Simple games in Łukasiewicz calculus and their cores

Petr Cintula; Tomáš Kroupa

Kybernetika (2013)

  • Volume: 49, Issue: 3, page 404-419
  • ISSN: 0023-5954

Abstract

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We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness of core is completely characterized in terms of balanced systems and by the presence of strong veto players.

How to cite

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Cintula, Petr, and Kroupa, Tomáš. "Simple games in Łukasiewicz calculus and their cores." Kybernetika 49.3 (2013): 404-419. <http://eudml.org/doc/260726>.

@article{Cintula2013,
abstract = {We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness of core is completely characterized in terms of balanced systems and by the presence of strong veto players.},
author = {Cintula, Petr, Kroupa, Tomáš},
journal = {Kybernetika},
keywords = {simple game; game with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic; simple games; games with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic},
language = {eng},
number = {3},
pages = {404-419},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Simple games in Łukasiewicz calculus and their cores},
url = {http://eudml.org/doc/260726},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Cintula, Petr
AU - Kroupa, Tomáš
TI - Simple games in Łukasiewicz calculus and their cores
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 3
SP - 404
EP - 419
AB - We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness of core is completely characterized in terms of balanced systems and by the presence of strong veto players.
LA - eng
KW - simple game; game with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic; simple games; games with fuzzy coalitions; core; McNaughton function; Łukasiewicz logic
UR - http://eudml.org/doc/260726
ER -

References

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