-making environment easily. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. In application such as weak consistency...