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.

This article addresses orness measures to reflect the or-like degree of the Bonferroni mean (BM) and its variants. Some properties of these operators associated with their orness measures are portrayed analytically. However, the general orness measure involves the multiple integrals with the integral fold number being the number of the aggregated elements and as a result, the computation becomes complicated when the number of the aggregated elements is large. Furthermore, the analytical formula of the orness measure often cannot be obtained. For this reason, this study concentrates on Monte Carlo simulation to validate the result. We estimate the two parameters of the BM for a predefined orness value and a fixed length of the input vector. Besides the theoretical study of orness measure related to BM and its variants, the article also explores the simulation-based results. To support this, we provide four numerical examples.

Capturing specific interrelationship among input arguments has great importance in the process of aggregation as they may change the aggregation result significantly, which can lead viable changes in the overall decision outcome. In this study, we attempt to aggregate a set of inputs with certain heterogeneous interrelationship pattern among them. To do this, we introduce a new aggregation operator, which we call the extended geometric Bonferroni mean. We investigate its properties and develop an algorithm to learn its associated parameters based on decision maker's perceived view toward the aggregation process. Moreover, to learn such heterogeneous relationship among the inputs from the data set, we provide a learning algorithm. Examples are given to illustrate the realization of algorithm and to show certain advantages over the existing aggregation operators.