Generalized Fuzzy Rough Approximations on Hypergroups

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Akın C., Delice D. B., YAMAK S.

Mathematics, vol.12, no.16, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 16
  • Publication Date: 2024
  • Doi Number: 10.3390/math12162445
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: canonical hypergroup, fuzzy rough approximation, fuzzy set-valued homomorphism
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we define the fuzzy set-valued homomorphisms of the canonical hypergroups as a generalization of fuzzy congruences and investigate some of their features. This structure is an extension of the definition of set-valued homomorphism defined for groups to hypergroups. With this extension, it has become possible to study generalized fuzzy rough approximations in hyperalgebraic structures such as semihypergroups, polygroups, hyperrings, hypermodules, etc. This paper presents the generalized fuzzy rough approximations based on two-universe (Formula presented.) -fuzzy model on canonical hypergroups.