Intuitionistic fuzzy sets are generalized fuzzy sets whose elements are characterized by a membership, as well as a non-membership value. The membership value indicates the degree of belongingness, whereas the nonmembership value indicates the degree of non-belongingness of an element to that set. The utility of intuitionistic fuzzy sets theory in computer vision is increasingly becoming appare...

In this paper, the concept of extended intersection and restricted union of intuitionistic fuzzy soft sets are introduced. Some operations on intuitionistic fuzzy soft sets are investigated, and we prove that De Morgan’s laws hold in intuitionistic fuzzy soft sets theory. Based on these properties, we discuss the algebraic structures of intuitionistic fuzzy soft sets, which is lattice structure...

In this paper we define multiplication between intuitionistic fuzzy matrices (IFMs) and we derive the conditions for a block IFM to be regular. Also a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described. Again, it is shown that a block intuitionistic fuzzy matrix can be decomposed into an upper triangular idemp...

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

Dimensional analysis, for multi-criteria decision making, is a mathematical method that includes diverse heterogeneous criteria into a single dimensionless index. Dimensional Analysis, in its current definition, presents the drawback to manipulate fuzzy information commonly presented in a multi-criteria decision making problem. To overcome such limitation, we propose two dimensional analysis ba...

–In this paper, we present an application of intuitionistic fuzzy programming to two person matrix games for the solution with mixed strategies. We use linear membership and non membership functions for such computation. We introduce the intuitionistic fuzzy (IF) goal for the choice of a strategy in a pay-off matrix in order to incorporate ambiguity of human judgments and a player wants to opti...

Intuitionistic preference relations constitute a flexible and simple representation format of experts’ preference on a set of alternative options, while at the same time allowing to accommodate degrees of hesitation inherent to all decision making processes. In comparison with fuzzy preference relations, the use of intuitionistic fuzzy preference relations in decision making is limited, which i...

Belief and plausibility functions based on Dempster–Shafer theory have been used to measure uncertainty. They are also widely studied and applied in diverse areas. Numerous studies in the literature have presented various generalizations of belief and plausibility functions to fuzzy sets. However, there are still less generalizations of belief and plausibility functions to intuitionistic fuzzy ...

The main goal of the structural optimization is to minimize the weight of structure or the vertical deflection of loaded joint while satisfying all design requirements imposed by design codes. In general fuzzy sets are used to analyze the fuzzy structural optimization. In this paper, a planer truss structural model in intuitionistic fuzzy environment has been developed. This paper proposes an i...

In this paper, we define the concept of an intuitionistic Q-fuzzy normal HX group and some related properties are investigated. We also define the level subsets of an intuitionistic Q-fuzzy normal HX group and discussed some of its properties. A few equivalent propositions of fuzzy HX group constituting an intuitionistic Q-fuzzy normal HX group are given.