Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups

Article Computer Science, Artificial Intelligence

Multi-fuzzy soft groups

Canan Akin

Summary: This study extends the concept of multi-fuzzy soft sets to group theory, introducing new definitions such as restricted and extended intersections, unions, boolean AND-intersections, and boolean OR-unions. The concept of multi-fuzzy soft sets is applied to groups, proposing the notion of a multi-fuzzy soft group and defining homomorphisms of multi-fuzzy soft groups. The study concludes that the image (or pre-image) of a multi-fuzzy soft group remains a multi-fuzzy soft group.

SOFT COMPUTING (2021)

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Review Mathematics

An Overview of the Foundations of the Hypergroup Theory

Christos Massouros et al.

Summary: This paper discusses the importance of hypergroups in hypercompositional algebra, focusing on the structural relationship between hypergroups and groups, different types of hypergroups, and the ability of subhypergroups in decomposing hypergroups.

MATHEMATICS (2021)

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Article Mathematics

Application Multi-Fuzzy Soft Sets in Hypermodules

Osman Kazanci et al.

Summary: This paper introduces a novel soft hyperstructure called multi-fuzzy soft hyperstructure, investigates the multi-fuzzy soft hypermodules and discusses their structural properties, and examines the behavior image and inverse image of a multi-fuzzy soft set under the multi-fuzzy soft function. According to Zadeh's extension principle, it is proven that the image and inverse image of a multi-fuzzy soft hypermodues are further multi-fuzzy soft hypermodule.

MATHEMATICS (2021)

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Article Computer Science, Artificial Intelligence