Abstract
Abstract In this paper, we propose a new entropy measure with geometrical interpretation of intuitionistic fuzzy sets. Compared with the entropy measure provided by Szmidt and Kacprzyk, the new entropy formula in this paper can measure both fuzziness and intuitionism for intuitionistic fuzzy sets. According to the relationship between entropy and similarity measure, we construct a new similarity measure for intuitionistic fuzzy sets. Then we present two methods, based on entropy and similarity measure, to determine weights of experts for multi-attribute group decision making with intuitionistic fuzzy information.
Highlights
As a generalized form of fuzzy sets (FSs)[1], intuitionistic fuzzy sets (IFSs)[2], characterized by membership functions and non-membership functions, can depict the fuzziness and uncertainty of objective world more exquisitely than fuzzy sets[3,4].Zadeh[5], Gau and Buehrer[6] introduced the notion of interval-valued fuzzy sets (IVFSs) and vague sets
According to the equivalence of IVFSs and IFSs8,9, we propose a transforming method by which one can establish a similarity measure based on an entropy of IFSs
In order to show the rationality and effectiveness of the new entropy and similarity measure proposed in Section 3 and 4, we apply them to multi-attribute group decision making with intuitionistic fuzzy information
Summary
As a generalized form of fuzzy sets (FSs)[1], intuitionistic fuzzy sets (IFSs)[2], characterized by membership functions and non-membership functions, can depict the fuzziness and uncertainty of objective world more exquisitely than fuzzy sets[3,4]. Zeng and Guo[35] discussed the relationship of normalized distance, similarity measure, inclusion measure and entropy measure of IVFSs. Wei and Wang[36] gave an approach to construct similarity measures using entropy for interval-valued intuitionistic fuzzy sets (IVIFSs) and proposed new similarity measures for IFSs and IVIFSs. Szmidt and Kacprzyk[26] proposed an entropy measure with geometrical interpretation of IFSs to measure the fuzziness of an IFS. We propose a new entropy measure by the geometrical interpretation of IFSs. The new formula can measure the fuzziness and the intuitionism of an IFS.
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