Abstract
p,q-quasirung orthopair fuzzy set (p,q-QOFS) is an extension of the q-rung orthopair fuzzy set (q-ROFS) theory used to represent uncertainty and vagueness in decision-making processes. The paper aims to utilize robust sine-trigonometric operational laws to investigate the group decision-making process within the p,q-QOFSs framework. The p,q-QOFS possess a distinctive characteristic of handling uncertain information by utilizing a wider space for membership representation compared to q-ROFS. Consequently, the current paper has been categorized into three distinct phases. In the initial phase, novel operational laws will be presented for p,q-QOFSs. The fundamental concept behind these newly proposed operations is to integrate the properties of the sine function, which include being periodic and symmetric about the origin, into the decision-making process for objects. Then, based on these laws, several operators for aggregating information will be obtained, along with their necessary properties and relationships. Lastly, an algorithm will be presented for interpreting the problem of multi attribute group decision-making (MAGDM), utilizing the operators, and demonstrating it with an illustrative example. A comprehensive comparative analysis will be conducted with some of the existing methods to uncover their impacts.
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