The Symmetric Banzhaf Value for Fuzzy Games with a Coalition Structure

In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.

Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

The Well-Posedness for Generalized Fuzzy Games

This paper establishes the stable results for generalized fuzzy games by using a nonlinear scalarization technique. The authors introduce some concepts of well-posedness for generalized fuzzy games. Moreover, the authors identify a class of generalized fuzzy games such that every element of the collection is generalized well-posed, and there exists a dense residual subset of the collection, where every generalized fuzzy game is robust well-posed.

Bi-matrix Games with Fuzzy Strategies and Fuzzy Payoffs and Their Mathematical Programming Equivalents

A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

Profit Allocation Scheme among Partners in Virtual Enterprises Based on Fuzzy Shapley Values

Fuzzy Shapley values are developed based on classical Shapley values and used to allocate profit among partners in virtual enterprises （VE）. Axioms of the classical Shapley value are extended to Shapley values with fuzzy payoffs by using fuzzy sets theory. Fuzzy Shapley function is defined based on these extended axioms. From the viewpoint the allocation for each partner should be a crisp value rather a fuzzy membership function at the end of cooperation, a crisp allocation scheme based on fuzzy Shapley values is proposed.

Application of fuzzy optimization model in the evaluationof urban flood-waterloggedvulnerabilitybased on the synthetic weight ofgame theory

The evaluation of urban flood-waterlogged vulnerability is very important to the safety of urban flood control. In this paper, the evaluation of consolidated index is used. Respectively, AHP and entropy method calculate the subjective and objective weight of the evaluation indicators, and combine them by game theory. So we can obtain synthetic weight based on objective and subjective weights. The evaluation of urban flood-waterlogged vulnerability as target layer, a single variable multi-objective fuzzy optimization model is established. We use the model to evaluate flood-waterlogged vulnerability of 13 prefecture-level city in Hunan, and compare it with other evaluation method. The results show that the evaluation method has certain adaptability and reliability, and it＇ s helpfid to the construction planning of urban flood control.

Dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network

Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. The algorithm uses the minimum cost spanning tree strategy and fuzzy game theory. First, it virtualizes two planes to calculate the multicast tree and the multicast protection tree respectively. Then, it performs a fuzzy game to form a cooperative alliance to optimize the path composition of each multicast tree. Finally, it generates a pair of optimal multicast work tree and multicast protection tree for dynamic multicast services. The time complexity of the algorithm is O(k3 m2 n), where n represents the number of nodes in the networks, k represents the number of dynamic multicast requests, and m represents the number of destination nodes for each multicast request. The experimental results show that the proposed algorithm reduces significantly the blocking rate of dynamic multicast services, and improves the utilization of optical network resources within a certain number of dynamic multicast request ranges.