On the enumeration of some inequivalent monotone Boolean functions

This paper considers inequivalent monotone Boolean functions of an arbitrary number of variables, two monotone Boolean functions are equivalent if one can be obtained from the other by permuting the variables. It focuses on some inequivalent  monotone Boolean functions with three and four types of e...

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Veröffentlicht in:Optimization Jg. 73; H. 4; S. 1253 - 1266
1. Verfasser: Freixas, Josep
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis LLC
Schlagworte:
Artificial intelligence
Boolean functions
Decision theory
Dedekind numbers
Enumeration
enumeration of Boolean functions
enumeration of tripartite and quadripartite simple games
Equivalence
Game theory
inequivalent monotone Boolean functions
Mathematical analysis
Multiple criterion
Network reliability
Neural networks
simple games
ISSN:0233-1934, 1029-4945
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Beschreibung
Zusammenfassung:This paper considers inequivalent monotone Boolean functions of an arbitrary number of variables, two monotone Boolean functions are equivalent if one can be obtained from the other by permuting the variables. It focuses on some inequivalent  monotone Boolean functions with three and four types of equivalent variables, where the variables are either dominant or dominated. The paper provides closed formulas for their enumeration as a function of the number of variables. The problem we deal with is very versatile since inequivalent monotone Boolean functions are monotonic simple games, structures that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiple-criteria decision-making.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2154126