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Structures of Opposition in Fuzzy Rough Sets

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Abstrakty
EN
The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.
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1--19
Opis fizyczny
Bibliogr. 46 poz., rys.
Twórcy
autor
  • DISCo, Universit`a di Milano – Bicocca Viale Sarca 336/14, 20126 Milano, Italia
autor
  • IRIT, Universit´e Paul Sabatier 118 route de Narbonne, 31062 Toulouse cedex 9, France
autor
  • IRIT, Universit´e Paul Sabatier 118 route de Narbonne, 31062 Toulouse cedex 9, France
Bibliografia
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  • [5] Béziau, J.-Y., Gan-Krzywoszy´nska,K., Eds.: Handbook of abstracts of the 2ndWorld Congress on the Square of Opposition, Corte, Corsica, June 17-20, 2010.
  • [6] Béziau, J.-Y., Gan-Krzywoszy´nska,K., Eds.: Handbook of abstracts of the 3rdWorld Congress on the Square of Opposition, Beirut, Lebanon, June 26-30, 2010.
  • [7] Béziau, J.-Y., Gan-Krzywoszy´nska,K., Eds.: Handbook of abstracts of the 4thWorld Congress on the Square of Opposition, Roma, Vatican, May 5-9, 2014.
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  • [19] Dubois, D., Prade, H.: From Blanché’s hexagonal organization of concepts to formal concept analysis and possibility theory, Logica Univers., 6, 2012, 149–169.
  • [20] Dubois, D., Prade, H.: Gradual structures of oppositions, in: Enric Trillas: Passion for Fuzzy Sets (F. Esteva, L. Magdalena, J. L. Verdegay, Eds.), Studies in Fuzziness and Soft Computing, Springer, to appear.
  • [21] Dubois, D., Prade, H., Rico, A.: The cube of opposition: A structure underlying many knowledge representation formalisms, in: Proc. 24th Int. Joint Conf. on Artificial Intelligence (IJCAI’15), Buenos Aires, July 25-31 (Q. Yang, M. Wooldridge, Eds.), AAAI Press, 2015, 2933–2939.
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  • [39] Yao, Y.: Combination of Rough and Fuzzy Sets based on α-level sets, Kluwer Academic Press, Boston, 1997, 301–321.
  • [40] Yao, Y. Y.: Duality in rough set theory based on the square of opposition, Fundamenta Informaticae, 127, 2013, 49–64.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3a3748b6-2424-48a7-8a33-deea3186e5ba
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