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Advances in Fuzzy Systems
Volume 2016, Article ID 6475403, 12 pages
Research Article

An Efficient Ranking Technique for Intuitionistic Fuzzy Numbers with Its Application in Chance Constrained Bilevel Programming

1Department of Mathematics, University of Kalyani, Kalyani 741235, India
2Department of Mathematics, Government College of Engineering and Textile Technology, Serampore 712201, India

Received 22 November 2015; Revised 24 March 2016; Accepted 3 April 2016

Academic Editor: Kemal Kilic

Copyright © 2016 Animesh Biswas and Arnab Kumar De. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques.