| Title of paper:
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On the (min,max)-transitivity of some intuitionistic fuzzy binary relations associated with probability distributions on pre-orders
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| Author(s):
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Landry Ngibasona  0000-0002-6329-534X
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| Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Bertoua, P.O.Box 416, Bertoua, Cameroon
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| landryngibasona@yahoo.fr
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| Bertrand Mbama Engoulou
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| Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24.157, Douala, Cameroon
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| mbama0479@yahoo.fr
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| Louis Aimé Fono 0000-0002-7315-0427
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| Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24.157, Douala, Cameroon
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| lfono2000@yahoo.fr
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 305–319
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.3.305-319
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| Download:
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 PDF (294 Kb, File info)
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| Abstract:
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In this paper, we introduce an intuitionistic fuzzy binary relation on a finite universe generated by a probability distribution on a set of complete pre-orders of the universe. We establish necessary and sufficient conditions on the probability distribution under which the obtained relation is (min,max)-transitive. We study two specific cases where the relation is generated by the generalized parametric Mallows and Plackett–Luce probability distributions.
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| Keywords:
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Probability distribution on pre-orders, Intuitionistic fuzzy binary relation, (min, max)-transitivity.
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| AMS Classification:
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03E72, 60E05.
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| References:
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- Diffo Lambo, L., Tchantcho, B., & Moulen, J. (2012). Comparing influence theories in voting games under locally generated measures of dissatisfaction. International Journal on Game Theory, 41, 719–731.
- Fono, L. A., Nana, G. N., Salles, M., & Gwet, H. (2009). A binary intuitionistic fuzzy relation: Some new results, a general factorization and two properties of strict components. International Journal of Mathematics and Mathematical Sciences, 2009, Article ID 580918.
- Kamdem, T. V., Fotso, S., Fono, L. A., & Hüllermeier, E. (2019). Choice functions generated by Mallows and Plackett–Luce relations. New Mathematics and Natural Computation, 15(2), 191–213.
- Ngibasona, L., Mbama Engoulou, B., Fotso, S., & Fono, L. A. (2019). On two parametric probabilisty distributions on crisp complete pre-orders. Afrika Statistika, 14(1), 1903–1915.
- Pekala, B., Bentkowska, U., Bustince, H., Fernandez, J., & Galar, M. (2015). Operators on intuitionistic fuzzy relations. Proceeding of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2015, Istanbul, Turkey, August 2–5, 2015. DOI: 10.1109/FUZZ-IEEE.2015.733795.
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