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Best Approximation of Ruspini Partitions in Gödel Logic

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4724))

Abstract

A Ruspini partition is a finite family of fuzzy sets {f 1, ..., f n }, f i : [0, 1] →[0, 1], such that \(\sum^n_{i=1} f_i(x) = 1\) for all x ∈ [0, 1]. We analyze such partitions in the language of Gödel logic. Our main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a constructive procedure to axiomatize a given Ruspini partition by a theory in Gödel logic.

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Authors and Affiliations

  1. Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, via Saldini 50, I-20133, Milano, Italy

    Pietro Codara

  2. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39, I-20135, Milano, Italy

    Ottavio M. D’Antona & Vincenzo Marra

Authors
  1. Pietro Codara
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  2. Ottavio M. D’Antona
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  3. Vincenzo Marra
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Editor information

Editors and Affiliations

  1. LARODEC, Institut Supérieur de Gestion de Tunis, 41 Avenue de la liberté, 2000, Le Bardo, Tunisie

    Khaled Mellouli

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© 2007 Springer-Verlag Berlin Heidelberg

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Codara, P., D’Antona, O.M., Marra, V. (2007). Best Approximation of Ruspini Partitions in Gödel Logic. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_17

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  • DOI: https://doi.org/10.1007/978-3-540-75256-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75255-4

  • Online ISBN: 978-3-540-75256-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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