Bernstein Approximations for Fuzzy-Valued Functions

Hsien-Chung Wu ()
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Hsien-Chung Wu: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Mathematics, 2025, vol. 13, issue 15, 1-27

Abstract: Studying the Bernstein approximations for fuzzy functions is a new attempt. With the help of considering the support functions of fuzzy sets in which the weak* topology for the normed dual space is involved, we are able to approximate continuous fuzzy functions by considering the Bernstein polynomials for fuzzy functions. We first study the Bernstein approximations for the support functions of fuzzy sets. Using the concept of isometry between the metric spaces of fuzzy sets and the normed spaces of support functions of fuzzy sets, the Bernstein approximations for the support functions of fuzzy sets can naturally lead to the Bernstein approximations for continuous fuzzy functions.

Keywords: Bernstein approximation; closed unit ball; fuzzy set; support function; weak* topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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