Discrete mathematics and mathematical cybernetics

Parametric closed sets of multioperations on two-element set

V. I. Panteleev^a, L. V. Ryabets<sup>b

a</sup> Dorzhi Banzarov Buryat State University, 24a, Smolina str., 670000, Ulan-Ude, Russia
^b Institute of Mathematics and Information Technologies, Irkutsk State University, K. Marx st, 1, 664000, Irkutsk, Russia

Abstract: In this paper the problem of classifying a set of multioperations of rank $2$ with respect to the parametric closure operator is considered. A completeness criterion was found and it was shown that the set of all multioperations contains two parametrically closed classes.

Keywords: multifunction, multioperation, parametric closure, superposition, completeness criterion, $k$-valued logic.

UDC: 519.716

MSC: 03B50, 08A99

Received July 3, 2024, published December 11, 2024

DOI: 10.33048/semi.2024.21.083