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The Approximation of Fuzzy Number Value, Ambiguity and Expected Interval

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Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2020)

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 88))

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Abstract

The complexity of the membership function of fuzzy numbers affects the solution to fuzzy problems. When the membership function is relatively complex, it is necessary to use other forms of simple fuzzy numbers to approximate the general fuzzy numbers. In this paper, we mainly use fuzzy sequence to deal with the approximation of general fuzzy numbers. First, we introduce some relevant definitions and properties of fuzzy numbers and define the value, ambiguity and expected interval of the fuzzy number. we use the 1-norm to define the distance between any two fuzzy numbers. In addition, using the given continuous reduction function and its definition of variable upper limited integral function and continuous modulus to help the approximation operation. Using these tools, we can further study the approximation of the value, ambiguity and expected interval of the fuzzy number. Finally, some examples are given to illustrate that the accuracy of the result obtained by keeping the parameter approximation is higher.

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Authors and Affiliations

  1. China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Hong Zhang & Xiaoqiu Song

Authors
  1. Hong Zhang
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  2. Xiaoqiu Song
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Editor information

Editors and Affiliations

  1. College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UK

    Hongying Meng

  2. School of Electronical Information and Artificial Engineering, Shaanxi University of Science and Technology, Xi’an, China

    Tao Lei

  3. College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge, UK

    Maozhen Li

  4. College of Electrical and Information, Hunan University, Changsha, China

    Kenli Li

  5. Division of Intelligent Future Technologies, Mälardalen University, Västerås, Västmanlands Län, Sweden

    Ning Xiong

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

    Lipo Wang

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Zhang, H., Song, X. (2021). The Approximation of Fuzzy Number Value, Ambiguity and Expected Interval. In: Meng, H., Lei, T., Li, M., Li, K., Xiong, N., Wang, L. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2020. Lecture Notes on Data Engineering and Communications Technologies, vol 88. Springer, Cham. https://doi.org/10.1007/978-3-030-70665-4_118

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