How to compare uncertain data types: towards robust similarity measures

Kabir, Shaily (2020) How to compare uncertain data types: towards robust similarity measures. PhD thesis, University of Nottingham.

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Abstract

In view of the importance of effective comparison of uncertain data in real-world applications, this thesis focuses on developing new similarity measures with high accuracy. As it identifies and articulates an inherent limitation of the popular set-theoretic similarity measures for continuous intervals where they return the same similarity value for very different sets of intervals (termed as aliasing), this thesis first underpins a new axiomatic definition of a robust similarity measure and then proposes a new similarity measure for continuous intervals based on their bidirectional subsethood. Beyond establishing theoretical foundation of the new measure, the thesis also demonstrates its robust results vis-a-vis existing measures and suitability for real world applications. In the next stage, it develops a generalized framework to assess similarity between discontinuous intervals as current approaches involve loss of discontinuity information and are also affected by aliasing of the popular measures— these weaknesses impact the accuracy of similarity results. This thesis further integrates Allen’s theory with the new generalized framework to make the latter more efficient.

Moving beyond intervals, this thesis extends the new similarity measure both vertically and horizontally (α-cut based) for comparing type-1 (T1) fuzzy sets as the shortcoming of popular similarity measures persists with their extension to T1 fuzzy sets. The empirical evaluation of the extended new measures with respect to key existing fuzzy set-theoretic similarity measures shows that the vertically extended new measure behaves intuitively for various types of fuzzy sets, except for non-normal fuzzy sets; however, the α-cut based extended new measure meets expectation in all cases. At the final stage, the utility of the new similarity measure is explored to improve the robustness of fuzzy integral (FI) based uncertain-data aggregation. As existing approaches to generate fuzzy measures (FMs) rely on popular similarity measures to capture the degree of similarity among individual sources (and their combinations), they are also impacted by their aforesaid limitation. Therefore, this thesis develops a new FM based on the new similarity measure which can generate intuitive aggregation outcome when used in combination with an FI.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Wagner, Christian
McCulloch, Josie
Subjects: Q Science > QA Mathematics > QA 75 Electronic computers. Computer science
Faculties/Schools: UK Campuses > Faculty of Science > School of Computer Science
Item ID: 59792
Depositing User: Kabir, Shaily
Date Deposited: 21 Jul 2020 04:40
Last Modified: 21 Jul 2020 04:40
URI: http://eprints.nottingham.ac.uk/id/eprint/59792

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