Abstract
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.
Highlights
Three-way decision-making, which is a decision-making model based on human cognition, has a very unique function in dealing with uncertainty
In order to avoid the incomprehensiveness of individual decisions, we extend IVIFDTRSs from single-person decision-making to group decision-making
This paper extends IFDTRSs to IVIFDTRSs, and extends IVIFDTRSs from single-person decision-making to group decision-making, which provides a more scientific and rational way to deal with the uncertainty of decision-making
Summary
Three-way decision-making, which is a decision-making model based on human cognition, has a very unique function in dealing with uncertainty. Extended the entropy and subsethood from IFSs to general IVIFSs. Xu et al [29] introduced the clustering technique of IVIFSs. The IVIFSs, which use the interval-valued intuitionistic fuzzy numbers instead of precision numbers to describe the membership and non-membership function, are more flexible and practical in dealing with ambiguity and uncertainty. Unlike the existing works, presented in [15,16,17,18], this article uses IVIFNs, instead of precise numbers, to describe the loss functions of the DTRSs and construct a new framework of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). We adopted the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to aggregate the group opinions and compute the scores and accuracies of the expected losses By comparing these scores and accuracies, we develop a simple and straightforward algorithm to deduce three-way decisions.
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