Consistency threshold- and score function-based multi-attribute decision-making with Q-rung orthopair fuzzy preference relations

Abstract

As a general form of intuitionistic fuzzy preference relations (IFPRs) and Pythagorean fuzzy preference relations (PFPRs), q-rung orthopair fuzzy preference relations (q-ROFPRs) provide a more flexible information representation for decision makers (DMs) to express their vagueness and uncertainty. However, there have been only a few studies conducted on q-ROFPRs. Therefore, in the context of multi-attribute decision-making (MADM), a decision framework for MADM with q-ROFPRs is proposed. First, a novel score function is proposed to compare two different q‐rung orthopair fuzzy numbers (q‐ROFNs). Subsequently, an algorithm is developed to check and improve the multiplicative consistency of q-ROFPRs. Moreover, to consider the rationality of the threshold determination, an objective method for determining the threshold of q-ROFPRs is developed considering the number of alternatives and rung q. Finally, a new method for determining the weights of attributes is discussed. In addition, an illustrative example involving the brand evaluation of new energy vehicles is used to verify the applicability of the above methods. The rationality and superiority of the proposed methods are highlighted by a comparative analysis with existing studies.