Analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials

Authors:
Puyin Liu
Affiliations:
Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China and Department of Mathematics, National University of Defense Technology, Changsha 410073, People's ...
Venue:
Fuzzy Sets and Systems - Mathematics
Year:
2002

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Abstract

For the given fuzzy valued function J: Rn → F0(R), the fuzzy valued Bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set U ⊂ Rn. Some equivalent condition for the continuous fuzzy function F:F0(R)n → F0(R) that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set U ⊂ F0(R)n are presented.