Abstract
We further develop the theory of vague soft groups by establishing the concept of normalistic vague soft groups and normalistic vague soft group homomorphism as a continuation to the notion of vague soft groups and vague soft homomorphism. The properties and structural characteristics of these concepts as well as the structures that are preserved under the normalistic vague soft group homomorphism are studied and discussed.
Highlights
Soft set theory introduced by Molodtsov in 1999 is a general mathematical tool that is commonly used to deal with imprecision, uncertainties, and vagueness that are pervasive in a lot of complicated problems affecting various areas in the real world
Sezgin and Atagun on the other hand introduced the notion of normalistic soft groups and normalistic soft group homomorphism as an extension to the notion of soft groups introduced by [2]. All this led to the study of fuzzy soft algebra by Aygunoglu and Aygun who introduced the notion of fuzzy soft groups
Research in the area of vague soft algebra was initiated by Varol et al who developed the theory of vague soft groups and defined the concepts of vague soft groups, normal vague soft groups, and vague soft homomorphism
Summary
Soft set theory introduced by Molodtsov in 1999 (see [1]) is a general mathematical tool that is commonly used to deal with imprecision, uncertainties, and vagueness that are pervasive in a lot of complicated problems affecting various areas in the real world. Research in the area of vague soft algebra was initiated by Varol et al (see [7]) who developed the theory of vague soft groups and defined the concepts of vague soft groups, normal vague soft groups, and vague soft homomorphism. Varol et al in [7] defined the concept of normal vague soft groups as an Abelian vague soft group; that is, (F, A) is a vague soft group that satisfies the Advances in Fuzzy Systems commutative law given by tFa (x⋅y) = tFa (y⋅x) and 1 − fFa (x⋅ y) = 1 − fFa (y ⋅ x) This definition is incomplete as there exist two other statements which describe the normality of a vague soft set that is equivalent to the commutative law used in [7]. We prove that there exists a one-to-one correspondence between normalistic vague soft groups and some of the corresponding concepts in soft group theory and classical group theory
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