q-rung orthopair neutrosophic fuzzy rough sets with an application based on multi-criteria decision-making

Fuzzy set theory, introduced in the 1960s, has grown significantly through various generalizations, including intuitionistic, pythagorean, and fermatean fuzzy sets. These extensions enhance the theory’s flexibility in managing uncertainty. Also, q-rung orthopair fuzzy sets extend these concepts by broadening the scope of hesitation, offering a more versatile tool for decision-making. Neutrosophic fuzzy sets further incorporate three membership degrees—truth, indeterminacy, and falsity to handle uncertainty better. Meanwhile, rough set theory excels at addressing indiscernibility through relations and approximations. Combining these strengths, q-rung orthopair neutrosophic fuzzy rough sets are introduced in this paper. Based on the proposed theory, an algorithm is designed to rank the alternatives based on various criteria and then an application is discussed, where a student uses the proposed theory to choose the best university from the given choices.