Applied Mathematical Modelling, Vol. 30, No. 12, Dec. 2006, Pages 1525-1534

One of the interesting, important and attractive problems in applied mathematics is approximation of functions in a given space. In this paper the problem is considered for fuzzy data and fuzzy functions using the defuzzification function of Fortemps and Roubens. Approximation of a fuzzy function on some given points $(x_i,\tilde{f}_i)$ for $i=1,2,\ldots,m$ is considered by some researchers as interpolation problem. But in interpolation problem
we find a polynomial from degree at most $n=m-1$ where $m$ is the number of points. But when we have lots of points ($m$ is very large) it’s not good or even possible to find such polynomials. In this case we want to find a polynomial with arbitrary degree which is an approximation to original function. One of the works has done is regression by some researchers and wei ntroduced a different method. In this case we have $m$ points but we ant to find a
polynomial with degree at most $n<m$ but not $n=m-1$ necessarily. We introduce a fuzzy polynomial approximation as universal approximation of a fuzzy function on a discrete set of points and we present a method to compute it. We show that this approximation can
be non-unique, however we choose one of them with the smallest amount of fuzziness.

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