STRUCTURES OF GENERALIZED FUZZY SETS IN NON-ASSOCIATIVE RINGS

I. Rehman at all

IJPAM: Volume 113, No. 2 (2017)

Title

STRUCTURES OF GENERALIZED FUZZY SETS
IN NON-ASSOCIATIVE RINGS

Authors

Inayatur Rehman

, Muhammad Gulistan

,
Muhammad Asif Gondal

, Shah Nawaz

$^{1,3}$ Department of Mathematics and Sciences
College of Arts and Applied Sciences
Dhofar University
Salalah, OMAN
$^{2,4}$ Department of Mathematics
Hazara University
Mansehra, PAKISTAN

Abstract

Since the introduction of the concept of fuzzy sets, the theoretical application of fuzzy sets has been restricted to associative algebraic structures (groups, semigroups, associative rings, semi-rings etc). In addition, the study of fuzzy sets, where the base set is a commutative structure, has attracted the attention of many researchers. On the other hand there are many sets which are naturally endowed with two compatible binary operations forming a non-associative ring and we may dig out examples which investigate a non-associative structure in the context of fuzzy sets. Intuitively one can apply the concept of fuzzy sets to non-commutative and non-associative structures.In this paper, we introduce the concept of ( $\alpha,\beta$ )-fuzzy ideals in LA-rings (a non-associative structure). We discuss the important features of a non-associative regular LA-ring by using ( $\alpha,\beta$ ) -fuzzy bi-ideals, ( $\alpha,\beta$ )-fuzzy generalized bi-ideals, ( $\alpha,\beta$ )-fuzzy quasi-ideals, and ( $\alpha,\beta$ )-fuzzy interior ideals. Ultimately, we identify upper and lower parts of these structures and characterize regular LA-rings using the identified properties of these structures.

History

Received: November 13, 2016
Revised: January 20, 2017
Published: March 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 17D99
Key Words and Phrases: LA-rings, Fuzzy LA-rings, $\left( \alpha,\beta\right)$ -fuzzy ideals, Regular LA-Rings

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How to Cite?

DOI: 10.12732/ijpam.v113i2.10 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 2
Pages: 299 - 325

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