Soft Sets with Atoms

Andrei Alexandru and Gabriel Ciobanu
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Andrei Alexandru: Institute of Computer Science, Romanian Academy, 700505 Iaşi, Romania
Gabriel Ciobanu: Faculty of Computer Science, Alexandru Ioan Cuza University, 700506 Iaşi, Romania

Mathematics, 2022, vol. 10, issue 12, 1-14

Abstract: The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal structure (atoms) and by equipping classical sets with group actions of the permutation group over these basic elements. On the other hand, soft sets represent a generalization of the fuzzy sets to deal with uncertainty in a parametric manner. In this paper, we study the soft sets in the new framework of finitely supported structures, associating to any crisp set a family of atoms describing it. We prove some finiteness properties for infinite soft sets, some order properties and Tarski-like fixed point results for mappings between soft sets with atoms.

Keywords: finitely supported sets; finitely supported complete lattices; soft sets; un-finite sets; fixed points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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