Interval Fuzzy Linear Programming Models to Solve Interval-valued Fuzzy Zero-Sum Games
Stephanie Loi Briao, Graçaliz Pereira Dimuro, Catia Maria Dos Santos Machado
Stephanie Loi Briao
Available Online June 2015.
- https://doi.org/10.2991/ifsa-eusflat-15.2015.45How to use a DOI?
- Interval fuzzy numbers, ranking interval fuzzy numbers, interval fuzzy zero-sum games, interval fuzzy linear programming.
- 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.
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 SP - 305 EP - 312 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 -