The multi-objective linear production planning games in triangular hesitant fuzzy sets

TLDR: In this paper, a multi-objective linear production planning (MOLPP) problem was formulated as a mathematical programming problem with triangular hesitant fuzzy (THF) parameters and two approaches, namely weighted sum method (WSM) and extended technique for order preference by similarity to ideal solution (TOPSIS), were chosen to obtain the optimal strategy and payoff vectors of the players to the MOLPPG.

Abstract: The hesitant fuzzy set (HFS) is a very fruitful mathematical approach to deal with uncertain or imprecise information. In this work, we consider a multi-objective linear production planning (MOLPP) problem in which multiple decision makers pool resources to make various products and analyze them with the help of cooperative game theory. It can be formulated as a mathematical programming problem with triangular hesitant fuzzy (THF) parameters. The main aim of this paper is to analyze the MOLPP problem in THF environment. In view of realistic sense we choose the coefficients of multi-objective linear production planning game (MOLPPG) as triangular hesitant fuzzy numbers (THFNs), and hereby it is referred to as THF-MOLPPG. The THF-MOLPPG is converted to fuzzy MOLPPG by taking an average aggregation operator (AAO) of the THFNs. Thereafter we consider $$\alpha $$ -cut of a fuzzy number to obtain MOLPPG with interval parameters. Two approaches, namely weighted sum method (WSM) and extended technique for order preference by similarity to ideal solution (TOPSIS), are chosen to obtain the optimal strategy and payoff vectors of the players to the MOLPPG. For solving MOLPPG, we apply WSM and extended TOPSIS by considering the various values of $$\alpha $$ for finding the value of the game in such a way that the total income is maximized. A comparison is drawn among the payoff vectors, which are determined from the approaches. Finally, the applicability and feasibility of the proposed methods are illustrated by a numerical example. WSM and extended TOPSIS provide better results at the values $$\alpha = 0.3$$ and $$\alpha =0.9$$ , respectively, for the proposed problem. From the results, we infer that TOPSIS is far better than WSM of the proposed problem. Also, the conclusions and outlooks of the paper are delineated.