Covering-Based Variable Precision $(\\mathcal {I},\\mathcal {T})$-Fuzzy Rough Sets With Applications to Multiattribute Decision-Making

Abstract

At present, there is no unified method for solving multiattribute decision-making problems. In this paper, we propose two methods that benefit from some novel fuzzy rough set models. Some theoretical preliminaries pave the way. First, by means of a fuzzy logical implicator <inline-formula><tex-math notation= LaTeX >$\\mathcal {I}$</tex-math></inline-formula> and a triangular norm <inline-formula><tex-math notation= LaTeX >$\\mathcal {T}$</tex-math></inline-formula>, four types of coverings-based variable precision <inline-formula><tex-math notation= LaTeX >$(\\mathcal {I},\\mathcal {T})$</tex-math></inline-formula>-fuzzy rough set models are proposed. They can be used to deal with misclassification and perturbation (here, misclassification refers to error or missing values in classification, while perturbation refers to small changes in digital data). Second, the properties and the relationships among these models are investigated. Finally, we rely on their remarkable features in order to establish two approaches to multiattribute decision-making. Some numerical examples illustrate the application of these new approaches. The sensitivity and comparative analyses show that the respective ranking results produced by these decision-making methods have a high consensus for multiattribute decision-making problems with fuzzy evaluation information.