Bustince, H.; Fernandez, J.; Kolesárová, A.; Mesiar, R. Directional monotonicity of fusion functions. (English) Zbl 1346.26004 Eur. J. Oper. Res. 244, No. 1, 300-308 (2015). Summary: In this paper we deal with fusion functions, i.e., mappings from \([0, 1]^n\) into \([0, 1]\). As a generalization of the standard monotonicity and recently introduced weak monotonicity, we introduce and study the directional monotonicity of fusion functions. For distinguished fusion functions the sets of all directions in which they are increasing are determined. Moreover, in the paper the directional monotonicity of piecewise linear fusion functions is completely characterized. These results cover, among others, weighted arithmetic means, OWA operators, the Choquet, Sugeno and Shilkret integrals. Cited in 38 Documents MSC: 26A48 Monotonic functions, generalizations 26B35 Special properties of functions of several variables, Hölder conditions, etc. 91B06 Decision theory Keywords:multiple criteria analysis; aggregation function; fusion function; directional monotonicity; piecewise linear function PDFBibTeX XMLCite \textit{H. Bustince} et al., Eur. J. Oper. 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