Vector valued information measures and integration with respect to fuzzy vector capacities

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2019 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 355, pages 1-25 (issn: 0165-0114,

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Authors: Enrique Alfonso Sánchez-Pérez; Radoslaw Szwedek;

doi: 10.1016/j.fss.2018.05.004

Vector valued information measures and integration with respect to fuzzy vector capacities

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Abstract

[EN] Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities. Bartle-Dunford-Schwartz integration (for the additive case) and Choquet type integration (for the non-additive case) are considered, showing that these formalisms can be used to define and develop vector-valued impact measures. Examples related to existing bibliometric tools as well as to new measuring indices are given.

The authors would like to thank both Prof. Dr. Olvido Delgado and the referee for their valuable comments and suggestions which helped to prepare the manuscript. The first author gratefully acknowledges the support of the Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2016-77054-C2-1-P.

Related Organizations

Universitat Politècnica de València
Spain
Adam Mickiewicz University in Poznań
Poland

Keywords

Banach lattices, Non-additive measures, measures of information, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), Measures of information, Fuzzy functional analysis, Choquet integral, Vector-valued measures and integration, MATEMATICA APLICADA, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), non-additive measures

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