THE PERCENTILES OF FUZZY NUMBERS AND THEIR APPLICATIONS

Document Type: Research Paper

Authors

1 Department of Mathematics, The teacher Training University, Tehran, Iran

2 Department of Statistics, Science and Research branch, Islamic Azad University, Tehran 14515-775, Iran

3 Department of Mathematics, Islamic Azad University, Arak, Iran

Abstract

The purpose of this study is to find the percentiles of fuzzy numbers
and to demonstrate their applications, which include finding weighted
means, dispersion indices, and the percentile intervals of fuzzy numbers. The
crisp approximations of fuzzy numbers introduced in this paper are new and
interesting for the comparison of fuzzy environments, such as a variety of economic,
financial, and engineering systems control problems.

Keywords


[1] S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciencees,
172 (2005), 73-89.
[2] G. K. Bhattacharyya and R. A. Johnson, Statistical concepts and methods, John Wiley and
Sons, 1977.
[3] C. Carlsson and R. Full´er, On possibilistic mean value and variance of fuzzy numbers, Fuzzy
Sets and Systems, 122 (2001), 315-326.
[4] D. Dubois and H. Prade, Fuzzy sets and systems, theory and applications, Academikc press,
New York, 1980.
[5] D. Dubois and H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24
(1987), 279-300.
[6] D. Dubois and H. Prade, Fundamentals of fuzzy sets, The Handbooks of Fuzzy Sets Series,
Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
[7] A. Galvan, Univariate equtions, Internet, 2005.
[8] M. Ma, A. Kandel and M. Friedman, A new approach for defuzzification, Fuzzy Sets and
Systems, 111 (2000), 351-356.
[9] C. R. Marques, P. D. Neves and L. M. Sarmento, Evaluating core inflation indicator, Economic
Modelling, 20 (2003), 765-775.
[10] P. McAdam and P. McNelis, Forecasting inflation with thick model and neural networks,
Economic Modelling, 22 (2005), 848-867.
[11] A. V. Patel and B. M. Mohan, Some numerical aspects of center of area defuzzification
method, Fuzzy Sets and Systems, 132 (2002), 401-409.
[12] A. K. Rose, A stable internatinal monetary systems emerges: Inflation targeting is Bretton
Woods, reversed, Journal of International Money and Finance, 26 (2007), 663-681.
[13] A. Saiedifar and E. Pasha, The percentiles of trapezoidal fuzzy numbers and their applications,
ICREM3, Kuala Lumpur, Malaysia, Proceedings of Pure Mathemathics Statistics, 2007, 61-
66.
[14] A. Stuart, J. K. Ord and Kendall’s, Advanced theory of statistics, Distribution Theory 6th
ed. New York, Oxford University Press, 1 (1998).
[15] L. A. Zadeh, A fuzzy set-theoritic interpretation of linguistic hedges, Journal of Cybernetics,
2 (1972), 4-34.