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

UR - http://www.scopus.com/inward/record.url?scp=78751629246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751629246&partnerID=8YFLogxK

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 -