On the variance of random fuzzy variables

In this paper a generalized definition of the variance of a random fuzzy variable is introduced on the basis of a suitable generalized metric defined on the wide class of the variable values.

[1]  Rudolf Kruse,et al.  Fuzzy set-theoretic methods in statistics , 1999 .

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

[3]  G. Matheron Random Sets and Integral Geometry , 1976 .

[4]  María Asunción Lubiano,et al.  The λ-mean squared dispersion associated with a fuzzy random variable , 2000, Fuzzy Sets Syst..

[5]  Carlo Bertoluzza,et al.  On a new class of distances between fuzzy numbers , 1995 .

[6]  H. Rådström An embedding theorem for spaces of convex sets , 1952 .

[7]  N. N. Lyashenko,et al.  Statistics of random compacts in euclidean space , 1983 .

[8]  Ilya Molchanov Limit Theorems for Unions of Random Closed Sets , 1993 .

[9]  Rudolf Kruse,et al.  On the variance of random sets , 1987 .

[10]  Michel Loève,et al.  Probability Theory I , 1977 .

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

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

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

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

[15]  B. Hambly Fractals, random shapes, and point fields , 1994 .

[16]  K. Hirota Concepts of probabilistic sets , 1981 .

[17]  Wolfgang Näther,et al.  Linear regression with random fuzzy observations , 1990 .

[18]  Pedro Gil,et al.  The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information , 1986 .

[19]  S. B. Boswell,et al.  A central limit theorem for fuzzy random variables , 1987 .

[20]  M. Fréchet Les éléments aléatoires de nature quelconque dans un espace distancié , 1948 .

[21]  R. Aumann INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[22]  Tadashi Imaizumi,et al.  A fuzzy statistical test of fuzzy hypotheses , 1993 .

[23]  J. Kacprzyk,et al.  Fuzzy regression analysis , 1992 .

[24]  R. Słowiński Fuzzy sets in decision analysis, operations research and statistics , 1999 .

[25]  V. Sazonov A Remark on Characteristic Functionals , 1958 .

[26]  Ralf Körner,et al.  An asymptotic α-test for the expectation of random fuzzy variables , 2000 .

[27]  Ralf Körner,et al.  On the variance of fuzzy random variables , 1997, Fuzzy Sets Syst..

[28]  Wolfgang Näther,et al.  Linear Regression With Random Fuzzy Numbers , 1998 .

[29]  D. Aldous The Central Limit Theorem for Real and Banach Valued Random Variables , 1981 .

[30]  Wolfgang Weil,et al.  An application of the central limit theorem for banach-space-valued random variables to the theory of random sets , 1982 .

[31]  Wolfgang Näther Linear Statistical Inference for Random Fuzzy Data , 1997 .

[32]  Phil Diamond,et al.  Fuzzy least squares , 1988, Inf. Sci..