Hesitant triangular fuzzy FlowSort method: the multi-criteria decision-making problems

Multi-criteria sorting problems have gained significant importance across various fields. However, when experts express their opinions using linguistic terms and quantitative evaluation criteria are not feasible, the fuzzy set theory proves to be a suitable framework. Moreover, in such scenarios, the use of hesitant fuzzy sets becomes necessary because each criterion might have multiple values compared with other alternatives. This paper introduces a novel method called Hesitant Triangular Fuzzy Sorting (HTFFS), which is a variation of the fuzzy FlowSort method based on the preference ranking organisation method for enrichment evaluation (PROMETHEE). The HTFFS method incorporates the theory of fuzzy sets and establishes theoretical foundations for calculating the degree of superiority of each alternative over others. This calculation uses mathematical operators specifically designed for uncertain fuzzy sets and uncertain triangular fuzzy numbers. To demonstrate the effectiveness and practicality of the proposed HTFFS method, two numerical examples are presented. The results obtained from these examples showcase the applicability and validity of the HTFFS method in handling multi-criteria sorting problems.