On fixed point theorems of Gregori and Sapena

Abstract

The fixed point theorem of Gregori and Sapena was studied. It was found that the t-norms and related t-conorms were important operation in fuzzy sets and fuzzy logics. A t-norm T was extended to a countable infinitary operation. The Dombi family of t-norms and the Aczel-Alsina family of t-norms was also elaborated.