Multi-criteria decision making based on q-rung orthopair fuzzy promethee approach

The preference ranking organization method for enrichment of evaluations (PROMETHEE) {constitutes a family of outranking} multiple-attribute decision-making (MADM) methods {that has been adopted by researchers from many areas during} the last years. It provides reliable and clear results {thanks to the} advantages of different types of preference functions. {In this paper, we incorporate the benefits of $q$-rung orthopair fuzzy set (for short, $q$-ROFS) in this strategy of solution.} {This model, $q$-ROFS, is a generalized form of Pythagorean fuzzy set (PFS)}, as it {broadens} the space of acceptable orthopairs and {has} an ability to deal with more elaborate and vague information. The technique of {our extension of the} PROMETHEE method {uses} $q$-rung orthopair fuzzy numbers to {render} the ratings of alternatives, {which allows us} to express {uncertain and vague information more accurately}. The usual criterion preference function {has} been used to measure the preferences of {the} alternatives. A partial ordering of alternatives is obtained by considering the outgoing and incoming flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ordering is accomplished by taking into account the procedure of PROMETHEE II. As a numerical {exercise, we consider the selection of a contractor for a construction project}. {A full analysis} is performed {to illustrate the application of the technique that stems from our approach}. {Then we compare the results that we obtain with the results from existing approaches, including $q$-rung orthopair fuzzy ELECTRE, $q$-rung orthopair fuzzy TOPSIS, $q$-rung orthopair fuzzy VIKOR and $q$-rung orthopair fuzzy aggregation operators. In this way the accuracy and effectiveness of the presented work is conclusively validated