Linear programming approach to matrix games with intuitionistic fuzzy goals

DOI

10.1080/18756891.2013.761781How to use a DOI?

Keywords

Fuzzy game, Intuitionistic fuzzy set, Game theory, Linear programming, Soft computing

Abstract

Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-sets. In this methodology, the concepts of IF-set goals and the solutions of matrix games with IF-set goals are proposed. It is proven that solutions of matrix games with IF-set goals can be obtained through solving the developed auxiliary linear programming models, which are the generalization of matrix games with fuzzy goals. The proposed methodology is illustrated with a numerical example. Furthermore, comparison analysis of the proposed methodology is conducted to show its advantages over matrix games with fuzzy goals.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jiang-Xia Nan
AU  - Deng-Feng Li
PY  - 2013
DA  - 2013/01/02
TI  - Linear programming approach to matrix games with intuitionistic fuzzy goals
JO  - International Journal of Computational Intelligence Systems
SP  - 186
EP  - 197
VL  - 6
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.1080/18756891.2013.761781
DO  - 10.1080/18756891.2013.761781
ID  - Nan2013
ER  -