Shapley mappings and the cumulative value for n-person games with fuzzy coalitions

In recent years, uneven distribution of available water resources as well as increasing water demands and overexploiting the water resources have brought severe need for transferring water from basins having sufficient water to basins facing water shortages. Therefore, optimal allocation of shared water resources in water transfer projects, considering the utilities of different stakeholders, physical limitations of the system and socioeconomic criteria is an important task. In this paper, a new methodology based on crisp and fuzzy Shapley games is developed for optimal allocation of inter-basin water resources. In the proposed methodology, initial water allocations are obtained using an optimization model considering an equity criterion. In the second step, the stakeholders form crisp coalitions to increase the total net benefit of the system as well as their own benefits and a crisp Shapley Value game is used to reallocate the benefits produced in the crisp coalitions. Lastly, to provide maximum total net benefit, fuzzy coalitions are constituted and the participation rates of water users to fuzzy coalitions are optimized. Then, the total net benefit is reallocated to water users in a rational and equitable way using Fuzzy Shapley Value game. The effectiveness of this method is examined by applying it to a large scale case study of water transfer from the Karoon river basin in southern Iran to the Rafsanjan plain in central Iran.

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“…The game ν is named a fuzzy game with weight function ψ, if it has the following property (Butnariu and Kroupa 2008):…”

Section: Definitionmentioning

confidence: 99%

Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games

Sadegh

Mahjouri

Kerachian

2009

Water Resour Manage

125

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“…After that, many researchers studied fuzzy games deeply. For example, the Shapley function for fuzzy games was researched in Butnariu (1980), Butnariu and Kroupa (2008), Li and Zhang (2009), Meng and Zhang (2010), Tsurumi et al (2001), Yu and Zhang (2010). It is worth noting that Li and Zhang (2009) introduced a simple expression of the Shapley value for fuzzy games, which can be applied to all kinds of fuzzy games with crisp characteristic functions.…”

Section: Introductionmentioning

confidence: 99%

Cooperative fuzzy games with interval characteristic functions

2015

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In this paper, a generalized form of fuzzy games with interval characteristic functions is proposed, which can be seen as an extension of games with crisp characteristic functions. Based on the extended Hukuhara difference, the interval Shapley function for interval fuzzy games is studied. Then, the concept of interval population monotonic allocation function (IPMAF) is defined. When interval fuzzy games are convex, we prove that the interval Shapley function is an IPMAF. Furthermore, two special types of interval fuzzy games are researched, and the associated interval Shapley function is studied.

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“…The Shapley function is discussed on the limited class of fuzzy games. Recently, Butnariu and Kroupa (2008) defined fuzzy games with weighted function, and the corresponding Shapley function is given. The Shapley function for fuzzy games is studied by Butnariu (1980), Tsurumi et al (2001), Butnariu and Kroupa (2008), Li and Zhang (2009), Meng and Zhang (2010).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Butnariu and Kroupa (2008) defined fuzzy games with weighted function, and the corresponding Shapley function is given. The Shapley function for fuzzy games is studied by Butnariu (1980), Tsurumi et al (2001), Butnariu and Kroupa (2008), Li and Zhang (2009), Meng and Zhang (2010). The fuzzy core of fuzzy games is focused on by Branzei et al (2003), Tijs et al (2004), Butnariu and Kroupa (2009), Yu and Zhang (2009).…”

Section: Introductionmentioning

confidence: 99%

The fuzzy core and Shapley function for dynamic fuzzy games on matroids

Meng

Zhang

2011

Fuzzy Optim Decis Making

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In this paper, the generalized forms of the fuzzy core and the Shapley function for dynamic fuzzy games on matroids are given. An equivalent form of the fuzzy core is researched. In order to better understand the fuzzy core and the Shapley function for dynamic fuzzy games on matroids, we pay more attention to study three kinds of dynamic fuzzy games on matroids, which are named as fuzzy games with multilinear extension form, with proportional value and with Choquet integral form, respectively. Meantime, the relationship between the fuzzy core and the Shapley function for dynamic fuzzy games on matroids is researched, which coincides with the crisp case.

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Shapley mappings and the cumulative value for n-person games with fuzzy coalitions

Cited by 72 publications

References 9 publications

Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games

Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games

Cooperative fuzzy games with interval characteristic functions

The fuzzy core and Shapley function for dynamic fuzzy games on matroids

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