基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法

研究模糊联盟合作对策tau值的计算方法及其性质. 利用多维线性扩展方法定义了模糊联盟合作对策的tau值, 证明了其存在性、唯一性等性质, 并推导出基于多维线性扩展凸模糊联盟合作对策tau值的计算公式. 研究结果发现, 基于多维线性扩展的模糊联盟合作对策tau值是对清晰联盟合作对策tau值的扩展, 而清晰联盟合作对策tau值仅是其特例. 特别地, 对于凸模糊联盟合作对策, 利用其tau值计算公式, 可进一步简化求解过程.

Properties and solving method of tau-value for fuzzy cooperative games with multilinear extension form

In this paper, we research the solving method and properties of tau-value for fuzzy cooperative games. Using the multilinear extensive method, we define thetau-value for fuzzy cooperative games, prove its existence, uniqueness and other properties, and deduce the computational formulae of the tau-value for convex fuzzy cooperative games. The research result shows that the tau-value for the fuzzy cooperative games with multilinear extension form is an extension of the tau-value for crisp cooperative games. Especially, for the convex fuzzy cooperative games, the computational process of the tau-value can be simplified.