Abstract
Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.
Highlights
Optimization problems exhibit some level of imprecisions and vagueness
An attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem
Fuzzy linear programming problem (FLPP) with fuzzy coefficients was formulated by Negoita [3] and called robust programming
Summary
Optimization problems exhibit some level of imprecisions and vagueness. Such phenomena have been well-captured through fuzzy sets in modeling these problems. This concept was adopted to problems of mathematical programming by Tanaka and others. Zimmermann [2] presented a fuzzy approach to multi-objective linear programming problems He studied the duality relations in fuzzy linear programming. Tanaka and Asai proposed a formulation of fuzzy linear programming with fuzzy constraints and suggested a method for its solution which is based on inequality relation between fuzzy numbers [5]. This ranking of fuzzy numbers is an important issue in the study of optimization using fuzzy set theory
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