TY - JOUR
T1 - Studying distribution functions of fuzzy random variables and its applications to critical value functions
AU - Wang, Shuming
AU - Watada, Junzo
PY - 2009/2
Y1 - 2009/2
N2 - In many fuzzy random optimization models, the objectives and constraints may consist of some distribution functions and critical value functions of prescribed fuzzy random variables. Therefore, we need to analyze the properties of those distribution functions and critical value functions so as to design more precise algorithms to solve such optimization problems. In this paper, we deal with the analytical properties of distributions functions of fuzzy random variables and discuss its applications to critical value functions. We first establish some continuity theorems for distribution functions of fuzzy random variables, which characterize the properties of right continuity, left continuity and continuity, respectively. Then, applying those continuity theorems, we study the properties of critical value functions of fuzzy random variables. The results obtained in this paper are useful in fuzzy random programming models.
AB - In many fuzzy random optimization models, the objectives and constraints may consist of some distribution functions and critical value functions of prescribed fuzzy random variables. Therefore, we need to analyze the properties of those distribution functions and critical value functions so as to design more precise algorithms to solve such optimization problems. In this paper, we deal with the analytical properties of distributions functions of fuzzy random variables and discuss its applications to critical value functions. We first establish some continuity theorems for distribution functions of fuzzy random variables, which characterize the properties of right continuity, left continuity and continuity, respectively. Then, applying those continuity theorems, we study the properties of critical value functions of fuzzy random variables. The results obtained in this paper are useful in fuzzy random programming models.
KW - Continuity theorem
KW - Critical value function
KW - Distribution function
KW - Fuzzy random optimization
KW - Fuzzy random variable
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M3 - Article
AN - SCOPUS:61749100218
SN - 1349-4198
VL - 5
SP - 279
EP - 292
JO - International Journal of Innovative Computing, Information and Control
JF - International Journal of Innovative Computing, Information and Control
IS - 2
ER -