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Activating Generalized Fuzzy Implications from Galois Connections

  • Francisco J. Valverde-Albacete
  • Carmen Peláez-Moreno
  • Cristina del CampoEmail author
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 322)

Abstract

This paper deals with the relation between fuzzy implications and Galois connections, trying to raise the awareness that the fuzzy implications are indispensable to generalise Formal Concept Analysis. The concrete goal of the paper is to make evident that Galois connections, which are at the heart of some of the generalizations of Formal Concept Analysis, can be interpreted as fuzzy incidents. Thus knowledge processing, discovery, exploration and visualization as well as data mining are new research areas for fuzzy implications as they are areas where Formal Concept Analysis has a niche.

Keywords

Semiring theory Semiring-valued extensions of FCA Fuzzy implications Residuation Philosophical foundations 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Francisco J. Valverde-Albacete
    • 1
  • Carmen Peláez-Moreno
    • 2
  • Cristina del Campo
    • 3
    Email author
  1. 1.Depto. Lenguajes y Sistemas InformáticosUNEDMadridSpain
  2. 2.Depto. Teoría de Señal y ComunicacionesUC3MMadridSpain
  3. 3.Depto. Estadística e Investigación Operativa IIUCMMadridSpain

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