An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game

Standard

An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game. / Vasil′ev, V. A.

в: Automation and Remote Control, Том 80, № 6, 01.06.2019, стр. 1148-1163.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{48a0b546aaba430fa3f228dd7c817e78,

title = "An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game",

abstract = "This paper deals with a generalization of the famous Bondareva-Shapley theorem [1, 9] on the core of TU cooperative games to the case of fuzzy blocking. The suggested approach is based on the concept of a balanced collection of fuzzy coalitions. Introduced by the author, this extension of the classical balanced collection of standard coalitions yields a natural analog of balancedness for the so-called fuzzy TU cooperative games. As established below, the general balancedness is a necessary and sufficient condition for the non-emptiness of the core of fuzzy TU cooperative games. The non-emptiness criterion of the core is further refined using the classical Helly's theorem on the intersection of convex sets. The S*-representation of a fuzzy game is studied, which simplifies the existence conditions for non-blocking imputations of this game in a series of cases.",

keywords = "balanced family of fuzzy coalitions, fuzzy cooperative game, the core of a fuzzy game, V -balancedness",

author = "Vasil′ev, {V. A.}",

year = "2019",

month = jun,

day = "1",

doi = "10.1134/S0005117919060122",

language = "English",

volume = "80",

pages = "1148--1163",

journal = "Automation and Remote Control",

issn = "0005-1179",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "6",

}

RIS

TY - JOUR

T1 - An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game

AU - Vasil′ev, V. A.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - This paper deals with a generalization of the famous Bondareva-Shapley theorem [1, 9] on the core of TU cooperative games to the case of fuzzy blocking. The suggested approach is based on the concept of a balanced collection of fuzzy coalitions. Introduced by the author, this extension of the classical balanced collection of standard coalitions yields a natural analog of balancedness for the so-called fuzzy TU cooperative games. As established below, the general balancedness is a necessary and sufficient condition for the non-emptiness of the core of fuzzy TU cooperative games. The non-emptiness criterion of the core is further refined using the classical Helly's theorem on the intersection of convex sets. The S*-representation of a fuzzy game is studied, which simplifies the existence conditions for non-blocking imputations of this game in a series of cases.

AB - This paper deals with a generalization of the famous Bondareva-Shapley theorem [1, 9] on the core of TU cooperative games to the case of fuzzy blocking. The suggested approach is based on the concept of a balanced collection of fuzzy coalitions. Introduced by the author, this extension of the classical balanced collection of standard coalitions yields a natural analog of balancedness for the so-called fuzzy TU cooperative games. As established below, the general balancedness is a necessary and sufficient condition for the non-emptiness of the core of fuzzy TU cooperative games. The non-emptiness criterion of the core is further refined using the classical Helly's theorem on the intersection of convex sets. The S*-representation of a fuzzy game is studied, which simplifies the existence conditions for non-blocking imputations of this game in a series of cases.

KW - balanced family of fuzzy coalitions

KW - fuzzy cooperative game

KW - the core of a fuzzy game

KW - V -balancedness

UR - http://www.scopus.com/inward/record.url?scp=85067059104&partnerID=8YFLogxK

U2 - 10.1134/S0005117919060122

DO - 10.1134/S0005117919060122

M3 - Article

AN - SCOPUS:85067059104

VL - 80

SP - 1148

EP - 1163

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 6

ER -

ID: 20590748