Fuzzy sets featuring in applications to fuzzy control systems are often required to satisfy specific conditions such as, e.g., convexity or normality. In the same connection, a widespread choice is to work with fuzzy sets whose graphs have triangular shape. The purpose of this paper is to show that the former conditions may be regarded as attempts at approximating the latter choice. Specifically, as our main result we prove that a reasonable set of such conditions suffices to characterise families of triangular fuzzy sets. A second result provides an additional characterisation of such families in terms of properties of the curve that they parametrise.

A characterisation of bases of triangular fuzzy sets / P. Codara, O. M. D'Antona, V. Marra - In: 2009 IEEE International Conference on Fuzzy Systems : Proceedings,ICC Jeju, Jeju Island, Korea,August 20-24, 2009Piscataway : IEEE, 2009. - ISBN 9781424435968. - pp. 604-609 (( convegno IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) 2009 tenutosi a Jeju Island, South Korea nel 2009.

A characterisation of bases of triangular fuzzy sets

P. Codara
Primo
;
O. M. D'Antona
Secondo
;
V. Marra
Ultimo
2009

Abstract

Fuzzy sets featuring in applications to fuzzy control systems are often required to satisfy specific conditions such as, e.g., convexity or normality. In the same connection, a widespread choice is to work with fuzzy sets whose graphs have triangular shape. The purpose of this paper is to show that the former conditions may be regarded as attempts at approximating the latter choice. Specifically, as our main result we prove that a reasonable set of such conditions suffices to characterise families of triangular fuzzy sets. A second result provides an additional characterisation of such families in terms of properties of the curve that they parametrise.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/73131
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