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Open AccessArticle

Orness For Idempotent Aggregation Functions

Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain
Departamento de Matemáticas, Institute for Advanced Materials INAMAT, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain
Author to whom correspondence should be addressed.
Axioms 2017, 6(3), 25;
Received: 23 August 2017 / Revised: 15 September 2017 / Accepted: 17 September 2017 / Published: 20 September 2017
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
PDF [261 KB, uploaded 21 September 2017]


Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness—a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition. View Full-Text
Keywords: aggregation functions; lattice operators; idempotence; orness aggregation functions; lattice operators; idempotence; orness
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Legarreta, L.; Lizasoain, I.; Mardones-Pérez, I. Orness For Idempotent Aggregation Functions. Axioms 2017, 6, 25.

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