Characterizations of right modular groupoids by \((\in,\in\vee q_k)\)-fuzzy interior ideals.

zbMATH Open1289.20094arXiv1010.3510MaRDI QIDQ2868341

Shamas-ur-Rehman, Young Bae Jun, Madad Khan

Publication date: 16 December 2013

Published in: Scientific Bulletin. Series A. Applied Mathematics and Physics. Politehnica University of Bucharest (Search for Journal in Brave)

Abstract: In this paper, we have introduced the concept of $left(in,inveeqight)$-fuzzy ideals in a right modular groupoid. We have discussed several important features of a completely regular right modular groupoid by using the $left(in,inveeqight)$-fuzzy left (right, two-sided) ideals, $left(in,inveeqight)$-fuzzy (generalized) bi-ideals and $left(in,inveeqight)$-fuzzy $(1,2)$-ideals. We have also used the concept of $left(in,invee{q}_{k}ight)$-fuzzy left (right, two-sided) ideals, $left(in,invee{q}_{k}ight)$-fuzzy quasi-ideals $left(in,invee{q}_{k}ight)$-fuzzy bi-ideals and $\mathrm{\%}left(in,invee{q}_{k}ight)$-fuzzy interior ideals in completely regular right modular groupoid and proved that the $left(in,invee{q}_{k}ight)$-fuzzy left (right, two-sided), $left(in,invee{q}_{k}ight)$-fuzzy (generalized) bi-ideals, and $left(in,invee{q}_{k}ight)$-fuzzy interior ideals coincide in a completely regular right modular groupoid.

Full work available at URL: https://arxiv.org/abs/1010.3510

zbMATH Keywords

generalized fuzzy idealscompletely regular right modular groupoids

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72) Fuzzy groups (20N25) Sets with a single binary operation (groupoids) (20N02)

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