Three-way decisions with complex q-rung orthopair 2-tuple linguistic decision-theoretic rough sets based on generalized Maclaurin symmetric mean operators

Zeeshan Ali; Tahir Mahmood; Muhammad Bilal Khan; Zeeshan Ali; Tahir Mahmood; Muhammad Bilal Khan

doi:10.3934/math.2023913

AIMS Mathematics

2023, Volume 8, Issue 8: 17943-17980. doi: 10.3934/math.2023913

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Three-way decisions with complex q-rung orthopair 2-tuple linguistic decision-theoretic rough sets based on generalized Maclaurin symmetric mean operators

1.
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan

Received: 04 February 2023 Revised: 04 March 2023 Accepted: 02 April 2023 Published: 24 May 2023
MSC : 03B52, 03E72, 28E10, 68T27, 94D05

In this manuscript, we generalized the notions of three-way decisions (3WD) and decision theoretic rough sets (DTRS) in the framework of Complex q-rung orthopair 2-tuple linguistic variables (CQRO2-TLV) and then deliberated some of its important properties. Moreover, we considered some very useful and prominent aggregation operators in the framework of CQRO2-TLV, while further observing the importance of the generalized Maclurin symmetric mean (GMSM) due to its applications in symmetry analysis, interpolation techniques, analyzing inequalities, measuring central tendency, mathematical analysis and many other real life problems. We initiated complex q-rung orthopair 2-tuple linguistic (CQRO2-TL) information and GMSM to introduce the CQRO2-TL GMSM (CQRO2-TLGMSM) operator and the weighted CQRO2-TL GMSM (WCQRO2-TLGMSM) operator, and then demonstrated their properties such as idempotency, commutativity, monotonicity and boundedness. We also investigated a CQRO2-TL DTRS model. In the end, a comparative study is given to prove the authenticity, supremacy, and effectiveness of our proposed notions.
- three-way decision,
- complex q-rung orthopair 2-tuple linguistic variables,
- rough sets,
- generalized Maclaurin symmetric mean operators
Citation: Zeeshan Ali, Tahir Mahmood, Muhammad Bilal Khan. Three-way decisions with complex q-rung orthopair 2-tuple linguistic decision-theoretic rough sets based on generalized Maclaurin symmetric mean operators[J]. AIMS Mathematics, 2023, 8(8): 17943-17980. doi: 10.3934/math.2023913

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Abstract

In this manuscript, we generalized the notions of three-way decisions (3WD) and decision theoretic rough sets (DTRS) in the framework of Complex q-rung orthopair 2-tuple linguistic variables (CQRO2-TLV) and then deliberated some of its important properties. Moreover, we considered some very useful and prominent aggregation operators in the framework of CQRO2-TLV, while further observing the importance of the generalized Maclurin symmetric mean (GMSM) due to its applications in symmetry analysis, interpolation techniques, analyzing inequalities, measuring central tendency, mathematical analysis and many other real life problems. We initiated complex q-rung orthopair 2-tuple linguistic (CQRO2-TL) information and GMSM to introduce the CQRO2-TL GMSM (CQRO2-TLGMSM) operator and the weighted CQRO2-TL GMSM (WCQRO2-TLGMSM) operator, and then demonstrated their properties such as idempotency, commutativity, monotonicity and boundedness. We also investigated a CQRO2-TL DTRS model. In the end, a comparative study is given to prove the authenticity, supremacy, and effectiveness of our proposed notions.

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