COMPARATIVE ERROR ANALYSIS OF THE α-CUT METHOD AND STANDARD APPROXIMATION METHOD FOR DIVISION OF TRAPEZOIDAL AND TRIANGULAR FUZZY NUMBERS

Abstract

One of the fundamental operations in fuzzy arithmetic (FA) is fuzzy division, where the results can be either exact or approximate. This paper compares two methods for dividing trapezoidal fuzzy numbers (TrFN) and triangular fuzzy numbers (TFN). The first method is an exact approach that uses interval arithmetic via the -cut technique, while the second is an approximation known as the standard approximation method (SAM). This study presents numerical examples, graphical representations, and tabulated error analyses to illustrate the differences between the exact and approximate results. The findings show that the -cut method preserves the theoretical structure of fuzzy numbers (FNs), while SAM, although computationally simpler, introduces a measurable approximation error.