TY - JOUR
T1 - Some properties of T-independent fuzzy variables
AU - Wang, Shuming
AU - Watada, Junzo
PY - 2011/3
Y1 - 2011/3
N2 - T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variables under possibility, necessity and credibility measures. Subsequently, on the basis of left continuous t-norms, some formulas are derived on the "max" and "min" operations of the T-independent fuzzy variables in possibility distribution and in expectation. Finally, making use of continuous Archimedean t-norms, several convergence properties are discussed for T-independent fuzzy variables in credibility and in expectation, respectively, and some laws of large numbers are proved as well.
AB - T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variables under possibility, necessity and credibility measures. Subsequently, on the basis of left continuous t-norms, some formulas are derived on the "max" and "min" operations of the T-independent fuzzy variables in possibility distribution and in expectation. Finally, making use of continuous Archimedean t-norms, several convergence properties are discussed for T-independent fuzzy variables in credibility and in expectation, respectively, and some laws of large numbers are proved as well.
KW - Convergence
KW - Fuzzy variable
KW - Independence
KW - Law of large numbers
KW - Operation
KW - T-norm
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U2 - 10.1016/j.mcm.2010.11.006
DO - 10.1016/j.mcm.2010.11.006
M3 - Article
AN - SCOPUS:78751629246
VL - 53
SP - 970
EP - 984
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
SN - 0895-7177
IS - 5-6
ER -