Aggregation Operators Based on Indistinguishability Operators

Abstract

This article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value l that is as similar to a as to b or, in a more logical language, the degrees of equivalence of l with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability operators associated to t-norms that are ordinal sums.