FUZZIFIED BISECTION METHOD TO FIND THE ROOT OF AN ALGEBRAIC EQUATION USING n−POLYGONAL FUZZY NUMBERS

FUZZIFIED BISECTION METHOD TO FIND THE ROOT OF AN ALGEBRAIC EQUATION USING n−POLYGONAL FUZZY NUMBERS

K. N. Vable, P. G. Jadhav, S. B. Gaikwad

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Abstract

In this paper, we introduce a fuzzified bisection method to find the root of an algebraic equation using n-polygonal fuzzy numbers. We present a new approach for finding the root of an algebraic equation with the n-polygonal fuzzy number. To solve the given algebraic equation, we consider a fuzzy interval, and the method iteratively reduces the interval containing the fuzzy root by evaluating the value of a function at each midpoint. We continue this process until the desired level of approximation is achieved. The fuzzified bisection method has broad applications in engineering, economics, and decision-making. The results demonstrate that the method provides a flexible and effective way to find root.

Keywords

Triangular fuzzy number, Trapezoidal fuzzy number, n-Polygonal fuzzy number (n-PFN), Bisection method, Fuzzy membership function, Arithmetic operations on n-PFN, α - cut.