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q ‐Rung orthopair fuzzy sets‐based decision‐theoretic rough sets for three‐way decisions under group decision making
Author(s) -
Liang Decui,
Cao Wen
Publication year - 2019
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22187
Subject(s) - fuzzy logic , mathematics , group decision making , fuzzy set , fuzzy number , computer science , score , multiple criteria decision analysis , mathematical optimization , artificial intelligence , statistics , political science , law
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.