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Unblocked Imputations of Fuzzy Games. I : Existence. / Vasil’ev, V. A.

In: Journal of Mathematical Sciences (United States), Vol. 246, No. 6, 01.05.2020, p. 828-845.

Research output: Contribution to journalArticlepeer-review

Harvard

Vasil’ev, VA 2020, 'Unblocked Imputations of Fuzzy Games. I: Existence', Journal of Mathematical Sciences (United States), vol. 246, no. 6, pp. 828-845. https://doi.org/10.1007/s10958-020-04785-2

APA

Vasil’ev, V. A. (2020). Unblocked Imputations of Fuzzy Games. I: Existence. Journal of Mathematical Sciences (United States), 246(6), 828-845. https://doi.org/10.1007/s10958-020-04785-2

Vancouver

Vasil’ev VA. Unblocked Imputations of Fuzzy Games. I: Existence. Journal of Mathematical Sciences (United States). 2020 May 1;246(6):828-845. doi: 10.1007/s10958-020-04785-2

Author

Vasil’ev, V. A. / Unblocked Imputations of Fuzzy Games. I : Existence. In: Journal of Mathematical Sciences (United States). 2020 ; Vol. 246, No. 6. pp. 828-845.

BibTeX

@article{71496661ce074e9e92153333e81485b5,
title = "Unblocked Imputations of Fuzzy Games. I: Existence",
abstract = "We generalize the well-known Scarf theorem on the nonemptiness of the core to the case of generalized fuzzy cooperative games without side payments provided that the set of blocking coalitions is extended by the so-called fuzzy coalitions. The notion of a balanced family is extended to the case of an arbitrary set of fuzzy blocking coalitions, owing to which it is possible to introduce a natural analogue of balancedness of a fuzzy game for the characteristic function with an arbitrary efficiency domain. Based on an appropriate approximation of a fuzzy game by finitely-generated games, together with the seminal combinatorial Scarf lemma on ordinal and admissible bases, we obtain rather general conditions of the existence of unblocked imputations for F-balanced fuzzy cooperative games. Bibliography: 15 titles.",
author = "Vasil{\textquoteright}ev, {V. A.}",
year = "2020",
month = may,
day = "1",
doi = "10.1007/s10958-020-04785-2",
language = "English",
volume = "246",
pages = "828--845",
journal = "Journal of Mathematical Sciences (United States)",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - Unblocked Imputations of Fuzzy Games. I

T2 - Existence

AU - Vasil’ev, V. A.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - We generalize the well-known Scarf theorem on the nonemptiness of the core to the case of generalized fuzzy cooperative games without side payments provided that the set of blocking coalitions is extended by the so-called fuzzy coalitions. The notion of a balanced family is extended to the case of an arbitrary set of fuzzy blocking coalitions, owing to which it is possible to introduce a natural analogue of balancedness of a fuzzy game for the characteristic function with an arbitrary efficiency domain. Based on an appropriate approximation of a fuzzy game by finitely-generated games, together with the seminal combinatorial Scarf lemma on ordinal and admissible bases, we obtain rather general conditions of the existence of unblocked imputations for F-balanced fuzzy cooperative games. Bibliography: 15 titles.

AB - We generalize the well-known Scarf theorem on the nonemptiness of the core to the case of generalized fuzzy cooperative games without side payments provided that the set of blocking coalitions is extended by the so-called fuzzy coalitions. The notion of a balanced family is extended to the case of an arbitrary set of fuzzy blocking coalitions, owing to which it is possible to introduce a natural analogue of balancedness of a fuzzy game for the characteristic function with an arbitrary efficiency domain. Based on an appropriate approximation of a fuzzy game by finitely-generated games, together with the seminal combinatorial Scarf lemma on ordinal and admissible bases, we obtain rather general conditions of the existence of unblocked imputations for F-balanced fuzzy cooperative games. Bibliography: 15 titles.

UR - http://www.scopus.com/inward/record.url?scp=85084201013&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04785-2

DO - 10.1007/s10958-020-04785-2

M3 - Article

AN - SCOPUS:85084201013

VL - 246

SP - 828

EP - 845

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 6

ER -

ID: 24231906