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Enric Trillas: A Passion for Fuzzy Sets pp 79–91Cite as

Gradual Structures of Oppositions

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 322))

Abstract

There has been a renewal of interest in the use of squares of opposition and other related structures in the last decade, both for discussing issues in logical modeling and for their cognitive relevance. This paper outlines and motivates graded extensions of these structures (square, hexagon, cube, tetrahedron) of oppositions.

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Notes

  1. 1.

    Due to \(N(\overline{A})) = 1 - \varPi (A)\), it comes \(\max (0, \min (1,N(A) + N(\overline{A})) + \varPi (A) - 1) = \min (1 - N(\overline{A}), N(A)) = N(A)\) since \(\varPi (A) \ge N(A)\).

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Authors and Affiliations

  1. IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Didier Dubois & Henri Prade

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  1. Didier Dubois
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  2. Henri Prade
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Correspondence to Henri Prade .

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Editors and Affiliations

  1. European Centre for Soft Computing, Asturias, Spain

    Luis Magdalena

  2. Depto. de Ciencias de la Computación e Inteligencia Artificial, University of Granada, Granada, Spain

    Jose Luis Verdegay

  3. Spanish Council for Scientific Research (CSIC), Artificial Intelligence Research Institute (IIIA-CSIC), Catalonia, Spain

    Francesc Esteva

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Dubois, D., Prade, H. (2015). Gradual Structures of Oppositions. In: Magdalena, L., Verdegay, J., Esteva, F. (eds) Enric Trillas: A Passion for Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-16235-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-16235-5_7

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  • Online ISBN: 978-3-319-16235-5

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