On distance between fuzzy variables

Distance between fuzzy variables has been defined in many ways, for example, Hausdorff-like distance and Hamming distance. This paper discusses the properties of a new distance between fuzzy variables defined by expected value operator. Furthermore, a metric space of fuzzy variables is defined and the completeness of this space is proved. Finally, the distances between fuzzy vectors, fuzzy random vectors, and random fuzzy vectors are given.

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

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

[3]  Azriel Rosenfeld,et al.  A Modified Hausdorff Distance Between Fuzzy Sets , 1999, Inf. Sci..

[4]  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.

[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]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

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

[9]  Azriel Rosenfeld,et al.  On a metric distance between fuzzy sets , 1996, Pattern Recognit. Lett..

[10]  Azriel Rosenfeld,et al.  Distances between fuzzy sets , 1985, Pattern Recognit. Lett..

[11]  M. Puri,et al.  Limit theorems for fuzzy random variables , 1986, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

[13]  Xiang Li,et al.  A Sufficient and Necessary Condition for Credibility Measures , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Laurence Boxer,et al.  On Hausdorff-like metrics for fuzzy sets , 1997, Pattern Recognit. Lett..

[15]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

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

[17]  Janusz Kacprzyk,et al.  Multistage Fuzzy Control: A Prescriptive Approach , 1997 .

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

[19]  Baoding Liu,et al.  Redundancy optimization problems with uncertainty of combining randomness and fuzziness , 2004, Eur. J. Oper. Res..

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

[21]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[22]  A. Ralescu,et al.  Simulation, Knowledge-Based Computing, and Fuzzy Statistics , 1987 .

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

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

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

[26]  P. Kloeden,et al.  Metric spaces of fuzzy sets , 1990 .

[27]  Xiang Li,et al.  Maximum Entropy Principle for Fuzzy Variables , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[28]  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..

[29]  Jiu-lun Fan.  Note on Hausdorff-like metrics for fuzzy sets , 1998, Pattern Recognit. Lett..

[30]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..