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The Estimation of the Amount of Vehicle Accident Damages

Insurance Co.

Tehran

Supervisor of mathematical modelling of the problem and implementation of it

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    Journal Paper

    A New Approach to Universal Approximation of Fuzzy Functions on a Discrete Set of Points

    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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    News

    New Paper

    The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations

    Our new paper on optimal shape parameter in Radial Basis Functions applied to differential equations. This work is a collaboration with Dr. Hassan Barzegar, Dr. M. A. Fariborzi Araghi, and me.

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    Publications

    a new Approach to Universal Approximation of Fuzzy Functions on a Discrete Set of points, Journal of Applied Mathematical Modelling

    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 (xi,f˜i) for i = 1, 2, … , m is considered by some researchers as interpolation problem. But in interpolation problem we find a polynomial of 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 is not good or even possible to find such polynomials. In this case we want to find a polynomial of arbitrary degree which is an approximation to original function. One of the works has done is regression by some researchers and we introduced a different method. In this case we have m points but we want to find a polynomial of 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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      @Copyright 2020  Dr. Amirfakhrian  | Powered by Applied Plan