Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game

Hinojosa, Miguel A.; Mármol, Amparo M.; Fernández, Francisco R.

doi:10.1016/j.ejor.2012.08.024

Cited by 21 publications

(12 citation statements)

References 16 publications

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“…As for the three types of fuzzy cooperative games mentioned above, the cooperative games with fuzzy coalition values gradually become a research hotspot in recent years. Some researchers extend the common solutions of crisp cooperative games to fuzzy cooperative games and propose some corresponding solution methods and solution concepts for solving fuzzy cooperative games, such as fuzzy Shapley value [9][10][11], fuzzy set-valued solution [12], fuzzy least square prenucleolus and B-nucleolus [13][14][15], fuzzy bargaining sets [16,17], and fuzzy equalizer and lexicographical solution [18].…”

Section: Introductionmentioning

confidence: 99%

Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

Liu

Zhu

Zhao

2019

Mathematical Problems in Engineering

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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.

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Section: Introductionmentioning

confidence: 99%

Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

Liu

Zhu

Zhao

2019

Mathematical Problems in Engineering

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“…Recently, researchers started studying fuzzy cooperative and matrix games whose payoffs contain various kinds of fuzzy information. Monroy et al [17] proposed a new model to solve the problem of cooperative fuzzy games and applied them to many real fields. Furthermore, the dominance core and preference core were established, and some characterizations were provided.…”

Section: Introductionmentioning

confidence: 99%

Triangular Fuzzy Number-Typed Fuzzy Cooperative Games and Their Application to Rural E-Commerce Regional Cooperation and Profit Sharing

Zhao

Liu

2018

Symmetry

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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.

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“…In the literature, one may find a large amount of research on fuzzy games, as discussed by Dang and Hong,13 where two main lines of research on fuzzy games were identified, namely, matrix fuzzy games and noncooperative fuzzy games, the majority focused on fuzzy zero-sum games, 14 which are strictly competitive. Some interesting contributions for the research on fuzzy cooperative games are due to, e.g., (i) Yu and Zhang, 21 who extended the notion of fuzzy cooperative fuzzy games to obtain a more general definition, (ii) Monroy et al, 22 with a study of cooperative games with fuzzy payoffs, and, more recently, (iii) Sagara, 23 who investigated fuzzy extensions of cooperative games and the coincidence of the solutions for fuzzy and crisp games, and (iv) Borkotokey et al, 24 who proposed a bicooperative game with fuzzy bicoalitions in multilinear extension form. 18 On the other hand, cooperative game theory is concerned with the situation where the agents have only two alternative possibilities, namely, to join or not a coalition, without any option for the degree of commitment.…”

Section: Introductionmentioning

confidence: 99%

“…Cooperative fuzzy games 19,20 allow for the partial participation of agents in coalitions, where the attainable outcomes of a game depend on the degree of commitment of the agents, so modeling ambiguous decision making as observed in most group behaviors. Some interesting contributions for the research on fuzzy cooperative games are due to, e.g., (i) Yu and Zhang, 21 who extended the notion of fuzzy cooperative fuzzy games to obtain a more general definition, (ii) Monroy et al, 22 with a study of cooperative games with fuzzy payoffs, and, more recently, (iii) Sagara, 23 who investigated fuzzy extensions of cooperative games and the coincidence of the solutions for fuzzy and crisp games, and (iv) Borkotokey et al, 24 who proposed a bicooperative game with fuzzy bicoalitions in multilinear extension form.…”

Section: Introductionmentioning

confidence: 99%

On Two-Player Interval-Valued Fuzzy Bayesian Games

Asmus

Dimuro

Bedregal

2016

Int. J. Intell. Syst.

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Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval‐based fuzzy Bayesian games, based on interval‐valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not.

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Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game

Cited by 21 publications

References 16 publications

Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

Triangular Fuzzy Number-Typed Fuzzy Cooperative Games and Their Application to Rural E-Commerce Regional Cooperation and Profit Sharing

On Two-Player Interval-Valued Fuzzy Bayesian Games

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