Chance measure for hybrid events with fuzziness and randomness

In many cases, fuzziness and randomness simultaneously appear in a system. Hybrid variable is a tool to describe this phenomena. Fuzzy random variable and random fuzzy variable are instances of hybrid variable. In order to measure hybrid event, a concept of chance measure is proposed in this paper. Furthermore, several useful properties about this measure are proved such as self-duality, subadditivity and semicontinuity. Some concepts are also presented such as chance distribution, expected value, variance, moments, critical values, entropy, distance and sequence convergences.

[1]  Yian-Kui Liu,et al.  A Bank Hedging Decision Problem , and formulated it as a stochastic possibilistic bank hedging decision model , 2004 .

[2]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[3]  Xiang Li,et al.  On distance between fuzzy variables , 2008, J. Intell. Fuzzy Syst..

[4]  Baoding Liu,et al.  Random fuzzy dependent-chance programming and its hybrid intelligent algorithm , 2002, Inf. Sci..

[5]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[6]  R. Kruse,et al.  Statistics with vague data , 1987 .

[7]  Baoding Liu,et al.  Entropy of Credibility Distributions for Fuzzy Variables , 2008, IEEE Transactions on Fuzzy Systems.

[8]  Baoding Liu,et al.  Continuity theorems and chance distribution of random fuzzy variables , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[10]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[11]  Jinwu Gao,et al.  The Independence of Fuzzy Variables with Applications to Fuzzy Random Optimization , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  Lixing Yang,et al.  On Inequalities And Critical Values Of Fuzzy Random Variables , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[14]  Baoding Liu,et al.  Some inequalities of random fuzzy variableswith application to moment convergence , 2005 .

[15]  Liu Yian-Kui,et al.  Random fuzzy programming with chance measures defined by fuzzy integrals , 2002 .

[16]  Yian-Kui Liu,et al.  Fuzzy random programming with equilibrium chance constraints , 2005, Inf. Sci..

[17]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[18]  Yian-Kui Liu,et al.  Expected Value Operator of Random Fuzzy Variable, Random Fuzzy Expected Value Models , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[19]  Yian-Kui Liu,et al.  Fuzzy Random Variables: A Scalar Expected Value Operator , 2003, Fuzzy Optim. Decis. Mak..

[20]  Baoding Liu,et al.  Fuzzy random dependent-chance programming , 2001, IEEE Trans. Fuzzy Syst..

[21]  Huibert Kwakernaak,et al.  Fuzzy random variables--II. Algorithms and examples for the discrete case , 1979, Inf. Sci..

[22]  George Emanuel,et al.  Definitions and Theorems , 1986 .

[23]  Baoding Liu,et al.  Fuzzy random chance-constrained programming , 2001, IEEE Trans. Fuzzy Syst..