On a class of binary operations: non-strict Archimedean aggregation functions

Abstract

The concept of nonstrict Archimedean aggregation function appears in a natural form when the orthomodularity property for pairs of aggregation function-t-norm and aggregation function-t-conorm connectives is studied. A theorem for the unicity of generator of these functions is proved. By using this result, which is already known for Archimedean t-norms, this kind of aggregation functions can be manipulated very easily. This is particularly interesting when dealing with classes obtained from the isomorphism relation.<>