Generalizations and Properties of Normalized Similarity Measures for Boolean Models

Amelia Bădică, Costin Bădică (), Doina Logofătu and Ionuţ-Dragoş Neremzoiu
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Amelia Bădică: Department of Statistics and Business Informatics, University of Craiova, 200585 Craiova, Romania
Costin Bădică: Department of Computers and Information Technology, University of Craiova, 200440 Craiova, Romania
Doina Logofătu: Faculty of Computer Science and Engineering, Frankfurt University of Applied Sciences, Nibelungenplatz 1, 60318 Frankfurt am Main, Germany
Ionuţ-Dragoş Neremzoiu: Department of Computers and Information Technology, University of Craiova, 200440 Craiova, Romania

Mathematics, 2025, vol. 13, issue 3, 1-18

Abstract: In this paper, we provide a closer look at some of the most popular normalized similarity/distance measures for Boolean models. This work includes the generalization of three classes of measures described as generalized Kulczynski, generalized Jaccard, and generalized Consonni and Todeschini measures, theoretical ordering of the similarity measures inside each class, as well as between classes, and positive and negative results regarding the metric properties of measures related to satisfying or not satisfying the triangle inequality axiom.

Keywords: distance measure; similarity measure; metric; Boolean model; finite set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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