On ? -Limit Sets of Zadeh’s Extension of Nonautonomous Discrete Systems on an Interval

Guangwang Su and Taixiang Sun
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Guangwang Su: College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, China
Taixiang Sun: College of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, China

Mathematics, 2019, vol. 7, issue 11, 1-7

Abstract: Let I = [ 0 , 1 ] and f n be a sequence of continuous self-maps on I which converge uniformly to a self-map f on I . Denote by F ( I ) the set of fuzzy numbers on I , and denote by ( F ( I ) , f ^ ) and ( F ( I ) , f ^ n ) the Zadeh ? s extensions of ( I , f ) and ( I , f n ) , respectively. In this paper, we study the ? -limit sets of ( F ( I ) , f ^ n ) and show that, if all periodic points of f are fixed points, then ? ( A , f ^ n ) ? F ( f ^ ) for any A ? F ( I ) , where ? ( A , f ^ n ) is the ? -limit set of A under ( F ( I ) , f ^ n ) and F ( f ^ ) = { A ? F ( I ) : f ^ ( A ) = A } .

Keywords: fuzzy number; ?-limit set; periodic point; Zadeh’s extension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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