The Symmetry Related to the Characteristic Function of a Fuzzy Variable

Abstract:

In the paper, some properties related to characteristic function of a fuzzy variable are discussed based on uncertainty theory.

• Periodical: Advanced Materials Research (Volumes 821-822)
• Pages: 1484-1487
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.821-822.1484
• Online since: September 2013
• Authors: Sheng Ma*, Qin Jiang
• Keywords: Credibility Distribution, Fuzzy Variable, Symmetry

References

[1] Dubois D, Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, (1988).

[2] Kaufmann A. Introduction to the Theory of Fuzzy Subsets. Academic Press, New York, (1975).

[3] Liu B., Liu Y. K. Expected value of fuzzy variable and fuzzy expected value model. IEEE Transactions on Fuzzy Systems, Vol. 10, No. 4, 445-450, (2002).

DOI: 10.1109/tfuzz.2002.800692

[4] Liu B. Uncertainty Theory: An Introduction to its axiomatic Foundations. Springer-Verlag, Heidelberg, (2004).

[5] Lee E.S., Li R.J. Comparison of fuzzy numbers based on the probability measure of fuzzy events. Computer and Mathematics with Applications 15(1988)887-896.

DOI: 10.1016/0898-1221(88)90124-1

[6] Liou T.S., Wang M.J. Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems 50(1992)247-255.

DOI: 10.1016/0165-0114(92)90223-q

[7] Liu, B. A survey of credibility theory. Fuzzy Optimization and Decision Making 5(2006) 1-19.

[8] Nahmias S. Fuzzy variables. Fuzzy Sets and Systems, Vol. 1, 97-100, (1978).

[9] Peng J., Henry M.K. Mok, Wai-Man Tse. From Credibility Distribution to Fuzzy Dominance with Applications to Economics and Finance. Proceedings of the 4th International Conference on Information and Management Sciences (IMS2005), (2005).

[10] Peng,J., Liu, B. Some properties of optimistic and pessimistic values of fuzzy variables. Proceedings of the Tenth IEEE International Conference on Fuzzy Systems 2 (2004) 292-295.

DOI: 10.1109/fuzzy.2004.1375493

[11] Peng, J., Mok, H. M. K., Tse, W. -M. Fuzzy dominance based on credibility distributions. Lecture Notes in Artificial Intelligent (LNAI 3613) (2005) 295-303.

[12] J. Peng, Q. Jiang, C. Rao. Fuzzy Dominance: A new approach for ranking fuzzy variable using inverse credibility distributions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. Vol, 15, (2007), 29 –41.

DOI: 10.1142/s0218488507004583

[13] Q. Jiang, S. Ma. Some Remarks on properties related to characteristic function of fuzzy variable and rough variable. Proceedings of 2009 International Conference on Management Science and Information System, 2009, Vol 1, 1601-1608.

[14] Q. Jiang, Some Remarks on Charactertics Function and Density Function of Uncertain Variable. The 2011 International Symposium on Intelligence Information Processing and Trusted Computing , 2011, Vol 1, 801-804.

DOI: 10.1109/iptc.2011.36

[15] Wang, X., Kerre, E. E. Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 118 (2001) 375-385.

DOI: 10.1016/s0165-0114(99)00062-7

[16] Zhu Y, Liu B. Characteristic functions for fuzzy variables, Technical Report, (2003).

[17] Zadeh L.A. Fuzzy sets. Information and Control, Vol. 8, 338-353, (1965).