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On the approximation of compact fuzzy sets |
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| Authors: | Y. Chalco-Cano A.D. Báez-Sánchez H. Román-Flores M.A. Rojas-Medar |
| Affiliation: | 1. Departamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica, Chile;2. Instituto de Matemática Estatística e Computação Científica, Universidade Estadual de Campinas, Campinas - SP, Brazil;3. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;4. Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Chillán, Chile |
| Abstract: | This paper suggests an approximation for a compact fuzzy set by a sequence of Lipschitz fuzzy sets. This approximation method involves the construction of Lipschitz fuzzy sets using the sup–min convolution of a compact fuzzy set with a fuzzy zero. Considering a similar procedure, we present the approximation of a trapezoidal type fuzzy interval by a sequence of differentiable fuzzy intervals. We show some important properties of both approximations and we give some numerical examples illustrating the results. |
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