On admissible pairs of aggregation functions based on quasi-linear means and related families

Admissible orders play a key role in ranking subintervals of the unit interval. In 2013, Bustince et al. proposed constructing such relations by means of admissible pairs of aggregation functions. The only significant example in the literature is a pair of weighted arithmetic means with different weights. In this paper, we present a method for constructing admissible pairs of aggregation functions, which allows us to verify the admissibility of various function classes, including quasi-linear means, Archimedean t-norms (and t-conorms), and certain strictly Schur-convex (or Schur-concave) functions. Furthermore, we examine the relationship between admissible orders generated by admissible pairs of aggregation functions and the (α, \b{eta})-order, identifying cases where these two notions do not coincide.

💡 Research Summary

The paper addresses the problem of constructing total orders on the family of closed sub‑intervals of the unit interval