Zadeh’s extension and dynamical properties with respect to dp metrics

Document Type : Research Paper

Authors

1 Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, CDMX, México.

2 Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México

10.22111/ijfs.2026.53211.9413

Abstract

For a given metric space (X,d) by F(X) we denote the family of all normal fuzzy sets of X, which are upper semicontinuous and have compact support. In this paper, firstly, we prove that, if X is compact and f:X--> X is a continuous function, then its Zadeh's extension f:F(X)-->F(X)$ is continuous with respect to d_p metric. Then we analyze some properties of Zadeh's extension with respect to d_p metrics including positive Lyapunov stability, strong sensitivity and transitivity.

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References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 4
July and August 2026
Pages 171-182

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