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Uncertainty measure for Atanassov’s intuitionistic fuzzy sets

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Abstract

Uncertainty measure can supply a new viewpoint for analyzing knowledge conveyed by an Atanassov’s intuitionistic fuzzy set (AIFS). So uncertainty measurement is a key topic in AIFS theory, analogous to the role of entropy in probability theory. After reviewing the existing measures of uncertainty (entropy) for AIFSs, we argue that the existing measures of uncertainty cannot capture all facets of uncertainty associated with an AIFS. Then we point out and justify that there are at least three kinds of uncertainty for an AIFS, namely non-specificity, fuzziness, and intuitionism. We provide formal measures of non-specificity, fuzziness, and intuitionism, together with their properties and proofs. Properties of the proposed non-specificity measure are especially investigated. Finally, a general uncertainty measure consisting of these three uncertainties is presented. Illustrative examples show that the proposed uncertainty measure is consistent with intuitive cognize, and it is more sensitive to changes of AIFSs. Moreover, the proposed uncertainty measure can also discriminate uncertainty hiding in classical sets. Thus, it provides an alternative way to construct unified uncertainty measures.

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Acknowledgments

This work is supported by the Natural Science Foundation of China under grants No. 61273275, No. 60975026, No. 61573375 and No. 61503407.

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Authors and Affiliations

  1. Air Force Engineering University, Xi’an, 710051, People’s Republic of China

    Yafei Song, Xiaodan Wang, Lei Lei & Wen Quan

  2. Xi’an Communications Institute, Xi’an, 710106, People’s Republic of China

    Wenhua Wu

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  1. Yafei Song
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  2. Xiaodan Wang
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  3. Wenhua Wu
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  4. Lei Lei
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  5. Wen Quan
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Correspondence to Yafei Song.

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Song, Y., Wang, X., Wu, W. et al. Uncertainty measure for Atanassov’s intuitionistic fuzzy sets. Appl Intell 46, 757–774 (2017). https://doi.org/10.1007/s10489-016-0863-2

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  • DOI: https://doi.org/10.1007/s10489-016-0863-2

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