SMAA‐QUALIFLEX methodology to handle multicriteria decision‐making problems based on q‐rung fuzzy set with hierarchical structure of criteria using bipolar Choquet integral

The qualitative flexible multiple criteria method (QUALIFLEX) is a convenient outranking technique to handle multicriteria decision‐making (MCDM) problems due to its less complexity and high applicability, while the multiple criteria hierarchy process (MCHP) allows decision makers to deal with the hierarchical structure of criteria set where decision makers can even estimate results for a particular subcriterion at some intermediate level of the hierarchy. The main focus of our study is the amalgamation of the MCHP and QUALIFLEX methodology with special emphasis on modeling interaction among the criteria using the concept of bipolar Choquet integral. To give the decision makers more freedom for expressing their cognition about membership and nonmembership grades, the q‐rung orthopair fuzzy (q‐ROF) environment is adopted to expresses the criteria measurement. To facilitate this, it is first proposed a revised closeness index for q‐ROF to identify the appropriate ordering. Further, it is aimed to establish a new framework by implementing stochastic multiobjective acceptability analysis in our proposed extended QUALIFLEX method to take into account a variety of parameters compatible with the descriptive information regarding the relative importance and interaction of different criteria provided by the decision maker. Finally, a numerical example based on the supplier selection problem is presented to illustrate the proposed methodology in the decision problem.