In the real decision making,
q‐rung orthopair fuzzy sets (
q‐ROFSs) as a novel effective tool can depict and handle uncertain information in a broader perspective. Considering the interrelationships among the criteria, this paper extends Choquet integral to the
q‐rung orthopair fuzzy environment and further investigates its application in multicriteria two‐sided matching decision making. To determine the fuzzy measures used in Choquet integral, we first define a pair of
q‐rung orthopair fuzzy entropy and cross‐entropy. Then, by utilizing
λ‐fuzzy measure theory, we propose an entropy‐based method to calculate the fuzzy measures upon criteria. Furthermore, we discuss
q‐rung orthopair fuzzy Choquet integral operator and its properties. Thus, with the aid of
q‐rung orthopair fuzzy Choquet integral, we consider the preference heterogeneity of the matching subjects and further explore the corresponding generalized model and approach for the two‐sided matching. Finally, a simulated example of loan market matching is given to illustrate the validity and applicability of our proposed approach.
As an extension of Pythagorean fuzzy sets, the q‐rung orthopair fuzzy sets (q‐ROFSs) can easily solve uncertain information in a broader perspective. Considering the fine property of q‐ROFSs, we introduce q‐ROFSs into decision‐theoretic rough sets (DTRSs) and use it to portray the loss function. According to the Bayesian decision procedure, we further construct a basic model of q‐rung orthopair fuzzy decision‐theoretic rough sets (q‐ROFDTRSs) under the q‐rung orthopair fuzzy environment. At the same time, we design the corresponding method for the deduction of three‐way decisions by utilizing projection‐based distance measures and TOPSIS. Then, we extend q‐ROFDTRSs to adapt the group decision‐making (GDM) scenario. To fuse different experts’ evaluation results, we propose some new aggregation operators of q‐ROFSs by utilizing power average (PA) and power geometric (PG) operators, that is, q‐rung orthopair fuzzy power average, q‐rung orthopair fuzzy power weighted average (q‐ROFPWA), q‐rung orthopair fuzzy power geometric, and q‐rung orthopair fuzzy power weighted geometric (q‐ROFPWG). In addition, with the aid of q‐ROFPWA and q‐ROFPWG, we investigate three‐way decisions with q‐ROFDTRSs under the GDM situation. Finally, we give the example of a rural e‐commence GDM problem to illustrate the application of our proposed method and verify our results by conducting two comparative experiments.
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