Probabilistic implications

被引:41
作者
Grzegorzewski, Przemyslaw [1 ,2 ]
机构
[1] Polish Acad Sci, Syst Res Inst, PL-01447 Warsaw, Poland
[2] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw, Poland
关键词
Fuzzy implication; S-implication; Copula; Conditional probability; Dependence; Approximate reasoning; FUZZY IMPLICATION OPERATORS;
D O I
10.1016/j.fss.2013.01.003
中图分类号
TP301 [理论、方法];
学科分类号
080201 [机械制造及其自动化];
摘要
A new family of implication operators, called probabilistic implications, is discussed. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that probabilistic fuzzy implications have some interesting properties, especially those connected with the dependence structure of the underlying environment. Moreover, some other approaches for combining probability and theory of fuzzy implications are considered. In particular, it is shown that in probabilistic environment S-implications coincide with QL-implications. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码:53 / 66
页数:14
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