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Semi-properties of Atanassov Intuitionistic Fuzzy Relations

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Novel Developments in Uncertainty Representation and Processing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 401))

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Interdisciplinary Centre for Computational Modelling, University of Rzeszów, Pigonia 1, 35-310, Rzeszów, Poland

    Urszula Bentkowska & Barbara Pȩkala

  2. Departamento de Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince, Javier Fernandez & Edurne Barrenechea

Authors
  1. Urszula Bentkowska
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  2. Barbara Pȩkala
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  3. Humberto Bustince
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  4. Javier Fernandez
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  5. Edurne Barrenechea
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Corresponding author

Correspondence to Urszula Bentkowska .

Editor information

Editors and Affiliations

  1. Inst. of Biophy. & Biomedical Eng., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Division of Graduate Studies, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Sys Res Intit of Polish Acad of Science, Intelligent Systems Laboratory, Warsaw, Poland

    Janusz Kacprzyk

  4. Warsaw School of Information Technology, Polish Academy of Sciences, Warsaw, Poland

    Maciej Krawczak

  5. Div of Gdu Stud,CalzTecn sn,Fra.TomAqu, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  6. Intelligent Systems Laboratory, Asen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

  7. Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University, Burgas, Bulgaria

    Evdokia Sotirova

  8. Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland

    Eulalia Szmidt

  9. Dept. of Tele. & Info. Processing, Ghent University, Gent, Belgium

    Guy De Tré

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

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Bentkowska, U., Pȩkala, B., Bustince, H., Fernandez, J., Barrenechea, E. (2016). Semi-properties of Atanassov Intuitionistic Fuzzy Relations. In: Atanassov, K., et al. Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol 401. Springer, Cham. https://doi.org/10.1007/978-3-319-26211-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-26211-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26210-9

  • Online ISBN: 978-3-319-26211-6

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