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Transitive solutions of relational equations on finite sets and linear lattices

  • 3. Fuzzy Sets
  • Conference paper
  • First Online:
Uncertainty in Knowledge Bases (IPMU 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 521))

Abstract

The set of solutions of relational equations over a finite referential space and with values from a linear lattice is considered. We determine in this set the greatest max-min transitive solution and the related minimal ones. Further, we investigate for the determination of particular max-min transitive solutions, namely those having Schein rank equal to 1. Related properties of convergence of fuzzy systems represented by the involved relations are also given.

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Author information

Authors and Affiliations

  1. Istituto Matematico, Facoltà di Architettura, Università di Napoli, via Monteoliveto 3, 80134, Napoli, Italy

    Antonio Di Nola & Salvatore Sessa

  2. Institute of Production Engineering and Management, Technical University of Wroclaw, 50372, Wroclaw, Poland

    Waldemar Kolodziejczyk

Authors
  1. Antonio Di Nola
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  2. Waldemar Kolodziejczyk
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  3. Salvatore Sessa
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Editor information

Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1991 Springer-Verlag Berlin Heidelberg

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Di Nola, A., Kolodziejczyk, W., Sessa, S. (1991). Transitive solutions of relational equations on finite sets and linear lattices. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028101

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  • DOI: https://doi.org/10.1007/BFb0028101

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54346-6

  • Online ISBN: 978-3-540-47580-4

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