Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving...

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, ...

Fuzzy sets theory affirmed that the linguistic value for every contraries relation is complementary. It was stressed in the intuitionistic fuzzy sets (IFS) that the conditions for contraries relations, which are the fuzzy values, cannot be greater than one. However, complementary in two contradict phenomena are not always true. This paper proposes a new idea condition for conflicting bifuzzy se...

Triangular intuitionistic fuzzy numbers (TIFNs) is a special case of intuitionistic fuzzy (IF) set and the ranking of TIFNs is an important problem. The aim of this paper is to develop a new methodology for ranking TIFNs by using multiattribute decision making methods (MADM). In this methodology, the value and ambiguity indices of TIFNs may be considered as the attributes and the TIFNs in compa...

The critical path problem is a classical and important network optimization problem appearing in many applications, especially in planning and controlling the complex projects. However the result of classical critical path method computation cannot properly match the real-world problem. This gives rise to fuzzy environment and hence we have fuzzy critical path method. In this paper, two differe...

This paper is focused on arithmetic operations fuzzy and intuitionistic numbers to solve the unconstrained optimization problems with triangular trapezoidal, number coefficients. The optimal solution obtained by Newton’s method, MATLAB outputs are also provided illustrative examples. method proposed in this research work has been compared existing method.

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. in spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (cv index), distance between fuzzy set...

The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...