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Fuzzy Systems & Operations Research and Management pp 3–13Cite as

Analytic Representation Theorem of Fuzzy-Valued Function Based on Methods of Fuzzy Structured Element

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 367))

Abstract

The paper introduces the representation method of fuzzy structured element in fuzzy-valued function analytics systematically. It includes the concept of the fuzzy structured element, operations of fuzzy numbers, the analytic expression of fuzzy-valued functions and its differential and integral, they are all based on the fuzzy structured element. Theorems of the fuzzy structured element not only provide methods for analytic representation of fuzzy analysis and operations, but also start a new way for studying on the theory and application of fuzzy analysis.

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Author information

Authors and Affiliations

  1. Institute of Intelligence Engineering and Mathematics, Liaoning Technical University, Fuxin, 123000, China

    Ying Zhao

  2. Institute of Information Science and Engineering, Northeastern University, Shenyang, 110000, China

    Si-Cong Guo & Ying Zhao

  3. Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100190, China

    Hua-Dong Wang

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Hua-Dong Wang

Authors
  1. Si-Cong Guo
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  2. Ying Zhao
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  3. Hua-Dong Wang
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Corresponding author

Correspondence to Ying Zhao .

Editor information

Editors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Bing-Yuan Cao

  2. Foreign Affairs Office, National Defense University, Beijing, China

    Zeng-Liang Liu

  3. Higher Education Mega Center, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

  4. Zhuhai Campus, Beijing Normal University, Zhuhai, China

    Hong-Hai Mi

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© 2016 Springer International Publishing Switzerland

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Guo, SC., Zhao, Y., Wang, HD. (2016). Analytic Representation Theorem of Fuzzy-Valued Function Based on Methods of Fuzzy Structured Element. In: Cao, BY., Liu, ZL., Zhong, YB., Mi, HH. (eds) Fuzzy Systems & Operations Research and Management. Advances in Intelligent Systems and Computing, vol 367. Springer, Cham. https://doi.org/10.1007/978-3-319-19105-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-19105-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19104-1

  • Online ISBN: 978-3-319-19105-8

  • eBook Packages: EngineeringEngineering (R0)

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