Abstract
In this paper, we approximate an arbitrary fuzzy number by a polynomial fuzzy number through minimizing the distance between them. Throughout this work, we used a distance that is a meter on the set of all fuzzy numbers with continuous left and right spread functions. To support our claims analytically, we have proven some theorems and given supplementary corollaries.
Highlights
Comparison of fuzzy numbers is an indispensable part of most systems using such numbers
Throughout this work, we used a distance that is a meter on the set of all fuzzy numbers with continuous left and right spread functions
In order to measure the distance between two fuzzy numbers, here, we propose a new definition
Summary
Comparison of fuzzy numbers is an indispensable part of most systems using such numbers. Some authors have approximated a fuzzy number by a single crisp number This method which is called ranking suffers from loss of some useful information. Finding the nearest triangular or trapezoidal fuzzy number associated to an arbitrary given fuzzy number is another method on which some authors such as [2], [4], [6], [10] and [11] have concentrated. The parametric form of a fuzzy number is given by u = (u, u), where u and u are functions defined over [0, 1] and satisfy the following requirements:. Let Fc(R) be the set of all fuzzy numbers with continuous left and right spread functions and let Fm(R) be the set of all m−degree polynomial form fuzzy numbers [3].
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