%0 Journal Article
%T A New Approach to Solve Intuitionistic Fuzzy Optimization Problem Using Possibility, Necessity, and Credibility Measures
%A Dipankar Chakraborty
%A Dipak Kumar Jana
%A Tapan Kumar Roy
%J International Journal of Engineering Mathematics
%D 2014
%R 10.1155/2014/593185
%X Corresponding to chance constraints, real-life possibility, necessity, and credibility measures on intuitionistic fuzzy set are defined. For the first time the mathematical and graphical representations of different types of measures in trapezoidal intuitionistic fuzzy environment are defined in this paper. We have developed intuitionistic fuzzy chance constraints model (CCM) based on possibility and necessity measures. We have also proposed a new method for solving an intuitionistic fuzzy CCM using chance operators. To validate the proposed method, we have discussed three different approaches to solve the intuitionistic fuzzy linear programming (IFLPP) using possibility, necessity and credibility measures. Numerical and graphical representations of optimal solutions of the given example at different possibility and necessity, levels have been discussed. 1. Introduction In the real world some data often provide imprecision and vagueness at certain level. Such vagueness has been represented through fuzzy sets. Zadeh [1] first introduced the fuzzy sets. The perception of intuitionistic fuzzy set (IFS) can be analysed as an unconventional approach to define a fuzzy set where available information is not adequate for the definition of an imprecise concept by means of a usual fuzzy set. This IFS was first introduced by Atanassov [2]. Many researchers have shown their interest in the study of intuitionistic fuzzy sets/numbers [3¨C7]. Fuzzy sets are defined by the membership function in all its entirety (c.f. Pramanik et al. [8, 9]), but IFS is characterized by a membership function and a nonmembership function so that the sum of both values lies between zero and one [10]. Esmailzadeh and Esmailzadeh [11] provided new distance between triangular intuitionistic fuzzy numbers. Recently, the IFN has also found its application in fuzzy optimization. Angelov [12] proposed the optimization in an intuitionistic fuzzy environment. Dubey and Mehra [13] solved linear programming with triangular intuitionistic fuzzy number. Parvathi and Malathi [14] developed intuitionistic fuzzy simplex method. Hussain and Kumar [15] and Nagoor Gani and Abbas [16] proposed a method for solving intuitionistic fuzzy transportation problem. Ye [17] discussed expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems. Wan and Dong [18] used possibility degree method for interval-valued intuitionistic fuzzy for decision making. Possibility, necessity, and credibility measures have a significant role in fuzzy and intuitionistic fuzzy optimization. Buckley
%U http://www.hindawi.com/journals/ijem/2014/593185/