Research output: Contribution to journal › Article › peer-review
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 journal › Article › peer-review
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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