Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups

Osman Kazancı, Sarka Hoskova-Mayerova and Bijan Davvaz
Additional contact information
Osman Kazancı: Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Türkiye
Sarka Hoskova-Mayerova: Department of Mathematics and Physics, University of Defence, Kounicova 65, 662 10 Brno, Czech Republic
Bijan Davvaz: Department of Mathematics, Yazd University, Yazd 89136, Iran

Mathematics, 2022, vol. 10, issue 13, 1-16

Abstract: The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. If we substitute the set of all fuzzy subsets of the universal set instead of crisp subsets, then we obtain fuzzy soft sets. Similarly, multi-fuzzy soft sets can be obtained. In this paper, we combine the multi-fuzzy soft set and polygroup structure, from which we obtain a new soft structure called the multi-fuzzy soft polygroup. We analyze the relation between multi-fuzzy soft sets and polygroups. Some algebraic properties of fuzzy soft polygroups and soft polygroups are extended to multi-fuzzy soft polygroups. Some new operations on a multi-fuzzy soft set are defined. In addition to this, we investigate normal multi-fuzzy soft polygroups and present some of their algebraic properties.

Keywords: multi-fuzzy soft set; multi-fuzzy soft polygroup; normal multi-fuzzy soft polygroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/13/2178/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/13/2178/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:13:p:2178-:d:845213

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().