Extended PROMETHEE approach with 2-tuple linguistic m-polar fuzzy sets for selection of elliptical cardio machine

The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking series of multi-attribute decision making used to assess a finite collection of alternatives based on conflicting criteria. One of its significant benefits is its adjustability in response to a set of acceptable preference functions that may quantify the differences between alternatives conditional on the kind and structure of the criteria. This article offers the novel approach of the PROMETHEE method, named the 2TLmF PROMETHEE method, which combines the multi-polarity with linguistic information of decision problems. The customary procedure of the offered technique begins with the normalized weights of the attributes assigned by decision-makers. After that, Gaussian and the usual preference functions are utilized to determine the preferences of the alternatives. The ultimate choice is based on the alternative's positive and negative outranking flow. The positive outranking demonstrates how one alternative outranks all other options, while the negative preference flow implies an alternative is superior to all other options. There are several modifications to the PROMETHEE approach, two of which are discussed in this article. The first is PROMETHEE I, which uses positive and negative preference flows to generate a partial ranking. Secondly, PROMETHEE II gives a comprehensive rating list based on the net flow, representing the balance of positive and negative preference flows. Further, a comprehensive flowchart is used to show the entire picture of the proposed methodology. As an application, a real-life situation related to selecting an elliptical machine for a home gym is chosen to illustrate the transparency and reliability of the presented work. Finally, a comparative study is carried out to illustrate the strength and applicability of the proposed method.