Solving Fuzzy Multi-objective Linear Programming Problems Using Multi-player Zero-Sum Game

Temelcan G., Albayrak I. , Köçken H. , Sivri M.

International Conference on Intelligent and Fuzzy Systems, INFUS 2020, İstanbul, Turkey, 21 - 23 July 2020, vol.1197 AISC, pp.1483-1490 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1197 AISC
  • Doi Number: 10.1007/978-3-030-51156-2_172
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.1483-1490
  • Keywords: Fuzzy multi-objective linear programming problem, Ranking function, Zero-sum game

Abstract

© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.The difficulty in solving either multi-objective linear programming (MOLP) problems or fuzzy multi-objective linear programming (FMOLP) problems is the trade-off among objectives. To deal with this difficulty, we proposed a new algorithm for solving FMOLP problems by using zero-sum game. First, FMOLP problem given is converted to a crisp MOLP problem by using ranking function, and then a payoff matrix is constructed to find the weights of each objective function of the MOLP problem. After that, each weight is multiplied with the corresponding objective function, a single-objective LP problem is obtained and thus, FMOLP problem is solved. The proposed algorithm is illustrated by numerical examples for the FMLOP problems having fuzzy constraints or not.