Axiomatization and construction of orness measures for aggregation functions

• Published in: International journal of intelligent systems Vol. 36; no. 5; pp. 2208 - 2228
• Main Authors: Pérez‐Fernández, Raúl, Ochoa, Gustavo, Montes, Susana, Díaz, Irene, Fernández, Javier, Paternain, Daniel, Bustince, Humberto
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.05.2021
• Subjects: Agglomeration; aggregation function; Axioms; Construction methods; Intelligent systems; orness measure; OWA function
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.22376

The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the choice of aggregation function is sometimes restricted to a desired value of orness (orness‐directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.