A new kind of generalized fuzzy integrals

Volume 9, Issue 3, pp 1396--1401 http://dx.doi.org/10.22436/jnsa.009.03.63

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1789 Downloads
• 2596 Views

Authors

Cuilian You - College of Mathematics and Information Science, Hebei University, Baoding 071002, China. Hongyan Ma - College of Mathematics and Information Science, Hebei University, Baoding 071002, China. Huae Huo - College of Mathematics and Information Science, Hebei University, Baoding 071002, China.

Abstract

Fuzzy integral is an important tool to study fuzzy differential equations. Under normal circumstances, there are two basic limitations: limited of integral interval and boundedness of integrand. However, in practical problems, it is dificult to calculate when integral interval is not common interval. Then fuzzy integral on infinite interval is taken into consideration. In this paper, definition of a kind of generalized Liu integral is given. Moreover, properties and theorems of this kind of generalized fuzzy integral are obtained.

Share and Cite

Keywords

• Fuzzy variable
• fuzzy process
• Liu process
• generalized fuzzy integral.

MSC

•  34A07

References

• [1] X. Chen, Z. Qin, A new existence and uniqueness theorem for fuzzy differential equation , Int. J. Fuzzy Syst., 13 (2011), 148-151.


• [2] W. Dai, Reflection principle of Liu process, http://orsc.edu.cn/process /071110.pdf. , (),


• [3] W. Dai, Lipschitz continuity of Liu process, http://orsc.edu.cn/process /080831.pdf. , (),


• [4] J. Gao, Credibiltistic option pricing: A new model, http://orsc.edu.cn/process /071124.pdf. , (),


• [5] M. Ha, X. Li , Choquet integral based on self-dual measure, Journal of Hebei University (Natrual Science Edition), 28 (2008), 113-115.


• [6] X. Li, B. Liu, A sufficent and necessary condition for credibility measures, Int. J. Uncertainty, Fuzziness & Knowledge-Based Syst., 14 (2006), 527-535.


• [7] B. Liu, Uncertainty Theory, Springer-Verlag, Berlin (2004)


• [8] B. Liu, A survey of credibility theory, Fuzzy Optim. and Decis. Mak., 5 (2006), 387-408.


• [9] B. Liu , Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin (2007)


• [10] B. Liu, Fuzzy process, hybrid process and uncertain process, J. Uncertain Syst., 2 (2008), 3-16.


• [11] B. Liu, Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Trans. Fuzzy Syst., 10 (2002), 445-450.


• [12] J. Peng, A general stock model for fuzzy markets, J. Uncertain Syst., 2 (2008), 248-254.


• [13] Z. Qin, X. Li, Option pricing formula for fuzzy financial market , J. Uncertain Syst., 2 (2008), 17-21.


• [14] Z. Qin, M. Wen , On analytic functions of complex Liu process, J. Intell. Fuzzy Syst., 28 (2015), 1627-1633.


• [15] M. Radko, Fuzzy measure and integral, Fuzzy Sets Syst., 156 (2005), 365-370.


• [16] M. Sugeno, Theory of fuzzy integrals and its applications, Ph. D. Dissertation, Institute of Technology, Tokyo (1974)


• [17] C. You, H. Huo, W. Wang, Multi-dimensional Liu process, differential and integral , J. East Asian Math., 29 (2013), 13-22.


• [18] C. You, G. Wang , Properties of a new kind of fuzzy integral, J. Hebei University (Natural Science Edition), 31 (2011), 337-340.


• [19] C. You, W. Wang, H. Huo, Existence and uniqueness theorem for fuzzy differential equations, J. Uncertain Syst., 7 (2013), 303-315.


• [20] L. A. Zadeh, Fuzzy sets, Info. Control, 8 (1965), 338-353.


• [21] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1 (1978), 3-28.


• [22] Y. Zhu, Fuzzy optimal control with application to portfolio selection , http://orsc.edu.cn/process /080117.pdf., (),