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A note on projection of fuzzy sets on hyperplanes

  • Román Flores, Heriberto [1] ; Flores Franulic, Arturo [1]
    1. [1] Universidad de Tarapacá

      Universidad de Tarapacá

      Arica, Chile

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 3, 2001, págs. 339-349
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172001000300006
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  • Resumen
    • The aim of this paper is to realize a comparative study between the concepts of projection and shadow of fuzzy sets on a closed hyperplane in a Hilbert space X , this last one introduced by Zadeh in [8] on finite dimensional spaces and recently studied by Takahashi [1,7] in a real Hilbert space X.

  • Referencias bibliográficas
    • Citas [1] M. Amemiya and W. Takahashi, Generalization of shadows and fixed point theorems- for fuzzy sets, Fuzzy Sets and Systems 114, pp....
    • [2] H. Brézis, Analyse fonctionnelle: théorie et applications, Masson, Paris, (1987).
    • [3] E. Klein and A. Thompson, Theory of correspondences, Wiley, New York, (1984).
    • [4] M. Puri and D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114, pp. 402-422, (1986).
    • [5] H. Román-Flores, The compactness of E(X), Appl. Math. Lett. 11, pp. 13-17, (1998).
    • [6] H. Román-Flores, L.C. Barros and R.C. Bassanezi, A note on the Zadeh’s extensions, Fuzzy Sets Systems 117, pp. 327-331, (2001).
    • [7] M. Takahashi and W. Takahashi, Separation theorems and minimax theorems for fuzzy sets, J. Opt. Th. Appl. 31, pp. 177-194, (1980).
    • [8] L. Zadeh, Fuzzy sets, Information and Control 8, pp. 338-353, (1965).

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