Implementing Fuzzified Trapezoidal Rule with Triangular Fuzzy Numbers: An Analytical Study

Abstract

Fuzzy logic was introduced by Lotfi A. Zadeh in 1965 as part of his proposal of fuzzy set theory and it has since been utilized in a wide range of disciplines. This study involves fuzzification of Trapezoidal rule. Choice of this topic involves extensive study of large number of literatures for a long period of time. Subsequently, this method has been selected for fuzzification. To implement this fuzzified method, a dedicated computer program was created. Scientific analysis is always needed for successful completion of any research work and to draw acceptable conclusion. For this purpose, inclusive study has been made in the area of statistics to apply the correct statistical tools to achieve the right goal.

Fuzzification of the numerical method was carried out using triangular fuzzy number.  The fuzzification method is accompanied by examples to aid in understanding how it works. To compare the fuzzified and classical methods, fifteen examples were considered. A computer program has been developed for the fuzzified methods, and the solutions to these examples were obtained using this newly developed program. Appropriate statistical tools were used to compare the results from the newly developed method with those from the classical methods. It has been observed that the results of the mathematical problems obtained by newly developed fuzzified Trapezoidal rule is more or less same with the classical method.