Interval fuzzy cooperative games with Choquet integral form

2011 ◽  
Author(s):  
Linlin Sun ◽  
Zuofeng Gao
Keyword(s):  
Cooperative Games ◽  
Choquet Integral ◽  
Integral Form

scholarly journals A Simplified Expression of Share Functions for Cooperative Games with Fuzzy Coalitions

2017 ◽  
Vol 69 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Rajib Biswakarma ◽  
Surajit Borkotokey ◽  
Radko Mesiar
Keyword(s):  
Cooperative Games ◽  
Choquet Integral ◽  
Integral Form ◽  
Fuzzy Games ◽  
Proportional Value ◽  
Fuzzy Coalitions ◽  
Special Classes

Abstract In this paper, we discuss the notion of Share functions for cooperative games with fuzzy coalitions or simply fuzzy cooperative games. We obtain the Share functions for some special classes of fuzzy games, namely the fuzzy games in proportional value form and the fuzzy games in Choquet integral form. The Shapley Share and Banzhaf Share functions for these classes are derived.

scholarly journals Solidarity Value and Solidarity Share Functions for TU Fuzzy Games

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Rajib Biswakarma ◽  
Surajit Borkotokey ◽  
Radko Mesiar
Keyword(s):  
Choquet Integral ◽  
Integral Form ◽  
Tu Games ◽  
Suitable Solution ◽  
Multilinear Extension ◽  
Fuzzy Games ◽  
Special Classes

TU games under both crisp and fuzzy environments describe situations where players make full (crisp) or partial (fuzzy) binding agreements and generate worth in return. The challenge is then to decide how to distribute the profit among them in a rational manner: we call this a solution. In this paper, we introduce the notion of solidarity value and the solidarity share function as a suitable solution to TU fuzzy games. Two special classes of TU fuzzy games, namely, TU fuzzy games in Choquet integral form and in multilinear extension form, are studied and the corresponding solidarity value and the solidarity share functions are characterized.

Public resources allocation using an uncertain cooperative game among vulnerable groups

Kybernetes ◽  
2019 ◽  
Vol 48 (8) ◽  
pp. 1606-1625 ◽  
Author(s):  
Pei Liang ◽  
Junhua Hu ◽  
Yongmei Liu ◽  
Xiaohong Chen
Keyword(s):  
Resource Allocation ◽  
Cooperative Game ◽  
Shapley Value ◽  
Choquet Integral ◽  
Convex Combination ◽  
Integral Form ◽  
Vulnerable Groups ◽  
Content Type ◽  
Public Resource ◽  
Public Resources

Purpose This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game. Design/methodology/approach First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game. Findings The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness. Originality/value In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.

CHOQUET EXTENSION OF COOPERATIVE GAMES

2013 ◽  
Vol 30 (04) ◽  
pp. 1350005 ◽  
Author(s):  
CHUNQIAO TAN ◽  
ZHONG-ZHONG JIANG ◽  
XIAOHONG CHEN
Keyword(s):  
Explicit Formula ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Extension Method ◽  
Equivalent Definition ◽  
Multilinear Extension ◽  
Shapley Function ◽  
Definition Of

A multilinear extension of the n-person cooperative game was introduced by Owen in 1972, and a new extension method is proposed in this paper. For n-person cooperative games, any coalition can equivalently be represented by its characteristic vectors. By means of the Choquet integral, a new fuzzy extension, called the Choquet extension, is developed. Furthermore, a Shapley function in this class of fuzzy cooperative games with the Choquet extension form is defined. Axioms of the Shapley function are proposed, and an explicit formula for the Shapley function is given. Finally, an equivalent definition of this Shapley function is discussed.

scholarly journals CAPACITIES AND GAMES ON LATTICES: A SURVEY OF RESULTS

2006 ◽  
Vol 14 (04) ◽  
pp. 371-392 ◽  
Author(s):  
MICHEL GRABISCH
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Characteristic Form ◽  
Möbius Transform ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
Power Set ◽  
Recent Developments

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

ДОСВІД У ДИСКУСІЙНОМУ ПОЛІ ПОЗИЦІЮВАННЯ КАТЕГОРІЇ "ТВОРЧИЙ ПОТЕНЦІАЛ"

1970 ◽  
Vol 6 (1) ◽  
pp. 62-71
Author(s):  
Лариса Міщиха
Keyword(s):  
Coming Out ◽  
Motion Vector ◽  
Integral Form ◽  
Phenomenological Approach ◽  
Humanistic Psychology ◽  
Creative Potential ◽  
Form Of Life ◽  
Conceptual Background ◽  
Creative Experience ◽  
The One

У статті зроблено спробу проаналізувати феномен "досвід" у форматі дослідження творчого потенціалу особистості. Теоретико-методологічними засадами заявленої вище проблеми стали концептуальні засади гуманістичної психології, феноменологічного підходу. Досвід, як вагома складова творчого потенціалу особистості, розглядається у співвідношенні таких провідних тенденцій, як стереотипність та оригінальність. Наголошується, що досвід, з одного боку, може сприяти все більшій алгоритмізації та стереотипізації, консерватизму у розв’язанні нових задач, що безумовно перешкоджає творчості. З іншого боку, в осіб з високим творчим потенціалом він стає інтегрованою формою життєтворчості, де в структурі старих знань завжди знайдеться місце новим знанням як привнесених "ззовні", так і знанням, що їх отримує автор через власні ініціації, пошук, накреслюючи власноруч вектор руху. Звідси він отримує "побічний продукт" творчої діяльності – саморозвиток. Відтак творчий досвід трактується як такий, що містить у собі акумуляцію та інтеграцію усіх прижиттєвих творчих напрацювань особистості, готовність її до творчої діяльності та безперервної освіти. Суб’єкт творчої діяльності залишається відкритим новому досвіду, сповнений готовності до нового пізнання, творчих пошуків. In the article there was an attempt to analyze the phenomenon "experience" in the form of investigating a person’s creative potential. The theoretic methodological background of the performed above problem is conceptual background of humanistic psychology and phenomenological approach. Experience as an essential part of a person’s creative potential is regarded in relation to such leading trends as stereotype and originality. On the one hand, the experience is emphasized to be able to promote the model of algorithm and stereotype, conservatism in solving new tasks that is certain to inhibit creativity. On the other hand, personalities with high creative potential have an experience that is becoming an integral form of life work where in the structure of old knowledge you can always find a place for both new ones coming out "from inside" and the ones the author takes due to his own initiation and search. In this way he sketches motion vector and gets the "by-product" of his creativity, it means self-development. Hence, creative experience is interpreted as the one to absorb accumulation and integration of all creative experience in a person’s life; also his/her readiness to creativity and continuing education. The subject of creativity remains opened to a new experience that is fully ready for a new cognition and creativity.

Share-out in Cooperative Games under Uncertainty

1999 ◽  
Vol 31 (11) ◽  
pp. 10-14
Author(s):  
Vladislav I. Zhukovskiy ◽  
E. N. Opletayeva
Keyword(s):  
Cooperative Games
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