A Proportional Fuzzy Elimination and Choice Translating Reality II Method for Multicriteria Decision-Making Problems: A Robust New Methodology for Practical Applications

As a result of the complexity of practical problems and the limitations of knowledge, it is often tricky for decision-makers (DMs) to give accurate information. How to accurately and effectively convey the evaluation information of DMs affects multicriteria decision-making (MCDM). Therefore, linguistically hesitant fuzzy sets can express people’s evaluations with greater flexibility and resemblance to human thought than exact numbers, particularly during highly complex decision-making processes. This article proposes the proportional interval term set (PITS) inspired by hesitant fuzzy sets to indicate more significant uncertainty. To more effectively compare two PITSs, the number of elements in each set must be identical. So the standardization of the PITS is presented for this purpose. The standardization improves the distance and possibility degree of two PITSs. Moreover, considering the more vital capability of the symmetrical interval term set to handle uncertain information, an integrated elimination and choice translating reality (ELECTRE) II method for addressing MCDM issues is proposed. The first phase aggregates the PITS opinions of experts on each alternative and criterion and determines the weights of the criteria with the aid of distance theory. Then, using possibility degrees, the method introduces three PITS outranking sets (concordance, indifferent, and discordance sets) and defines strong and weak outranking relations. Further, a dominance matrix ranks alternatives. Finally, applying the pilot study can fruitfully demonstrate and signify the practicality and feasibility of the proposed decision-making approach.