Fuzzy Information and Engineering 2010 pp 65-74 | Cite as
Discussion on Natural Fuzzy Extension and Joint Fuzzy Extension of the Rational Function
Conference paper
Abstract
According to the knowledge of interval analysis, relations between natural fuzzy extension and joint fuzzy extension of rational function are discussed in this paper . On the basis of the natural fuzzy extension of rational function , two solutions to the joint fuzzy extension of rational function are put forward. Based on the structured element method, the fuzzy arithmetic with equality constraints is turned into the operation of two monotone functions with the same monotonic form on [0,1]. From this transition we get analytical expression of joint fuzzy extension of the rational function.
Keywords
Interval analysis Joint fuzzy extension Natural fuzzy extension Structured elementPreview
Unable to display preview. Download preview PDF.
References
- 1.Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)MATHCrossRefMathSciNetGoogle Scholar
- 2.Chang, S.S.L., Zadeh, L.A.: On fuzzy mapping and control. IEEE Trans. Syst., Man Cybern. 2, 30–40 (1972)MATHMathSciNetGoogle Scholar
- 3.Shen, Z.H.: Interval analytical method and its application. Applied Mathematics and Computational Mathematics 2, 1–28 (1983)Google Scholar
- 4.Wu, C.X., Ma, M.: Fundamentals of Fuzzy Analysis. National Defence Industry Press, Bei Jing (1991)Google Scholar
- 5.Guo, S.Z., Su, Z.X., Wang, L.: Method of structured Element in Fuzzy Analysis and Calculation. Fuzzy System and Mathematics 18(3), 68–75 (2004)MathSciNetGoogle Scholar
- 6.Guo, S.Z.: Transformation group of monotone funtions with same monotonic form on [-1,1]and operations of fuzzy numbers. Fuzzy System and Mathematics 19(3), 105–110 (2005)Google Scholar
- 7.Guo, S.Z.: Principle of Fuzzy Mathematical Analysis Based on Strutured Element. Northeastern University Press, Shen Yang (2004)Google Scholar
- 8.Guo, S.Z., Liu, H.T.: Equality and Identity of Fuzzy Numbers and Fuzzy Arithmetic with Equality Constraints. Fuzzy System and Mathematics 22(6), 76–82 (2008)MathSciNetGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2010