On the Properties of Probabilistic Implications
A new family of implication operators, called probabilistic implications, are 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. Therefore, it seems that probabilistic implications might be a useful tool in approximate reasoning, knowledge extraction and decision making.
KeywordsFuzzy Logic Tail Dependence Continuous Random Variable Implication Operator Approximate Reasoning
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