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Functional Analysis and Economic Theory pp 17–46Cite as

A Topological Approach to the Study of Fuzzy Measures

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Abstract

A topological approach to the study of fuzzy measures is developed. To do so we need (instead of a clan of fuzzy sets) a more general structure of the domain of the fuzzy measures. This structure is defined by means of some equations. Our general setting allows us to treat simultaneously fuzzy measures, group-valued measures on Boolean rings, and linear operators on Riesz spaces. We deal with extension and decomposition theorems. Also we study connected, totally disconnected, and compact MV-algebras.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università Federico II, Via Cintia, Complesso Monte S. Angelo, Napoli, 80126, Italy

    Giuseppina Barbieri

  2. Dipartimento di Matematica e Informatica, Universitá degli studi di Udine, Via delle Scienze 206, Udine, 33100, Italy

    Hans Weber

Authors
  1. Giuseppina Barbieri
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  2. Hans Weber
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, IUPUI, Indianapolis, IN, 46202, USA

    Yuri Abramovich

  2. Department of Education, University of the Aegean, 1 Demokratias Ave., 85100, Rhodes, Greece

    Evgenios Avgerinos

  3. Department of Economics, University of Illinois at Urbana Champaign, Champaign, IL, 61801, USA

    Nicholas C. Yannelis

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© 1998 Springer-Verlag Berlin · Heidelberg

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Barbieri, G., Weber, H. (1998). A Topological Approach to the Study of Fuzzy Measures. In: Abramovich, Y., Avgerinos, E., Yannelis, N.C. (eds) Functional Analysis and Economic Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72222-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-72222-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72224-0

  • Online ISBN: 978-3-642-72222-6

  • eBook Packages: Springer Book Archive

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