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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)

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.

Keywords

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

References

  1. 1.
    Anastassiou, G.A.: On H-fuzzy differentiation. Math. Balkanica 16, 155–193 (2002)MathSciNetGoogle Scholar
  2. 2.
    Bedregal, B.C.: On interval fuzzy negations. Fuzzy Sets Syst. 161(17), 2290–2313 (2010)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Chang, S.L., Zadeh, L.A.: On fuzzy mapping and control. Trans. Syst. Man Cybern. 2(1), 30–34 (1972)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (1978)CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    Dubois, D., Prade, H.: Toward fuzzy differential calculus: part 3, differentiation. Fuzzy Sets Syst. 8(3), 225–233 (1982)CrossRefMATHGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Random sets and fuzzy interval analysis. Fuzzy Sets Syst. 42(1), 87–101 (1991)CrossRefMATHGoogle Scholar
  7. 7.
    Gehrke, C.M., Walker, E.: Some comments on interval valued fuzzy sets. Int. J. Intell. Syst. 11, 751–759 (1996)CrossRefMATHGoogle Scholar
  8. 8.
    Guo, S.C.: Methods of the structured element in fuzzy analysis (I), (II). J. Liaoning Tech. Univ. (Nat. Sci.) 21(5), 670–673, 808–810 (2002)Google Scholar
  9. 9.
    Guo, S.C.: Homeomorphic properties between fuzzy number space and the family of standard bounded monotonic functions. Adv. Nat. Sci. 14(11), 1318–1321 (2004)Google Scholar
  10. 10.
    Guo, S.C.: Principle of mathematical analysis based on structured element. Northeast University Press, Shenyang (2004)Google Scholar
  11. 11.
    Guo, S.C.: Analytic express methods and calculus of fuzzy-valued function based on structured element. Sci. Technol. Eng. 15(5), 513–517 (2005)Google Scholar
  12. 12.
    Luo, C.Z.: Introduction of Fuzzy Sets. Introduction of Fuzzy Sets. Beijing Normal University Press, Beijing (1994)Google Scholar
  13. 13.
    Mizumoto, M., Tanaka, K.: Algebraic Properties of Fuzzy Numbers. International Conference on Cybernetics and Society, Washington (1976)Google Scholar
  14. 14.
    Moore, R.E., Lodwick, W.: Interval analysis and fuzzy set theory. Fuzzy Sets Syst. 135(1), 5–9 (2003)Google Scholar
  15. 15.
    Puri, M., Ralescu, D.: Differentials of fuzzy functions. Math. Anal. Appl. 91, 552–558 (1983)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    Shen, Z.H.: Methods and applications for interval analysis. Appl. Math. Numer. Math. 2, 1–28 (1982)Google Scholar
  17. 17.
    Wu, C.Z., Gong, Z.T.: On Henstock integral of fuzzy-number-valued functions I. Fuzzy Sets Syst. 120(3), 523–532 (2001)CrossRefMathSciNetMATHGoogle Scholar

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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