# S. R. Barbhuiya, $(∈, ∈ ∨q)$-Interval-Valued Fuzzy Prime Ideals of BCK -Algebras, Volume 2017, Number 5, Pages 31-43, 2017.

**Abstract: **The notion of $(\in,\in \vee q)$-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in $(\in,\in \vee q)$-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between $(\in,\in \vee q)$-interval-valued fuzzy prime ideal and $(\in \vee q)$-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to be an $(\in,\in \vee q)$-interval-valued fuzzy prime ideals are provided.

**Keywords: **BCK-algebra, Prime ideal, Fuzzy prime ideal, $(\in,\in \vee q)$-fuzzy prime ideal, $(\in,\in \vee q)$-interval-valued fuzzy prime ideal.

**How to cite this article: **

S. R. Barbhuiya, $(∈, ∈ ∨q)$-Interval-Valued Fuzzy Prime Ideals of BCK-Algebras, International Journal of Advances in Mathematics, Volume 2017, Number 5, Pages 31-43, 2017.