Semi-properties of Atanassov Intuitionistic Fuzzy Relations

  • Urszula BentkowskaEmail author
  • Barbara Pȩkala
  • Humberto Bustince
  • Javier Fernandez
  • Edurne Barrenechea
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


In this paper properties of Atanassov intuitionistic fuzzy relations are examined, i.e.: semi-reflexivity, semi-irreflexivity, semi-symmetry, semi-connectedness, semi-asymmetry, semi-transitivity. The special attention is paid to the semi-transitivity property. Its characterization is given and connections with other transitivity properties are presented, i.e. transitivity itself and weak transitivity. Moreover, transformations of Atanassov intuitionistic fuzzy relations in the context of preservation of the given semi-properties of these relations are presented. The transformations that are considered: lattice operations, the converse, the complement, the composition of relations are the basic ones.


Atanassov intuitionistic fuzzy relations Properties of interval-valued fuzzy relations Weak transitivity Semi-transitivity 



This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów, through Project Number RPPK.01.03.00-18-001/10 and research project TIN2013-40765-P from the Spanish Government.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Urszula Bentkowska
    • 1
    Email author
  • Barbara Pȩkala
    • 1
  • Humberto Bustince
    • 2
  • Javier Fernandez
    • 2
  • Edurne Barrenechea
    • 2
  1. 1.Interdisciplinary Centre for Computational ModellingUniversity of RzeszówRzeszówPoland
  2. 2.Departamento de Automatica y ComputacionUniversidad Publica de NavarraPamplonaSpain

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