Interval-Valued Intuitionistic Fuzzy Linear Programming Problem

Abstract

In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind of uncertainty. Interval-valued intuitionistic fuzzy sets (IV-IFS) is a perfect key for handling uncertainty and hesitation than FS and IFS. In this paper, we define an interval-valued intuitionistic fuzzy number (IV-IFN) and its expected interval and expected values. We also introduce the concept of interval-valued intuitionistic fuzzy linear programming problem (IV-IFLPP). Further, we find the solutions of IV-IFLPP and compare the obtained optimal solutions with existing methods [D. Dubey and A. Mehra, Linear programming with Triangular Intuitionistic Fuzzy Numbers, in Proc. of the 7th Conf. and of the European Society for Fuzzy Logic and Technology (EUSFLAT-LFA 2011), R. Parvathi and C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets 18 (2012) 48–56]. Proposed technique may be used successfully in various areas in the formulation of our country’s five year plans, these include transportation, food-grain storage, urban development, national, state and district level plans, etc., The Indian Railways may use IV-IFLPP technique for linking different railway zones in more realistic way. Agricultural research institutes may use proposed technique for crop rotation mix of cash crops, food crops and fertilizer mix. Airlines can apply IV-IFLPP in the selection of routes and allocation of aircrafts to different routes. Private and public sector oil refineries may use IV-IFLPP for blending of oil ingredients to produce finished petroleum products.