Extended fuzzy $ N $-Soft PROMETHEE method and its application in robot butler selection

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow $ N $-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy $ N $-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy $ N $-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.