Direct Product of Finite Intuitionistic Fuzzy Normal Subrings Over Non-Associative Rings

Nasreen Kausar, Mohammad Munir, Sajida Kousar, Ali Farajzadeh, Bayram Ali Ersoy

Abstract

Shal et al [21], introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring. In this note, we extendthe concept of [21]. Spcefically we prove that, $X=A\times B$ and $Y=C\times D$ be two LA-subrings of an LA-ring $R_{1}\times R_{2}.$  Then $X\cap Y $ is an LA-subring of an LA-ring $R_{1}\times R_{2}$ if and only if the intuitionistic characteristic function $\chi _{Z}=\langle \mu _{\chi _{Z}},\gamma _{\chi _{Z}}\rangle $ of $Z=X\cap Y $ is an intuitionistic fuzzy normal LA-subring of an LA-ring $R_{1}\times R_{2}.$