The primary aim of this paper is to develop one kind of easy and effective method to solve fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers (TFNs). This method ensures that each player should receive a TFN-typed fuzzy pay-off from the grand coalition because each coalition value is expressed by a TFN. Using the concept of Alpha-cut sets, an arbitrary TFN’s Alpha-cut set can be shown as an interval. If the 1-cut sets and 0-cut sets of the TFN-typed coalition values are known, we can easily gain some important values, such as the means, the lower limits, and the upper limits of the TFN-typed payoffs via the proposed quadratic programming models and method. Furthermore, it is also easy for us to compute the lower and upper limits of Alpha-cut sets at any confidence levels of the TFN-typed payoffs for any TFN-typed cooperative game through solving the constructed quadratic programming models. Hereby the players’ TFN-typed payoffs for the TFN-typed cooperative game can be explicitly solved via the representation theorem for fuzzy sets. It is easy to prove that the proposed solutions of the fuzzy cooperative games with coalition values expressed by TFNs satisfy some useful and important properties, such as symmetry, additivity, and anonymity. Finally, the validity, applicability and advantages of the proposed method is proved and discussed through a numerical example.

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

This paper is mainly committed to constructing a new model for solving interval-valued fuzzy cooperative games based on the least square excess. We propose the interval-valued least square excess solution according to the solution concept of the least square prenucleolus and the least square nucleolus for solving crisp cooperative games. In order to obtain the corresponding optimal analytical solution, one mathematic programming model is constructed. The least square excess solution can be used to determine plays’ payoffs directly. Considering the fuzziness and uncertainty existing in the process of the road freight coalition, we establish the interval-valued fuzzy utility function of the road freight coalition that can properly reflect the real situation in view of the green logistics. The illustratively calculated results show that the least square excess solution proposed in this paper is effectual and ascendant, and satisfied many important and useful properties of cooperative games, such as symmetry and uniqueness. As for the problems of interval-valued cooperative games, the model proposed in this paper can be applied appropriately to obtain the players’ interval-valued payoffs.

No abstract

Animal models played an important role in osteoarthritis studies. Here, the complete mitochondrial genome sequence of the Guinea pig was reported for the first time. The total length of the mitogenome was 16,797 bp. It contained the typical structure, including two ribosomal RNA genes, 13 protein-coding genes, 22 transfer RNA genes and one non-coding control region (D-loop region). The overall composition of the mitogenome was estimated to be 34.9% for A, 26.1% for T, 26.0% for C and 13.0% for G showing an A-T (61.0%)-rich feature. This mitochondrial genome sequence will provide new genetic resource into osteoarthritis disease.