A note on projection of fuzzy sets on hyperplanes


  • Heriberto Román Flores Universidad de Tarapacá.
  • Arturo Flores Franulic Universidad de Tarapacá.




Compact-convex fuzzy sets, Metric projection, Closed hyperplanes.


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.

Author Biographies

Heriberto Román Flores, Universidad de Tarapacá.

Departamento de Matemática.

Arturo Flores Franulic, Universidad de Tarapacá.

Departamento de Matemática.


[1] M. Amemiya and W. Takahashi, Generalization of shadows and fixed point theorems- for fuzzy sets, Fuzzy Sets and Systems 114, pp. 469-476 (2000).

[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).



How to Cite

H. Román Flores and A. Flores Franulic, “A note on projection of fuzzy sets on hyperplanes”, Proyecciones (Antofagasta, On line), vol. 20, no. 3, pp. 339-349, Apr. 2017.




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