Construction of strong equality index from implication operators

  • Authors:

  • H. Bustince;J. Fernandez;J. Sanz;M. BaczyńSki;R. Mesiar

  • Affiliations:

  • Departamento de Automatica y Computacion, Universidad Publica de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Automatica y Computacion, Universidad Publica de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Automatica y Computacion, Universidad Publica de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland;Slovak University of Technology, Radlinskeho 11, Bratislava, Slovakia and Centre of Excellence IT4Innovations - Division University of Ostrava - IRAFM, 70103 Ostrava, Czech Republic

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2013

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Abstract

We present the concept of strong equality index, basing ourselves on the definition of strong inclusion given by Dubois and Prade in 1980. We develop different construction methods using implication operators that satisfy two additional properties. We make an exhaustive study of these two properties. We also show another two construction theorems for strong equality indexes, one of them making use of order automorphisms and the other using the parametric families of t-norms, t-conorms and strong negations of Hamacher. We finish with an analysis of different relationships between fuzzy entropies and strong equality indexes.