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Title: Solutions of quasi-homogeneity equation of aggregation functions (English)
Author: Zhu, Feng-qing
Author: Wang, Xue-ping
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 62
Issue: 2
Year: 2026
Pages: 147-162
Summary lang: English
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Category: math
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Summary: The homogeneous functions play an important role in image processing, decision making and other relevant fields. In this article, we first give solutions of quasi-homogeneity equation of aggregation functions completely, and then we introduce the concept of triple generator of a quasi-homogeneous aggregation function, which is applied to construct a quasi-homogeneous aggregation function. (English)
Keyword: aggregation function
Keyword: quasi-homogeneity
Keyword: triple generator
MSC: 03B52
MSC: 03E72
DOI: 10.14736/kyb-2026-2-0147
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Date available: 2026-05-21T07:51:02Z
Last updated: 2026-05-21
Stable URL: http://hdl.handle.net/10338.dmlcz/153628
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Reference: [1] Cabrera, G., Ehrgott, M., Mason, A., Philpott, A.: Multi-objective optimisation of positively homogeneous functions and an application in radiation therapy..Oper. Res. Lett. 42 (2014), 268-272.
Reference: [2] Ebanks, B.: Quasi-homogeneous associative functions..Int. J. Math. Math. Sci. 21 (1998), 351-358.
Reference: [3] Jurio, A., Bustince, H., Pagola, M., Pradera, A., Yager, R. R.: Some properties of overlap and grouping functions and their application to image thresholding..Fuzzy Sets Syst. 229 (2013), 69-90.
Reference: [4] Jurio, A., Bustince, H., Pagola, M., Couto, P., Pedrycz, W.: New measures of homogeneity for image processing: an application to fingerprint segmentation..Soft Comput. 18 (2014), 1055-1066.
Reference: [5] Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's Inequality..Polish Scientific (PWN)/Silesian University, Warszawa, Katowice 1985.
Reference: [6] Mayor, G., Mesiar, R., Torrens, J.: On quasi-homogeneous copulas..Kybernetika 44 (2008), 745-756.
Reference: [7] Rückschlossová, T.: Homogeneous aggregation operators, computational intelligence, theory and applications, bernd reusch..Adv. Soft Comput. 33 (2005), 555-563.
Reference: [8] Su, Y., Zong, W., Mesiar, R.: Characterization of homogeneous and quasi-homogeneous binary aggregation functions..Fuzzy Sets Syst. 433 (2022), 96-107.
Reference: [9] Su, Y., Zong, W., Mesiar, R., Halaš, R.: The multiplicative Cauchy equation on [0,1] and its application to the quasi-homogeneity equation..Fuzzy Sets Syst. 491 (2024), 109052.
Reference: [10] Wang, X. P., Zhu, F. Q.: Note on the pseudo-homogeneous overlap and grouping functions..Fuzzy Sets Syst. 473 (2023), 108715.
Reference: [11] Zhu, F. Q., Wang, X. P.: Characterizations of quasi-homogeneous aggregation functions..
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