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Journal Paper

Approximation of Fuzzy Functions by Distance Method

Mathematics Scientific Journal, 2 (2007) 15-28.

Approximation of functions in a given space is an old problem in applied mathematics. In this paper the problem is considered for fuzzy data and fuzzy functions using the defuzzification function introduced by Fortemps and Roubens. We introduce a fuzzy polynomial approximation as D-approximation of a fuzzy function on a discrete set of points and we present a method to compute it.

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Journal Paper

The Nearest Trapezoidal Form of a Generalized Left-Right Fuzzy Number

International Journal of Approximate Reasoning, Vol. 43, No. 2, Oct. 2006, Pages 166-178

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers and multiplication of trapezoidal fuzzy numbers are approximated.

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Journal Paper

Best Approximation of Fuzzy Functions

Journal of Nonlinear Studies, Vol. 14 No. 1 (2007) 88-103.

In this work we study approximation of fuzzy functions on a finite set of distinct points. Two types of approximation are considered, one method based on fuzzy linear programming problem, and the other method based on three independent linear programming problems.

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Journal Paper

Numerical Approximation of Fuzzy Functions by Fuzzy Polynomials

Applied Mathematics and Computation Vol. 174, No. 2, 15 Mar. 2006, Pages 1001-1006

One of the interesting, important and attractive problems in applied mathematics is how to best approximate a function in a given space. In this paper, the problem of best approximation is considered for fuzzy functions, by optimization to obtain a fuzzy polynomial.

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Journal Paper

The Nearest Approximation of a Fuzzy Quantity in Parametric Form

Applied Mathematics and Computations, Vol. 172, No. 1, 1 Jan. 2006, Pages 624-632

Applications of fuzzy logic and fuzzy mathematics are increasing widely all around the world. Thus working with fuzzy numbers are very important. In many applications of fuzzy mathematics we need (or it is better) to work with the same fuzzy numbers. In
this work we approximate parametric fuzzy numbers with polynomial parametric fuzzy numbers.

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conference paper

Computing The Nearest Trapezoidal Form of a Fuzzy Number by a New Operator

6th conference on fuzzy systems, (2006) Shiraz, Iran.

We propose a new approach to assigning distance between fuzzy numbers. A pseudo-metric on the set of fuzzy numbers and a metric on the set of trapezoidal fuzzy numbers are described. The regular reducing functions and the Hausdorff metric are used to define the metric. Using this metric, we can approximate an arbitrary generalized left right fuzzy number with a trapezoidal one. Finally, powers and multiplication of trapezoidal fuzzy numbers are approximated.

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conference paper

Best approximation of fuzzy functions by optimization

4th conference on fuzzy sets and its applications, (2003) Mazandaran University, Iran.

In this paper the problem of fuzzy function approximation is considered by optimization.

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conference paper

A New Method to Find Best Approximation of Fuzzy Functions by Optimization

AIMC34, (2003) Shahroud University of Technology, Iran.

In this paper a new method is considered for approximation of fuzzy functions by optimization.

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conference paper

Best Approximation of Fuzzy Functions

AIMC33, (2002), Ferdowsi University Mashhad, Iran.

One of the interesting, important and attractive problems in applied mathematics is the best approximation of functions in a given space. In this paper the problem has been considered for fuzzy functions.

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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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