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Directional and ordered directional monotonicity of mixture functions

conference contribution
posted on 2018-01-01, 00:00 authored by J Špirková, Gleb BeliakovGleb Beliakov, H Bustince, J Fernández
© Springer International Publishing AG 2018. In this contribution, we discuss the concepts of so-called fusion functions, pre-aggregation functions and their directional and ordered directional monotonicity in the context of mixture functions. Mixture functions represent a special class of weighted averaging functions whose weights are determined by continuous weighting functions which depend on the input values. They need not be monotone, in general. If they are monotone increasing, they also belong to the important class of aggregation functions. If the are directionally monotone, they belong to the class of pre-aggregation functions. Currently there is increased interest in studying generalized forms of monotonicity such as weak, directional or ordered directional monotonicity due to their possible application in fields such classification or image processing. This paper discusses properties of selected mixture functions with special emphasis on their directional and ordered directional monotonicity. The concept of directional and ordered directional monotonicity of mixture functions is investigated with respect to linear and quadratic weighting functions.

History

Volume

581

Pagination

96-105

Location

Skovde, Sweden

Start date

2017-06-19

End date

2017-06-22

ISSN

2194-5357

ISBN-13

9783319593050

Language

eng

Publication classification

E1 Full written paper - refereed

Editor/Contributor(s)

Torra V, Mesiar R, Baets B

Title of proceedings

AGOP 2017: Aggregation Functions in Theory and in Practice : Proceedings from the 9th International Summer School of Aggregation Operators

Event

Aggregation Operators. Summer School (2017 : 9th : Skovde, Sweden)

Publisher

Springer

Place of publication

Berlin, Germany

Series

Advances in Intelligent Systems and Computing

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