A Systematic Review on Generalized Fuzzy Numbers and Its Applications: Past, Present and Future

Abstract

Nowadays, the program’s mechanisms are becoming more dynamic. As a result, maintaining performance for a longer duration of time to increase the system’s long-term growth is tough. This is mostly because of the malfunction occurrence during the study, as the machine does not always have all details. In order to tackle this problem, the available data must be used to construct the problems. However, one of the most successful data theories is fuzzy set theory. The concept of fuzzy logic has recently grown in favour, and it plays an important role in engineering and management. Fuzzy arithmetic was very significant in research fields including decision-making problems, confidence analysis, optimization etc. as compare to others. Fuzzy numbers came into existence to perform operations on fuzzy observations. The distinction between generalised fuzzy and classic fuzzy arithmetic operations is that the former can handle both non-normal and normalised fuzzy, while the latter can only handle normalised fuzzy. The goal of this research is to give a broad overview of current techniques in this field. The methodology reported in this article focuses on improving the arithmetic process in a fuzzy environment. The current arithmetic operations take into account the same degree of precision with specific fuzzy numbers, it is found that the lack of knowledge is responsible for incorrect performance. To avoid and maintain the uniformity of the fuzzy numbers, an improved operator like adding, scaling, subtracting, multiplication has been derived for generalized trapezoidal (triangular), sigmoidal and parabolic fuzzy numbers.