Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

• Published in: Symmetry (Basel) Vol. 10; no. 7; p. 281
• Main Authors: Ye, Dajun, Liang, Decui, Hu, Pei
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2018
• Subjects: Accuracy; Correlation analysis; Decision making; Decision support systems; Decision theory; decision-theoretic rough sets; Decisions; Design; Entropy; Fuzzy sets; group decision-making; International conferences; interval-valued intuitionistic fuzzy sets; Methods; Researchers; three-way decisions; China
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym10070281

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.