0508311 20240103222526.720190912235959.9 85072862282 10.1007/978-3-030-29765-7_37 11 s. P cav_un_epca*0508310978-3-030-29764-0444-454ChamSpringer Intenational Publishing2019Kern-IsbernerG.OgnjanovicZ. balanced set system irreducible min-balanced system totally balanced games exact games cav_un_auth*0101202 Department of Decision Making Theory Studený Milan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Department of Decision Making Theory Kratochvíl Václav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101228 Department of Decision Making Theory Vomlel Jiří UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2019/MTR/studeny-0508311.pdf cav_un_auth*0380558 GA19-04579S GA ČR CZ 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. cav_un_auth*0379619 European Conference on Symbolic and Quantitative Approaches with Uncertainty (ECSQARU 2019) /15./ 20190918 20190920 Belgrade RS BA 10000 10100 10101 2020 3 PR RVO:67985556 http://hdl.handle.net/11104/0299782 S 2019 85072862282 SCOPUS PUBMED WOS cav_un_epca*0508310 Symbolic and Quantitative Approaches to Reasoning with Uncertainty : 15th European Conference, ECSQARU 2019, Belgrade, Serbia, September 18-20, 2019 Springer Intenational Publishing 2019 Cham 444 454 978-3-030-29764-0 Lecture Notes in Artificial Intelligence 11726 340 Kern-Isberner G. 340 Ognjanovic Z.