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Formal theory of the comparative relations: its application to the study of quantum similarity and dissimilarity measures and indices

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Abstract

The study proposes a formal theory of comparative relations characterized by a group of abstract definitions and axioms. This abstract characterization allows us to rigorously define in a very general form what a comparative relation is, which can in turn be used as starting point in every case where comparative analysis is used. Some of the consequences of this formalization—when applied to existing results- are analyzed, particularly those related with the consistency of the results of the comparisons. Following, a study was conducted of descriptors of Quantum Quantitative Structure–Property Relationships models proposed by Carbó-Dorca et al. Several quantum comparative indices such as: Carbó, Hodgkin–Richards, Petke, Tanimoto, conjugate Petke and conjugate Hodgkin–Richards were also analyzed. The proposed theory gives a solid theoretical basis for comparative analysis that will have a positive impact on a broad spectrum of disciplines, where the field of chemistry could be one of the most important beneficiaries.

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Author notes

  1. Edelsys Codorniu-Hernandez

    Present address: Department of Chemistry, University of Calgary, University drive T2N1N4, Calgary, Alberta, Canada

Authors and Affiliations

  1. Departament of Molecular Design and Synthesis, Higher Institute of Technologies and Applied Sciences, Ave. Salvador Allende y Luaces, Quinta de los Molinos, Plaza de la Revolución, POB 6163, 10600, Ciudad Habana, Cuba

    Ramón-Alain Miranda-Quintana & Edelsys Codorniu-Hernandez

  2. Department of Mathematics, University of Antioquia, Calle 67 No. 53-108, Apartado Aereo 1226, Medellín, Colombia

    Roberto Cruz-Rodes

  3. Department of General Physics and Mathematics, Higher Institute of Technologies and Applied Sciences, Ave. Salvador Allende y Luaces, Quinta de los Molinos, Plaza de la Revolución, POB 6163, 10600, Ciudad Habana, Cuba

    Alfo José Batista-Leyva

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  1. Ramón-Alain Miranda-Quintana
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  2. Roberto Cruz-Rodes
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  3. Edelsys Codorniu-Hernandez
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  4. Alfo José Batista-Leyva
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Correspondence to Alfo José Batista-Leyva.

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Miranda-Quintana, RA., Cruz-Rodes, R., Codorniu-Hernandez, E. et al. Formal theory of the comparative relations: its application to the study of quantum similarity and dissimilarity measures and indices. J Math Chem 47, 1344–1365 (2010). https://doi.org/10.1007/s10910-009-9658-6

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  • DOI: https://doi.org/10.1007/s10910-009-9658-6

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