The Quest for Transitivity, a Showcase of Fuzzy Relational Calculus

  • Bernard De Baets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7311)

Abstract

We present several relational frameworks for expressing similarities and preferences in a quantitative way. The main focus is on the occurrence of various types of transitivity in these frameworks. The first framework is that of fuzzy relations; the corresponding notion of transitivity is C-transitivity, with C a conjunctor. We discuss two approaches to the measurement of similarity of fuzzy sets: a logical approach based on biresidual operators and a cardinal approach based on fuzzy set cardinalities. The second framework is that of reciprocal relations; the corresponding notion of transitivity is cycle-transitivity. It plays a crucial role in the description of different types of transitivity arising in the comparison of (artificially coupled) random variables in terms of winning probabilities. It also embraces the study of mutual rank probability relations of partially ordered sets.

Keywords

Stochastic Dominance Reciprocal Relation Fuzzy Relation Hasse Diagram Fuzzy Preference Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bernard De Baets
    • 1
  1. 1.Department of Mathematical Modelling, Statistics and BioinformaticsGhent UniversityGentBelgium

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