University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 23 4 2026 08 01 Zadeh’s extension and dynamical properties with respect to dp metrics 171 182 10036 10.22111/ijfs.2026.53211.9413 EN Kinrha Aguirre De La Luz Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, CDMX, México. Daniel Roberto Jardón Arcos Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México Journal Article 2025 09 11 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. Fuzzy sets d_p metrics Zadeh's extension (strong) sensitivity positive Lyapunov stability https://ijfs.usb.ac.ir/article_10036_dc689611ff02d5e6b12c634773e10299.pdf