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Digitale Medien

Separation theorems and minimax theorems for fuzzy sets (1980)

Takahashi, M. ; Takahashi, W.

Springer

Journal of optimization theory and applications 31 (1980), S. 177-194

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Details

ISSN: 1573-2878

Schlagwort(e): Fuzzy sets ; Banach spaces ; Hilbert spaces ; minimax theorems ; separation theorems

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract In this paper, we prove some theorems on fuzzy sets. We first show that, in order to demonstrate that the equality of shadows ofA andB implies the equality ofA andB, it is necessary to assume thatA andB are closed and thatS H (A)=S H (B) for any closed hyperplane hyperplaneH. We also obtain a separation theorem for two convex fuzzy sets in a Hilbert space. Finally, we investigate results relating to minimax theorems for fuzzy sets. We obtain a necessary and sufficient condition for compactness.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00934109

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