An approximation to the extension principle using decomposition of fuzzy intervals

Authors:
Y. Chalco-Cano;M. Jiménez-Gamero;H. Román-Flores;M. A. Rojas-Medar
Affiliations:
Dpto. de Matemática, Universidad de Tarapacá, Casilla 7D, Arica, Chile;Dpto. de Estadística e I.O., Universidad de Sevilla, 41012 Sevilla, Spain;IAI, Universidad de Tarapacá, Casilla 7D, Arica, Chile;Dpto. de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

This article presents a proposal for the decomposition of large ranges of uncertainty associated with the Cartesian product of two fuzzy intervals. We compute an approximation of the fuzzy set obtained by applying extension principle to a real function by means of this decomposition and piecewise linearization of the function. It is proved the efficiency of the method via convergence in D-metric. We also extend the method to the case when the function has more than two arguments. Some examples are included to illustrate the proposed method and to compare it with others.