In this research, n-person cooperative games, arising from multi-objective linear production planning problem with fuzzy parameters, are considered. It is assumed that the fuzzy parameters are fuzzy numbers. The fuzzy multi-objective game problem is transformed to a single-objective game problem by group AHP method. The obtained problem is converted to a problem with interval parameters by considering the nearest interval approximation of the fuzzy numbers. | Yugoslav Journal of Operations Research 28 (2018), Number 2, 237–248 DOI: AN APPROACH TO SOLVE MULTI-OBJECTIVE LINEAR PRODUCTION PLANNING GAMES WITH FUZZY PARAMETERS Hamid BIGDELI Institute for the Study of War, Army Command and Staff University, Tehran, . Iran hamidbigdeli92@ Hassan HASSANPOUR Department of Mathematics, University of Birjand, Birjand, . Iran hhassanpour@ Received: February 2017 / Accepted: February 2018 Abstract: In this research, n-person cooperative games, arising from multi-objective linear production planning problem with fuzzy parameters, are considered. It is assumed that the fuzzy parameters are fuzzy numbers. The fuzzy multi-objective game problem is transformed to a single-objective game problem by group AHP method. The obtained problem is converted to a problem with interval parameters by considering the nearest interval approximation of the fuzzy numbers. Then, optimistic and pessimistic core concepts are introduced. The payoff vectors of the players are obtained by the duality theorem of linear programming. Finally, validity and applicability of the method are illustrated by a practical example. Keywords: Cooperative Game, Production Planning, Optimistic and Pessimistic Core, Nearest Interval Approximation. MSC: 90B85, 90C26. 1. INTRODUCTION Game theory is a formal way to analyze interaction among a group of rational decision makers who behave strategically. Games are broadly classified into two major categories: cooperative and non-cooperative games. In cooperative games, 238 H. Bigdeli, H. Hassanpour / An Approach to Solve Multi-objective Linear coalitions are organized by group agreement among some or all of the players and many coalitions are possible in the n-person case. Any player participating in a coalition must accept completely the decisions of the coalition, in other words, a coalition behaves like an individual decision maker [26]. In the field of .
