Some fuzzy stochastic orderings for fuzzy random variables

A new approach to stochastic ordering of fuzzy random variables is investigated in this paper. The traditional definitions of stochastic ordering, hazard rate ordering, and also mean residual life ordering were extended and proposed the unified indexes to ranking fuzzy random variables. Finally, we study the stochastic ordering of fuzzy order statistics by using our proposed approach and established some properties.

[1]  Marzieh Akbari,et al.  Order statistics using fuzzy random variables , 2009 .

[2]  Irina Georgescu,et al.  Ranking fuzzy choice functions by their rationality indicators , 2007, Fuzzy Optim. Decis. Mak..

[3]  P. Bickel,et al.  Descriptive Statistics for Nonparametric Models. III. Dispersion , 1976 .

[4]  Z. Birnbaum.  On Random Variables with Comparable Peakedness , 1948 .

[5]  Didier Dubois,et al.  An Extension of Stochastic Dominance to Fuzzy Random Variables , 2010, IPMU.

[6]  A. Yazenin.  Linear programming with random fuzzy data , 1992 .

[7]  Ching-Hsue Cheng,et al.  A new approach for ranking fuzzy numbers by distance method , 1998, Fuzzy Sets Syst..

[8]  Emmanuel Valvis,et al.  A new linear ordering of fuzzy numbers on subsets of $${{\mathcal F}({\pmb{\mathbb{R}}}})$$ , 2009, Fuzzy Optim. Decis. Mak..

[9]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[10]  V. Zwet.  Convex transformations: A new approach to skewness and kurtosis •) , 1964 .

[11]  Majid Asadi,et al.  The mean residual life function of a k-out-of-n structure at the system level , 2006, IEEE Transactions on Reliability.

[12]  H. B. Mann,et al.  On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other , 1947 .

[13]  Gisella Facchinetti.  Ranking Functions Induced by Weighted Average of Fuzzy Numbers , 2002, Fuzzy Optim. Decis. Mak..

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

[15]  Hsien-Chung Wu,et al.  The Central Limit Theorems for Fuzzy Random Variables , 1999, Inf. Sci..

[16]  Kuen-Suan Chen,et al.  Decision making in assessing process capability indices , 2001 .

[17]  James C. Bezdek,et al.  Analysis of fuzzy information , 1987 .

[18]  Soheil Sadi-Nezhad,et al.  Ranking fuzzy numbers by preference ratio , 2001, Fuzzy Sets Syst..

[19]  James J. Buckley,et al.  A fuzzy ranking of fuzzy numbers , 1989 .

[20]  Jing-Shing Yao,et al.  Ranking fuzzy numbers based on decomposition principle and signed distance , 2000, Fuzzy Sets Syst..

[21]  E. Lehmann.  Ordered Families of Distributions , 1955 .

[22]  F. Samaniego.  On Closure of the IFR Class Under Formation of Coherent Systems , 1985, IEEE Transactions on Reliability.

[23]  Emmanuel Valvis.  A new linear ordering of fuzzy numbers on subsets of F (\pmb\mathbb R ). , 2009 .

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

[25]  Hans-Jürgen Zimmermann,et al.  Fuzzy set theory , 1992 .

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

[27]  R. Zarei,et al.  Bayesian system reliability assessment under the vague environment , 2011, Appl. Soft Comput..