An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game Full article
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Automation and Remote Control
ISSN: 0005-1179 , E-ISSN: 1608-3032 |
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| Output data | Year: 2019, Volume: 80, Number: 6, Pages: 1148-1163 Pages count : 16 DOI: 10.1134/S0005117919060122 | ||||
| Tags | balanced family of fuzzy coalitions; fuzzy cooperative game; the core of a fuzzy game; V -balancedness | ||||
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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. © 2019, Pleiades Publishing, Ltd.
Cite:
Vasil′ev V.A.
An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game
Automation and Remote Control. 2019. V.80. N6. P.1148-1163. DOI: 10.1134/S0005117919060122 WOS Scopus OpenAlex
An Analog of the Bondareva-Shapley Theorem I. The Non-Emptiness of the Core of a Fuzzy Game
Automation and Remote Control. 2019. V.80. N6. P.1148-1163. DOI: 10.1134/S0005117919060122 WOS Scopus OpenAlex
Original:
Васильев В.А.
Аналог теоремы Бондаревой – Шепли I. Непустота ядра нечеткой игры
Математическая теория игр и ее приложения. 2017. Т.9. №1. С.3-26. РИНЦ
Аналог теоремы Бондаревой – Шепли I. Непустота ядра нечеткой игры
Математическая теория игр и ее приложения. 2017. Т.9. №1. С.3-26. РИНЦ
Identifiers:
| Web of science: | WOS:000470979400012 |
| Scopus: | 2-s2.0-85067059104 |
| OpenAlex: | W2950148791 |