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A New Distance Measure Between Atanassov’s Intuitionistic Fuzzy Sets Based on Mapping

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Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1074))

Abstract

A new trapezoidal approximation of Atanassov’s intuitionistic fuzzy sets (AIFSs) and a new distance measure between AIFSs based on the area relations of membership function graphs of their corresponding trapezoidal fuzzy sets are proposed. By the conversion from Atanassov’s intuitionistic fuzzy numbers (AIFNs) to trapezoidal fuzzy numbers, the measurement of distance between AIFSs can be transformed into the calculation of area relations of the corresponding trapezoidal fuzzy sets. Then the new distance measurement can integrate continuous information rather than only taking discrete variables into consideration as before. The main innovation of our distance is that it can integrate comprehensive and continuous information in calculation instead of partial discrete variables, which can efficiently avoid information loss. The contrastive tests demonstrate the efficiency and practicality of the approach.

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Author information

Authors and Affiliations

  1. School of Information and Telecommunication Engineering, Beijing University of Posts and Telecommunication, No. 10, Xitucheng Road, Haidian District, Beijing, 100876, China

    Fang Su, Jing Li, Dongxuan Xiao & Chengrui Duan

Authors
  1. Fang Su
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  2. Jing Li
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  3. Dongxuan Xiao
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  4. Chengrui Duan
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Corresponding author

Correspondence to Fang Su .

Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, The University of Aizu, Aizu-Wakamatsu, Fukushima, Japan

    Yong Liu

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Lipo Wang

  3. Computer Science and Mathematics, University of Sao Paulo, Ribeirao Preto, Brazil

    Liang Zhao

  4. School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China

    Zhengtao Yu

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Su, F., Li, J., Xiao, D., Duan, C. (2020). A New Distance Measure Between Atanassov’s Intuitionistic Fuzzy Sets Based on Mapping. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_78

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