On 0-Interval Valued Fuzzification of Lagrange’s Theorem of 0-Interval Valued Fuzzy Subgroups

مقال فى مجلة
نوع عمل المنشور
بحث أصيل
اسم الناشر
IEEE ACCESS
ملخص المنشورات

In this paper, we present the idea of interval valued fuzzy subgroup defined over a certain t-conorm (Γ-IVFSG) and prove that every IVFSG is Γ-IVFSG. We use this ideology to define the concepts of Γ-IVF cosets, Γ-IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subgroups of Γ-IVFSG and investigate the condition under which a Γ-IVFS is Γ-IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of quotient group of a group Ζ relative to the Γ-IVFNSG and acquire a correspondence between each Γ-IVF(N)SG of a group Ζ and Γ-IVF(N)SG of its quotient group. Furthermore, we define the index of Γ-IVFSG and establish the Γ-interval valued fuzzification of Lagrange’s theorem of any Γ-IVFSG of a finite group Ζ.