Hierarchical data fusion processes involving the Möbius representation of capacities Beliakov, Gleb, Gagolewski, Marek and James, Simon 2021, Hierarchical data fusion processes involving the Möbius representation of capacities, Fuzzy Sets and Systems, pp. 1-21, doi: 10.1016/j.fss.2021.02.006. Attached Files Name Description MIMEType Size Downloads Title Hierarchical data fusion processes involving the Möbius representation of capacities Author(s) Beliakov, Gleb orcid.org/0000-0002-9841-5292 Gagolewski, Marek orcid.org/0000-0003-0637-6028 James, Simon orcid.org/0000-0003-1150-0628 Journal name Fuzzy Sets and Systems Start page 1 End page 21 Total pages 21 Publisher Elsevier Place of publication Amsterdam, The Netherlands Publication date 2021-02-10 ISSN 0165-0114 Keyword(s) Non-additive measures Capacities Fuzzy measures 2-step Choquet integral Aggregation operators High dimensional data Summary The use of the Choquet integral in data fusion processes allows for the effective modelling of interactions and dependencies between data features or criteria. Its application requires identification of the defining capacity (also known as fuzzy measure) values. The main limiting factor is the complexity of the underlying parameter learning problem, which grows exponentially in the number of variables. However, in practice we may have expert knowledge regarding which of the subsets of criteria interact with each other, and which groups are independent. In this paper we study hierarchical aggregation processes, architecturally similar to feed-forward neural networks, but which allow for the simplification of the fitting problem both in terms of the number of variables and monotonicity constraints. We note that the Möbius representation lets us identify a number of relationships between the overall fuzzy measure and the data pipeline structure. Included in our findings are simplified fuzzy measures that generalise both k-intolerant and k-interactive capacities. Notes In Press Language eng DOI 10.1016/j.fss.2021.02.006 Indigenous content off Field of Research 0101 Pure Mathematics 0801 Artificial Intelligence and Image Processing HERDC Research category C1 Refereed article in a scholarly journal Persistent URL http://hdl.handle.net/10536/DRO/DU:30148104 Document type: Journal Article Collections: Faculty of Science, Engineering and Built Environment School of Information Technology Related Links Link Description Connect to published version Go to link with your DU access privileges     Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved. Versions Version Filter Type Wed, 17 Feb 2021, 08:32:16 EST Thu, 18 Feb 2021, 04:01:02 EST Thu, 18 Feb 2021, 05:03:55 EST Mon, 22 Feb 2021, 13:11:36 EST Mon, 22 Feb 2021, 13:12:51 EST Mon, 22 Feb 2021, 15:04:15 EST Sat, 06 Mar 2021, 01:46:45 EST Filtered Full Citation counts:   Cited 0 times in TR Web of Science Cited 0 times in Scopus Search Google Scholar Access Statistics: 15 Abstract Views, 1 File Downloads  -  Detailed Statistics Created: Wed, 17 Feb 2021, 08:32:16 EST

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