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Poset Valued Intuitionistic Preference Relations

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Computational Intelligence and Mathematics for Tackling Complex Problems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 819))

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Abstract

It is known that in every finite poset each element can be presented as a join of completely join-irreducible elements. This representation is used here to justify a new notion of poset-valued reciprocal (preference) relations and also the intuitionistic version of this definition. Join-irreducible elements would represent pieces of information representing grade of preference in this framework. It is demonstrated that no restriction on type of a poset is needed for developing the intuitionistic approach, except that the poset should be bounded with the top element T and the bottom element B (T representing the total preference). Some properties are proved and connections with previous definitions are shown. It is demonstrated that the new definition is in a sense more general (and in some aspects more convenient) than previous ones.

Supported by Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013, and by the Provincial Secretariat for Higher Education and Scientific Research, grant No. 142-451-3642/2017/01.

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Authors and Affiliations

  1. Technical college Čačak, Svetog Save 65, 32000, Čačak, Serbia

    Marija Djukić

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Andreja Tepavčević

  3. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001, Belgrade, Serbia

    Andreja Tepavčević

Authors
  1. Marija Djukić
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  2. Andreja Tepavčević
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Corresponding author

Correspondence to Marija Djukić .

Editor information

Editors and Affiliations

  1. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T Kóczy

  2. Science Faculty, Department of Mathematics, University of Cádiz, Cádiz, Spain

    Jesús Medina-Moreno

  3. Faculty of Economic and Business Sciences, Department of Mathematics, University of Cádiz, Cádiz, Spain

    Eloísa Ramírez-Poussa

  4. Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia

    Alexander Šostak

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Djukić, M., Tepavčević, A. (2020). Poset Valued Intuitionistic Preference Relations. In: Kóczy, L., Medina-Moreno, J., Ramírez-Poussa, E., Šostak, A. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems. Studies in Computational Intelligence, vol 819. Springer, Cham. https://doi.org/10.1007/978-3-030-16024-1_9

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