Towards Solving Matrix Games with Interval Type-2 Fuzzy Uncertainty through Linear Optimization

Hacia la solución de juegos matriciales con incertidumbre difusa Tipo-2 a través de optimización lineal

  • Juan Carlos Figueroa García Universidad Nacional de Colombia
  • Germán Hernández Universidad Nacional de Colombia
  • Carlos Franco Universidad Distrital Francisco José de Caldas
Keywords: Fuzzy linear programming, Type-2 fuzzy sets, Games theory (en_US)
Keywords: programación Lineal Difusa, Conjuntos difusos Tipo-2, Teoría de juegos (es_ES)

Abstract (en_US)

This paper presents some theoretical and computing considerations about how to deal with fuzzy uncertainty in the parameters of the classical games model. Indeed, when multiple experts are involved in a game situation, then their opinions lead to have uncertainty since most of the times they are not agree to each others. This kind of uncertainty can be modeled using Type-2 fuzzy sets, which implies a specialized methods and sub-models.

Some considerations about the use of Type-2 fuzzy sets and what does this imply when computing solutions, are presented. A general model which includes this kind of uncertainty is defi ned on the base of the extension principle and α-cuts representation theorem. A possible way for solving this model is glimpsed and put down for discussion and implementation.

Abstract (es_ES)

Este artículo presenta algunas consideraciones computacionales y teóricas acerca de cómo incluír incertidumbre difusa en los parámetros de un problema clásico de juegos. De hecho, cuando varios expertos están involucrados en un problema de juegos, todas sus opiniones llevan a pensar en una fuente incertidumbre, ya que muchas veces esos expertos no están de acuerdo entre sí. Ese tipo de incertidumbre puede modelarse mediante conjuntos difusos Tipo-2, lo que implica usar modelos y métodos especiales para llegar a una respuesta adecuada.

Se presentan algunos aspectos importantes acerca del cálculo de soluciones en presencia de este tipo de incertidumbre. Un modelo general que incluye incertidumbre difusa Tipo-2 es presentado, el cual se basa en el principio de extensión y el teorema de representación de α-cortes. Un posible método de solución es puesto a consideración para discusión e implementación.

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How to Cite
Figueroa García, J. C., Hernández, G., & Franco, C. (2013). Towards Solving Matrix Games with Interval Type-2 Fuzzy Uncertainty through Linear Optimization. Ingeniería, 18(2). https://doi.org/10.14483/udistrital.jour.reving.2013.2.a06
Published: 2013-11-06
Section
Sección Especial: Mejores Trabajos “VI Simposio en Optimización”