On the median and its extensions

Authors:
Gleb Beliakov;Humberto Bustince;Javier Fernandez
Affiliations:
School of Information Technology, Deakin University, Australia;Departamento de Automática y Computación, Universidad Pública de Navarra, Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Pamplona, Spain
Venue:
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Year:
2010

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Abstract

We review various representations of the median and related aggregation functions. An advantage of the median is that it discards extreme values of the inputs, and hence exhibits a better central tendency than the arithmetic mean. However the value of the median depends on only one or two central inputs. Our aim is to design median-like aggregation functions whose value depends on several central inputs. Such functions will preserve the stability of the median against extreme values, but will take more inputs into account. A method based on graduation curves is presented.