$(\in ,\in {\vee }_q)$– Fuzzy Ideals of $K$-Algebras

Abstract

Our work in this paper is concerned with a new kind of fuzzy ideal of a $K$-algebra called an $(\in ,\in {\vee }_q)$-fuzzy ideal. We investigate some interesting properties of $(\in ,\in {\vee }_q)$-fuzzy ideals of $K$-algebras. We study fuzzy ideals with thresholds which is a generalization of both fuzzy ideals and $(\in ,\in {\vee }_q)$-fuzzy ideals. We also present characterization theorems of implication-based fuzzy ideals.