Abstract
A quadratic programming model is constructed for solving the fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers, which will be abbreviated to TFN-typed cooperative games from now on. Based on the concept of α-cut set and the representation theorem for the fuzzy set, the least square distance solution for solving TFN-typed cooperative games is proposed. The least square distance solution successfully avoids the subtraction operation of TFNs, which may inevitably lead to the amplification of uncertainty and the distortion of decision information. A calculating example related to the profit distribution of logistics coalition is illustrated to show the advantages, validity, and applicability of the proposed method. Besides, the least square distance solution for solving TFN-typed cooperative games satisfies many important properties of cooperative games, such as uniqueness, additivity, symmetry, and uniqueness.
Highlights
There exist many problems and phenomena related to fuzzy cooperative games in our daily lives
Based on the comparative analysis of the calculated results, conclusions can be drawn as follows: (1) Through observing carefully the derivation process of the least square distance solution proposed in this paper, we can see that the least square distance solution proposed in this paper satisfies many important properties of cooperative games, such as uniqueness, additivity, symmetry, and uniqueness
(2) The least square distance solution proposed in this paper successfully avoids the subtraction operation of TFNs, which may inevitably lead to the amplification of uncertainty and the distortion of decision information
Summary
There exist many problems and phenomena related to fuzzy cooperative games in our daily lives. An increasing number of researchers turn their attention to the theory and application of fuzzy cooperative games. Many existing models and methods for solving fuzzy cooperative games inevitably use the subtraction operation of fuzzy numbers. We are absorbed in developing a new and intuitionistic method for the TFN-typed cooperative games, which can successfully avoid the subtraction operation of TFNs. The rest of the paper is arranged as follows.
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