A NOTE ON PROJECTION OF
FUZZY SETS ON HYPERPLANES*

HERIBERTO ROMAN F.

and

ARTURO FLORES F.
Universidad de Tarapacá, Chile

Abstract

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 , 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

Keywords : Compact-convex fuzzy sets; Metric projection; Closed hyperplanes.

* This work was partially supported by Fondecyt through projects 1970535 and 1000463 and Dipog-UTA 4732-00.

References

[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).        [ Links ]

[2] H. Brézis, Analyse fonctionnelle:théorie et applications, Masson, Paris, (1987).         [ Links ]

[3] E. Klein and A. Thompson, Theory of correspondences, Wiley, New York, (1984).         [ Links ]

[4] M. Puri and D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114, pp. 402-422, (1986).         [ Links ]

[5]H. Román-Flores, The compactness of E(X), Appl. Math. Lett. 11, pp. 13-17, (1998).         [ Links ]

[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).         [ Links ]

[7]M. Takahashi and W. Takahashi, Separation theorems and minimax theorems for fuzzy sets, J. Opt. Th. Appl. 31, pp. 177-194, (1980).         [ Links ]

[8]L. Zadeh, Fuzzy sets, Information and Control 8, pp. 338-353, (1965).         [ Links ]

Received : july 2001.

Heriberto Román Flores
Departamento de Matemática
Universidad de Tarapacá
Arica
Chile
e-mail : hroman@uta.cl

and

Arturo Flores Franulic
Departamento de Matemática
Universidad de Tarapacá
Arica
Chile
e-mail : aflores@uta.cl