Interval Fuzzy Linear Programming Models to Solve Interval-valued Fuzzy Zero-Sum Games

DOI

10.2991/ifsa-eusflat-15.2015.45How to use a DOI?

Keywords

Interval fuzzy numbers, ranking interval fuzzy numbers, interval fuzzy zero-sum games, interval fuzzy linear programming.

Abstract

In Game theory, there are situations in which it is very difficult to characterize the private information of each player. In this case, the payoffs can be given by approximate values, represented by fuzzy numbers. Whenever there is uncertainty in the modeling of those fuzzy numbers, interval fuzzy numbers may be used. This paper introduces two approaches for the solution of interval-valued fuzzy zero-sum games. First, we extend the Campos-Verdegay model, which uses triangular fuzzy numbers for the modeling of uncertain payoffs, to consider interval-valued fuzzy payoffs. Then, defining a ranking method for interval fuzzy numbers that induces a total order, we generalize the intervalvalued Campos-Verdegay model to consider payoffs modeled as any type of interval fuzzy numbers. In both models, we establish an Interval Fuzzy Linear Programming problem for each player, which are reduced to classical Linear Programming problems, used in the solution of classical zero-sum games. We show that the solutions are of the same nature of the parameters defining the game, corresponding to an uncertain predicate of type: “the value of the game is in the interval ”.

Copyright

© 2015, 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  - CONF
AU  - Stephanie Loi Briao
AU  - Graçaliz Pereira Dimuro
AU  - Catia Maria Dos Santos Machado
PY  - 2015/06
DA  - 2015/06
TI  - Interval Fuzzy Linear Programming Models to Solve Interval-valued Fuzzy Zero-Sum Games
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 305
EP  - 312
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.45
DO  - 10.2991/ifsa-eusflat-15.2015.45
ID  - LoiBriao2015/06
ER  -