2-Absorbing primary vague weakly completely ideals

Abstract

In commutative vague algebra, the primary ideals are the remarkably weighty structures. Gau et al. proposed the idea of vague sets as an extension of fuzzy set theory. The aim of this work is to introduce and characterize 2-absorbing primary vague weakly completely ideals of commutative rings as a generalization of primary vague ideals and study their properties. Firstly, we give the definitions prime vague weakly completely ideals, primary vague weakly completely ideals and 2-absorbing vague weakly completely ideals of a commutative ring $\Re$. Then, we introduce the notion of prime $K$-vague ideal, primary $K$-vague ideal, 2-absorbing  $K$-vague ideal. Also, we give the notion of  2-absorbing $K$-vague ideals and 2-absorbing primary  $K$-vague ideals of commutative rings. Moreover, we investigate vague quotient ring of $\Re$ induced by the 2-absorbing vague weakly completely ideal which is a 2-absorbing ring. Finally, we acquire a schema which transitions between definitions of these concepts.