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Three types of monotonicity of averaging functions
journal contribution
posted on 2014-12-01, 00:00 authored by Gleb BeliakovGleb Beliakov, T Calvo, Tim WilkinTim WilkinMonotonicity with respect to all arguments is fundamental to the definition of aggregation functions, which are one of the basic tools in knowledge-based systems. The functions known as means (or averages) are idempotent and typically are monotone, however there are many important classes of means that are non-monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. In this paper we discuss the concepts of directional and cone monotonicity, and monotonicity with respect to majority of inputs and coalitions of inputs. We establish the relations between various kinds of monotonicity, and illustrate it on various examples. We also provide a construction method for cone monotone functions.
History
Journal
Knowledge-Based SystemsVolume
72Pagination
114 - 122Publisher
ElsevierLocation
Amsterdam , NetherlandsPublisher DOI
ISSN
0950-7051Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2014, ElsevierUsage metrics
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