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An Algebraic Structure of Type-2 Soft Sets: Type-(1,2) Soft Groups

Author

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  • Fouzia Musbah Farag Abdualhamid
  • Faruk Karaaslan

Abstract

Recently, many researchers have been studying the algebraic structures of soft sets such as soft semigroups, soft groups, soft rings, etc., and they have obtained some properties of these structures by considering the properties of classical algebraic structures. However, the algebraic structures of Type-2 soft sets are still in their infancy. In this study, the concept of a Type-(1,2) soft group is defined based on the definitions of “soft group†and “soft int-group.†Additionally, certain properties inherent in group theory related to union, intersection, Cartesian product, AND-product, and OR-product operations are obtained for Type-(1,2) soft groups. Moreover, related examples for the given definitions and theorems are presented. For Type-2 soft sets, the concept of ε,α-level sets is defined for the first time, and some of their properties are obtained. Examples are also presented regarding the definition of ε,α-level sets and the obtained properties of ε,α-level sets.

Suggested Citation

  • Fouzia Musbah Farag Abdualhamid & Faruk Karaaslan, 2026. "An Algebraic Structure of Type-2 Soft Sets: Type-(1,2) Soft Groups," Journal of Mathematics, Hindawi, vol. 2026, pages 1-17, September.
    • Handle: RePEc:hin:jjmath:4674343
    DOI: 10.1155/jom/4674343
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