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Soft Sets with Atoms

Author

Listed:
  • Andrei Alexandru

    (Institute of Computer Science, Romanian Academy, 700505 Iaşi, Romania)

  • Gabriel Ciobanu

    (Faculty of Computer Science, Alexandru Ioan Cuza University, 700506 Iaşi, Romania)

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.

Suggested Citation

  • Andrei Alexandru & Gabriel Ciobanu, 2022. "Soft Sets with Atoms," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1956-:d:833022
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