Affiliations: [a] Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India
| [b] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Correspondence:
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Corresponding author. S. K. Gupta, Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247 667, Uttarakhand, India. E-mail: [email protected].
Abstract: In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainty involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.
Keywords: Intuitionistic fuzzy linear programming problem, accuracy function, crisp non-linear programming problem, triangular intuitionistic fuzzy number
