Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

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

Authors
Stephanie Loi Briao, Graçaliz Pereira Dimuro, Catia Maria Dos Santos Machado
Corresponding Author
Stephanie Loi Briao
Available Online June 2015.
DOI
https://doi.org/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 ”.
Open Access
This is an open access article distributed under the CC BY-NC license.

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Cite this article

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  - 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15)
PB  - Atlantis Press
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.45
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.45
ID  - LoiBriao2015/06
ER  -