Random Numbers and Monte Carlo Approximation in Fuzzy Riemann Integral

Volume 4, Issue 1, pp 93--101 http://dx.doi.org/10.22436/jmcs.04.01.12

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)

• 2548 Downloads
• 3695 Views

Authors

Behuroz Fathi-Vajargah - Department of statistics, University of Guilan, Iran Akram Heidary-Harzavily - Department of statistics, university of Guilan, Iran

Abstract

In this paper, we want to improve Monte Carlo approximation in fuzzy Riemann integral it means that calculate exact amount of fuzzy Riemann integral based on \(\alpha\)-level sets with partition of generating function of random numbers' RAND' in commercial software MATLAB.

Share and Cite

Keywords

• fuzzy Riemann integral
• \(\alpha\)-level sets.

MSC

•  65C05
•  26A42
•  26E50

References

• [1] H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer Academic Publishers, Boston (1991)
  • Google Scholar


• [2] H.-C. Wu , The fuzzy Riemann integral and its numerical integration, Fuzzy Sets and Systems, 110 (2000), 1--25
  • View Article
  • Google Scholar


• [3] T. M. Apostol, Mathematical Analysis, Addison-Wesly, Reading (1974)
  • View Article
  • Google Scholar


• [4] J. J. Buckly , Fuzzy probability and statistics, Springer, Berlin (2006)
  • View Article
  • Google Scholar


• [5] H.-C. Wu, The improper fuzzy Riemann integral and its numerical, Inform. Sci., 111 (1998), 109--137
  • View Article
  • Google Scholar


• [6] H.-C. Wu, Evaluate Fuzzy Riemann Integrals Using the Monte Carlo Method, Journal of Mathematical Analysis and Applications, 264 (2001), 324--343
  • View Article
  • Google Scholar


• [7] M. S. Bazarra, C. M. Shetty, Nonlinear programming, John Wiley & Sons, New York (1993)
  • Google Scholar


• [8] W. Rudin , Real and Complex Analysis, McGraw-Hill, New York (1987)
  • View Article
  • Google Scholar


• [9] M. Sakawa, H. Yano, Feasibility and pareto optimality for multiobjective linear and linear fractional programming problems with fuzzy parameters, in: The interface between artificial intelligence and operations research in fuzzy environment, 1990 (1990), 213--232
  • Google Scholar


• [10] J. R. Sims, Z. Y. Wang, Fuzzy measures and fuzzy integrals: an overview, Internat. J. Gen. Systems, 17 (1990), 157--189
  • View Article
  • Google Scholar