Abstract:
Hyperfunctions are functions that are defined on a finite set and return all non-empty subsets of the considered set as their values. This paper deals with the classification of hyperfunctions on a two-element set. We consider the composition and the closure operator with the equality predicate branching (E-operator). E-closed sets of hyperfunctions are sets that are obtained using the operations of adding dummy variables, identifying variables, composition, and E-operator. It is shown that the considered classification leads to a finite set of closed classes. The paper presents all 78 E-closed classes of hyperfunctions, among which there are 28 pairs of dual classes and 22 self-dual classes. The inclusion diagram of the E-closed classes is constructed, and for each class its generating system is obtained.
Received: 09.11.2019 Received in revised form: 06.01.2020 Accepted: 13.02.2020
Bibliographic databases:
Document Type:
Article
UDC:519.716
Language: English
Citation:
Vladimir I. Panteleyev, Leonid V. Riabets, “E-closed sets of hyperfunctions on two-element set”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 231–241
\Bibitem{PanRya20}
\by Vladimir~I.~Panteleyev, Leonid~V.~Riabets
\paper $E$-closed sets of hyperfunctions on two-element set
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 2
\pages 231--241
\mathnet{http://mi.mathnet.ru/jsfu834}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-2-231-241}
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https://www.mathnet.ru/eng/jsfu834
https://www.mathnet.ru/eng/jsfu/v13/i2/p231
This publication is cited in the following 5 articles:
Sergey Todikov, Yulia Shichkina, Nikolay Peryazev, “Applying the Theory of Multi-Operations to Building Decision-Making Systems with a Large Number of Uncertainties”, Mathematics, 12:23 (2024), 3694
A. S. Zinchenko, B. P. Ilin, V. I. Panteleev, L. V. Ryabets, “Ob odnom mnozhestve $E$-zamknutykh klassov multifunktsii ranga $2$”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 214, VINITI RAN, M., 2022, 30–36
V. I. Panteleev, E. S. Taglasov, “$ES_I $-zamykanie multifunktsii ranga $2$: kriterii polnoty, klassifikatsiya i tipy bazisov”, Intellektualnye sistemy. Teoriya i prilozheniya, 25:2 (2021), 55–80
V. I. Panteleev, E. S. Taglasov, “On the lattice of $ES_i$-closed classes of multifunctions on two-elements set”, Bull. Irkutsk State Univ.-Ser. Math., 38 (2021), 96–111
Panteleev I V., Riabets V L., “Classification of Multioperations of Rank 2 By E-Precomplete Sets”, Bull. Irkutsk State Univ.-Ser. Math., 34 (2020), 93–108
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