Transitive solutions of relational equations on finite sets and linear lattices

  • Antonio Di Nola
  • Waldemar Kolodziejczyk
  • Salvatore Sessa
3. Fuzzy Sets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)


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.

Key words

Finite matrix equation max-min transitive matrix Schein rank of a matrix 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Antonio Di Nola
    • 1
  • Waldemar Kolodziejczyk
    • 2
  • Salvatore Sessa
    • 1
  1. 1.Istituto Matematico, Facoltà di ArchitetturaUniversità di NapoliNapoliItaly
  2. 2.Institute of Production Engineering and ManagementTechnical University of WroclawWroclawPoland

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