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Conference Paper (international conference)

On irreducible min-balanced set systems

Studený Milan, Kratochvíl Václav, Vomlel Jiří

: Symbolic and Quantitative Approaches to Reasoning with Uncertainty : 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019, p. 444-454 , Eds: Kern-Isberner G., Ognjanovic Z.

: European Conference on Symbolic and Quantitative Approaches with Uncertainty (ECSQARU 2019) /15./, (Belgrade, RS, 20190918)

: GA19-04579S, GA ČR

: balanced set system, irreducible min-balanced system, totally balanced games, exact games

: 10.1007/978-3-030-29765-7_37

: http://library.utia.cas.cz/separaty/2019/MTR/studeny-0508311.pdf

(eng): Non-trivial minimal balanced systems (= collections) of sets are known to characterize through their induced linear inequalities the class of the so-called balanced (coalitional) games. In a recent paper a concept of an irreducible min-balanced (= minimal balanced) system of sets has been introduced and the irreducible systems have been shown to characterize through their induced inequalities the class of totally balanced games. In this paper we recall the relevant concepts and results, relate them to various contexts and offer a catalogue of permutational types of non-trivial min-balanced systems in which the irreducible systems are indicated. The present catalogue involves all types of such systems on sets with at most 5 elements. It has been obtained as a result of an alternative characterization of min-balanced systems.

: BA

: 10101