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

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.

Automated summary

In this paper, we extended the concepts 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 discussed their important properties. We also introduced the CQRO2-TL GMSM (CQRO2-TLGMSM) operator and the weighted CQRO2-TL GMSM (WCQRO2-TLGMSM) operator, and demonstrated their properties such as idempotency, commutativity, monotonicity and boundedness. Furthermore, we investigated a CQRO2-TL DTRS model and conducted a comparative study to validate the authenticity, supremacy, and effectiveness of our proposed notions.