CVaR Reduced Fuzzy Variables and Their Second Order Moments

Document Type : Research Paper

Authors

1 College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China

2 College of Management, Hebei University, Baoding 071002, Hebei, China

Abstract

Based on credibilistic value-at-risk (CVaR) of regular
fuzzy variable, we introduce a new CVaR reduction method for
type-2 fuzzy variables. The reduced fuzzy variables are
characterized by parametric possibility distributions. We establish
some useful analytical expressions for mean values and second
order moments of common reduced fuzzy variables. The convex properties of second order moments with respect to parameters are also discussed. Finally, we take second order moment as a new risk measure, and develop a mean-moment model to optimize fuzzy portfolio selection problems. According to the analytical formulas of second order moments, the mean-moment optimization model is equivalent to parametric
quadratic convex programming problems, which can be solved by general-purpose optimization software. The solution results reported in the numerical experiments demonstrate the credibility of the proposed optimization method.

Keywords

References

[1] J. Chachi and S. M. Taheri, A uni ed approach to similarity measure between intuitionistic
fuzzy sets, Int. J. Intell. Syst., 28 (2013), 669-685.
[2] S. Coupland and R. John, A fast geometric method for defuzzi cation of type-2 fuzzy sets,
IEEE T. Fuzzy Syst., 16(4) (2008), 929-941.
[3] D. Dubois and H. Prade, Operations in a fuzzy-valued logic, Inform. Control, 43(2) (1979),
224-240.
[4] M. Hao and J. M. Mendel, Similarity measures for general type-2 fuzzy sets based on the
-plane representation, Inform. Sciences, 227 (2014), 197-215.
[5] B. Hu and C. Wang, On type-2 fuzzy relations and interval-valued type-2 fuzzy sets, Fuzzy
Set. Syst., 236 (2014), 1-32.
[6] C. Huang, Y. Wang, H. Chen, H. Tsai, J. Jian, A. Cheng and J. Liao, Application of cellular
automata and type-2 fuzzy logic to dynamic vehicle path planning, Appl. Soft Comput., 19
(2014), 333-342.
[7] C. M. Hwang, M. S. Yang, W. L. Hung and M. G. Lee, A similarity measure of intuitionistic
fuzzy sets based on the Sugeno integral with its application to pattern recognition, Inform.
Sciences, 189 (2012), 93-109.
[8] P. Kundu, S. Kar and M. Maiti, Fixed charge transportation problem with type-2 fuzzy vari-
ables, Inform. Sciences, 255 (2014), 170-186.
[9] B. Liu, Uncertainty theory, Springer-Verlag, Berlin, 2004.
[10] F. Liu, An ecient centroid type-reduction strategy for general type-2 fuzzy logic system,
Inform. Sciences, 178(9) (2008), 2224-2236.
[11] H. M. Markowitz, Portfolio selection, J. Financ., 7 (1952), 77-91.
[12] J. M. Mendel, Uncertain rule-based fuzzy logic system: introduction and new directions,
Prentice Hall, Upper Saddle River, N.J., 2001.
[13] J. M. Mendel and R. I. John, Type-2 fuzzy sets made simple, IEEE T. Fuzzy Syst., 10(2)
(2002), 117-127.
[14] M. Mizumoto and K. Tanaka, Some properties of fuzzy sets of type 2, Inform. Control, 31(4)
(1976), 312-340.
[15] M. Moharrer, H. Tahayori, L. Livi, A. Sadeghian and A. Rizzi, Interval type-2 fuzzy sets to
model linguistic label perception in online services satisfaction, Soft Comput., 19(1) (2015),
237-250.
[16] S. C. Ngan, A type-2 linguistic set theory and its application to multi-criteria decision mak-
ing, Comput. Ind. Eng., 64(2) (2013), 721-730.
[17] A. D. Torshizi and M. H. F. Zarandi, A new cluster validity measure based on general type-2
fuzzy sets: application in gene expression data clustering, Knowl-Based. Syst., 64 (2014),
81-93.
[18] P. Wang, Fuzzy contactibility and fuzzy variables, Fuzzy Set. Syst., 8(1) (1982), 81-92.
[19] L. A. Zadeh, The concept of a linguistic variable and its application to approximate
reasoning{I,II,III, Inform. Sciences, 8(3) (1975), 199-249; 8(4) (1975), 301-357; 9(1) (1975),
43-80.
Iranian Journal of Fuzzy Systems
Volume 12, Issue 5 - Serial Number 5
September and October 2015
Pages 45-75

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