Pointwise equicontinuity of Zadeh’s extension of an interval map

Taixiang Sun, Guangwang Su and Bin Qin

Chaos, Solitons & Fractals, 2019, vol. 128, issue C, 1-4

Abstract: Let I be a compact interval and f:I⟶I be continuous. Assume that F(I) is the set of fuzzy numbers on I, and that f^:F(I)⟶F(I) is the Zadeh′s extension of f, and that lim←{F(I),f^} is the inverse limit space of (F(I),f^), and σf^:lim←{F(I),f^}⟶lim←{F(I),f^} is the left shift map. In this paper, we study the pointwise equicontinuity of f^ and show that the following statements are equivalent: (1) f^ is pointwise equicontinuous. (2) For some infinite subsequence S of positive integers, f^ is S pointwise equicontinuous. (3) {f^2n}n=1∞ is uniformly convergent on F(I). (4) σf^ is a periodic map with period 2.

Keywords: Fuzzy number; Pointwise equicontinuity; Zadeh′s extension (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:128:y:2019:i:c:p:1-4

DOI: 10.1016/j.chaos.2019.07.031

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