A note on projection of fuzzy sets on hyperplanes

Heriberto Román Flores, Arturo Flores Franulic

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.

Palabras clave


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

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Referencias


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

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

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).

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

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




DOI: http://dx.doi.org/10.4067/S0716-09172001000300006

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