Ideal theory of semigroups based on \((3,2)\)-fuzzy sets

Volume 28, Issue 2, pp 182--191 http://dx.doi.org/10.22436/jmcs.028.02.06

Publication Date: May 18, 2022 Submission Date: January 25, 2022 Revision Date: February 09, 2022 Accteptance Date: March 18, 2022

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Authors

M. Vanishree - Department of Mathematics, Rajah Serfoji Government College (affliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India. N. Rajesh - Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India. N. Rafi - Department of Mathematics, Bapatla Engineering College, Bapatla-522101, Andhra Pradesh, India. R. Bandaru - Department of Mathematics, GITAM (Deemed to be University), Hyderabad Campus, Telangana-502329, India.

Abstract

In this paper, the notions of \((3,2)\)-fuzzy ideal, \((3,2)\)-fuzzy bi-ideal, \((3,2)\)-fuzzy interior ideal and \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup are introduced and investigated their properties. The relation between (\((3,2)\)-fuzzy) ideal, bi-ideal, interior ideal and \((1,2)\)-ideal are given. We characterized \((3,2)\)-fuzzy \((1,2)\)-ideal in terms of \(f^3\)-level \(\alpha\)-cut and \(g^2\)-level \(\alpha\)-cut. A necessary and sufficient condition for a subset of a semigroup to be \((1,2)\)-ideal in terms of \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup is given.

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Keywords

• \((3,2)\)-fuzzy set
• \((3,2)\)-fuzzy subalgebra
• \((3,2)\)-fuzzy ideal

MSC

•  06F35
•  03G25
•  03E72

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