Zadeh’s extension of a strong sensitive semiflow

Manuel Fernández

https://orcid.org/0009-0008-8664-6895

Mexico

Universidad Autónoma de la Ciudad de México image/svg+xml

Daniel Jardón

https://orcid.org/0000-0001-9054-0788

Mexico

Universidad Autónoma de la Ciudad de México image/svg+xml

Submitted: 2024-12-19

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Accepted: 2025-07-22

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Published: 2025-10-01

DOI: https://doi.org/10.4995/agt.2025.23085

Copyright (c) 2025 Manuel Fernández, Daniel Jardón, Iván Sánchez

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Keywords:

Semiflow, sensitivity, positive Lyapunov stability, Fuzzy set, Zadeh's extension, Skorokhod metric, hyperspaces

Supporting agencies:

This research was not funded

Abstract:

For a given metric space X, the symbol ℱ(X) denotes the family of all normal upper semicontinuous fuzzy sets on X
with compact support. A semiflow is a continuous function f:T×X → X, where T is an abelian topological monoid.
We study when f^:T×ℱ(X) → ℱ(X) is strongly sensitive, multi-sensitive or positive Lyapunov stable, where f^ is the Zadeh's extension of the semiflow f and ℱ(X) is endowed with level-wise and Skorokhod metrics.  
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