Generation of linear orders for intervals by means of aggregation functions

This work proposes a method to build admissible orders in terms of two aggregation functions and proves that some of the most used examples of total orders that appear in the literature are specific cases of this construction.

Abstract

The problem of choosing an appropriate total order is crucial for many applications that make use of extensions of fuzzy sets. In this work we introduce the concept of an admissible order as a total order that extends the usual partial order between intervals. We propose a method to build these admissible orders in terms of two aggregation functions and we prove that some of the most used examples of total orders that appear in the literature are specific cases of our construction.