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

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


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.


Fuzzy structured element Fuzzy numbers Fuzzy-valued functions Analytic representation theorems Differential and integral calculus 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Intelligence Engineering and MathematicsLiaoning Technical UniversityFuxinChina
  2. 2.Institute of Information Science and EngineeringNortheastern UniversityShenyangChina
  3. 3.Research Center on Fictitious Economy and Data ScienceChinese Academy of SciencesBeijingChina
  4. 4.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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