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Three types of monotonicity of averaging functions

Beliakov,G, Calvo,T and Wilkin,T 2014, Three types of monotonicity of averaging functions, Knowledge-Based Systems, vol. 72, pp. 114-122, doi: 10.1016/j.knosys.2014.08.028.

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Title Three types of monotonicity of averaging functions
Author(s) Beliakov,GORCID iD for Beliakov,G orcid.org/0000-0002-9841-5292
Calvo,T
Wilkin,TORCID iD for Wilkin,T orcid.org/0000-0003-4059-1354
Journal name Knowledge-Based Systems
Volume number 72
Start page 114
End page 122
Total pages 9
Publisher Elsevier
Place of publication Amsterdam , Netherlands
Publication date 2014-12-01
ISSN 0950-7051
Keyword(s) Aggregation functions
Means
Monotonicity
Weak monotonicity
Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science
AGGREGATION OPERATORS
WEIGHTING FUNCTIONS
CONSTRUCTION
INTERPOLATION
SHIFT
Summary Monotonicity 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.
Language eng
DOI 10.1016/j.knosys.2014.08.028
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2014, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30069282

Document type: Journal Article
Collection: School of Information Technology
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