Fuzzy implications based on quasi-copula and fuzzy negations

Abstract

In this particular paper the connection of fuzzy implications to the basic concepts of probability theory such as copula, quasi-copula and semi-copula is being studied. This study showed that fuzzy implications produced through copula, quasicopula or semi-copula, apart from having as a common characteristic the Lipschitz condition with constant 1, this characteristic is also the cornerstone for grouping fuzzy implications according to the original generator which is no other than a copula, quasi-copula or semi-copula.