Abstract
The aim of this paper is to introduce strongest relation, cosets and middle cosets of anti \(Q\)-fuzzy subgroups of \(G\) with respect to \(t\)-conorm \(C.\) We investigate equivalent characterizations of them and we construct a new group induced by them, and give the homomorphism theorem between them.
Highlights
Introduction and PreliminariesI n mathematics and abstract algebra, group theory studies the algebraic structures known as groups
Other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms
The concept of a fuzzy set was introduced by Zadeh [1], and it is a rigorous area of research with manifold applications ranging from engineering and computer science to medical diagnosis and social behavior studies
Summary
I n mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra. Other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. The author by using norms, investigated some properties of fuzzy algebraic structures [4–6]. In [7] the author introduced the notion of anti Q−fuzzy subgroups of G with respect to t-conorm C and study their important properties. We introduce strongest relation with respect anti Q-fuzzy subgroups of G with respect to t-conorm C and obtain some properties of them. We define the middle coset of anti Q-fuzzy subgroups of G with respect to t-conorm C and investigate some results about them. We define new group under new operations of them and we prove isomorphism between them
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