INTRODUCTION There have been a number of generalizations of metric spaces. One such generalization is Menger space introduced in 1942 by Menger[9] who used distribution functions instead of nonnegative real numbers as values of the metric. This space was expanded rapidly with the pioneering works of Schweizer and Sklar [11, 12]. Modifying the idea of Kramosil and Michalek [7], George and Veeram...

Critical path method is a network based method planned for development and organization of complex project in real world application. In this paper, a new methodology has been made to find the critical path in a directed acyclic graph, whose activity time uncertain. The vague parameters in the network are represented by intuitionistic triangular fuzzy numbers, instead of crisp numbers. A new pr...

The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov’s TIFNs are defined. A pair of bi-object...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In this paper, the notions of (T, S)-composition matrix and (T, S)interval-valued intuitionistic fuzzy equivalence matrix are introduced where (T, S) is a dual pair of triangular module. They are the generalization of composition matrix and interval-valued intuitionistic fuzzy equivalence matrix. Furthermore, their properties and characterizations are presented. Then a new method based on α̃−mat...

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

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...

In this paper we discussed some nonlinear arithmetic operation on generalized triangular intuitionistic fuzzy numbers. Some examples and an application are given.

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.