Abstract: Aim of this paper is to investigate the characterizations of the concept of $(\alpha,\beta)$-fuzzy ideals of left near-rings, where $\alpha,\beta$ are any two of $\{\in,q,\in\vee q,\in\wedge q\}$ with $\alpha\neq \in\wedge q$ by using belongs to relation $(\in)$ and quasi-coincidence with relation $(q)$ between fuzzy points and fuzzy sets. An $(\alpha,\beta)$-fuzzy ideal, we can consider twelve different types of such structures because there are three types of $\alpha$ and four types of $\beta$. But in this paper, mainly the types $(\in,\in),(\in,\in\vee q),(q,\in\vee q),(\in\vee q,\in\vee q)$ are considered. We also discussed some characterizations of $(\in,\in\vee q_k)$-fuzzy subnear-rings and ideals of near-rings.

Key words: Near-rings, ideals and $(\alpha,\beta)$-fuzzy ideals (subnear-rings).

How to cite this article:

V. Chinnadurai and S. Kadalarasi, Characterizations of near-rings by (α, β)-fuzzy ideals, International Journal of Advances in Mathematics, Volume 2017, Number 5, Pages 55-69, 2017.