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Permutability of Fuzzy Consequence Operators and Fuzzy Interior Operators

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Advances in Artificial Intelligence (CAEPIA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8109))

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Abstract

In this paper we study the permutability of the composition of fuzzy consequence operators (fuzzy closings) and fuzzy interior operators (fuzzy openings). We establish several characterizations and we show the relation of permutability with the fuzzy closure and fuzzy interior of a fuzzy operator. We also study the connection between permutability and the preservation of the operator type through the composition. More precisely, when the composition of two openings is an opening and the composition of two closings is a closing.

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References

  1. Bĕlohlávek, R., Funioková, T.: Fuzzy interior operators. International Journal of General Systems 33(4), 415–430 (2004)

    Article  MATH  Google Scholar 

  2. Bloch, I.: Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology. Information Sciences 181, 2002–2015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. De Baets, B., Kerre, E., Gupta, M.: The fundamentals of fuzzy mathematical morphology part 1: Basic concepts. International Journal of General Systems 23(2), 155–171 (1995)

    Article  MATH  Google Scholar 

  4. Deng, T.Q., Heijmans, H.J.A.M.: Grey-scale morphology based on fuzzy logic. J. Math. Imaging Vision 16, 155–171 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Elorza, J., Burillo, P.: Connecting fuzzy preorders, fuzzy consequence operators and fuzzy closure and co-closure systems. Fuzzy Sets and Systems 139(3), 601–613 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Elorza, J., et al.: On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems. Fuzzy Sets and Systems 218, 73–89 (2013)

    Article  MathSciNet  Google Scholar 

  7. Maragos, P.: Lattice image processing: a unication of morphological and fuzzy algebraic systems. J. Math. Imaging Vision 22, 333–353 (2005)

    Article  MathSciNet  Google Scholar 

  8. Pavelka, J.: On Fuzzy Logic I. Zeitschr. f. Math. Logik und Grundlagen d. Math. 25, 45–52 (1979)

    Google Scholar 

  9. Recasens, J.: Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups. Information Sciences 196, 129–142 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ronse, C., Heijmans, H.J.A.M.: The algebraic basis of mathematical morphology: II. Openings and Closings. CVGIP: Image Understanding 54(1), 74–97 (1991)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, Pamplona, Spain

    Neus Carmona, Jorge Elorza & Jean Bragard

  2. Secció Matemàtiques i Informàtica, ETS Arquitectura del Vallès, Universitat Politècnica de Catalunya, Sant Cugat del Vallès, Spain

    Jordi Recasens

Authors
  1. Neus Carmona
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  2. Jorge Elorza
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  3. Jordi Recasens
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  4. Jean Bragard
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Editor information

Editors and Affiliations

  1. Universidad Politécnica de Madrid, 28660, Madrid, Spain

    Concha Bielza

  2. Universidad de Almería, 04120, Almería, Spain

    Antonio Salmerón

  3. Universdad de A Coruña, 15071, A Coruña, Spain

    Amparo Alonso-Betanzos

  4. Universidad Complutense de Madrid, 28040, Madrid, Spain

    J. Ignacio Hidalgo

  5. Universidad de Jaén, 23071, Jaén, Spain

    Luis Martínez

  6. Universidad Pablo de Olavide, 41013, Sevilla, Spain

    Alicia Troncoso

  7. Universidad de Salamanca, 37008, Salamanca, Spain

    Emilio Corchado  & Juan M. Corchado  & 

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Carmona, N., Elorza, J., Recasens, J., Bragard, J. (2013). Permutability of Fuzzy Consequence Operators and Fuzzy Interior Operators. In: Bielza, C., et al. Advances in Artificial Intelligence. CAEPIA 2013. Lecture Notes in Computer Science(), vol 8109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40643-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-40643-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40642-3

  • Online ISBN: 978-3-642-40643-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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