Abstract
Type-2 fuzzy sets (T2FSs) have the advantage of representing higher-order uncertainty, they have demonstrated superior performance in several applications. In order to fully measure the uncertainty for T2FSs. In this study, several distribution characteristics of uncertainties within T2FSs are analyzed through type-1 fuzzy sets (T1FSs), and the axiomatic framework of fuzzy entropy and overall entropy of T2FSs is established as well. First, a new representation method for T2FSs is given. On this basis, the axiomatic definitions of fuzzy entropy for T1FSs and T2FSs are constructed by analyzing the distribution characteristics of fuzziness, and the construction theorems and basic properties of fuzzy entropy are studied. Further, the overall entropy of T2FSs is given, on this basis, a novel type-2 fuzzy entropy-based decision-making method is proposed, and applied to the selection of cold medicine through online reviews on AliHealth.cn. Finally, the feasibility and effectiveness of the developed definitions and methods are demonstrated by three comparative analyses.
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