On some characterization of \(Q\)-complex fuzzy sub-rings

Volume 22, Issue 3, pp 295--305 http://dx.doi.org/10.22436/jmcs.022.03.08

Publication Date: August 31, 2020 Submission Date: June 19, 2020 Revision Date: July 06, 2020 Accteptance Date: July 21, 2020

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Authors

Muhammad Gulzar - Department of Mathematics, Government College University Faisalabad, 38000, Pakistan. Dilshad Alghazzawi - Department of Mathematics, King Abdulaziz University (Rabigh), Saudi Arabia. M. Haris Mateen - Department of Mathematics, University of the Punjab, Lahore, Pakistan. M. Premkumar - Research Scholar, PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), (Affiliated to Bharathidasan University), India. - Department of Mathematics, Kongunadu College of Engineering and Technology, Tiruchirappalli-620020, Tamilnadu, India.

Abstract

In this paper, we introduce the idea of \(Q\)-complex fuzzy sub-ring (\(Q\)-CFSR) and discuss its various algebraic aspects. We prove that every \(Q\)-CFSR generates two \(Q\)-fuzzy sub-rings (\(Q\)-FSRs). We also present the concept of level subsets of \(Q\)-CFSR and show that level subset of \(Q\)-CFSR form sub-ring. Furthermore, we extend this idea to define the notion of the direct product of two \(Q\)-CFSR Moreover, we investigate the homomorphic image and inverse image of \(Q\)-CFSR.

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Keywords

• Complex fuzzy set (CFS)
• \(Q\)-complex fuzzy set (\(Q\)-CFS)
• \(Q\)-complex fuzzy sub-ring (\(Q\)-CFSR)

MSC

•  03E72
•  08A72
•  20N25

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