Chaotic iterations of fuzzy sets
Fuzzy Sets and Systems - Special issue on mathematical aspects of fuzzy sets
Chaos, entropy and a generalized extension principle
Fuzzy Sets and Systems
Attractors and asymptotic stability for fuzzy dynamical systems
Fuzzy Sets and Systems
On metrization of the hit-or-miss topology using Alexandroff compactification
International Journal of Approximate Reasoning
On Choquet theorem for random upper semicontinuous functions
International Journal of Approximate Reasoning
The extension principle and a decomposition of fuzzy sets
Information Sciences: an International Journal
An approximation to the extension principle using decomposition of fuzzy intervals
Fuzzy Sets and Systems
Fuzzy numbers and fuzzification of the Choquet integral
Fuzzy Sets and Systems
On the upper semicontinuity of Choquet capacities
International Journal of Approximate Reasoning
Topological entropy of fuzzified dynamical systems
Fuzzy Sets and Systems
On fuzzifications of discrete dynamical systems
Information Sciences: an International Journal
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Given a locally compact separable metric space E, a perfect transformation defined on E induces a Zadeh extension, which is a transformation from the space of all upper semicontinuous fuzzy sets defined on E to itself. Here, the latter space is equipped with the hit-or-miss topology. In this setting, each upper semicontinuous fuzzy set is identified with its hypograph, a closed subset in the product space of E and [0,1]. This approach does not require the relevant fuzzy sets to hold a compact support, and it also overcomes the drawback of the traditional level-set method. Further, it is proved that the Zadeh extension with this setting is continuous in the hit-or-miss topology; and dynamical properties of Zadeh extension regarding iteration have been explored.