On the Distributivity of Fuzzy Implications over Continuous Archimedean Triangular Norms

Recently, the distributivity of fuzzy implications over t-norms, t-conorms and uninorms was studied in many articles. In this paper we characterize functions which satisfy one of the four generalized distributivity equations of classical implication in the case when t-conorms are continuous and Archimedean. Using the obtained characterizations we describe some solutions which are fuzzy implications. The methods presented in this work can be applied to the remaining equations in the case when t-norms and t-conorms are continuous Archimedean and corresponding results obtained. Other than the main theorems some new results connected with the additive Cauchy functional equation are also shown.

• Type: Conference
• Year: 2010
• Where: ICAISC
• Authors: Michal Baczynski
• Keywords: Artificial Intelligence, Classical Implication, Distributivity Equations, Fuzzy Implications, ICAISC 2010