Fuzzy numbers from raw discrete data using linear regression

This paper focuses on modelling fuzzy numbers with meaningful membership functions. More precisely, it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data. In many applications, input information is numerical, and therefore, particular fuzzy sets, such as fuzzy numbers, hold great interest and relevance in managing data imprecision and vagueness. The proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression. The technique is simple, fast, and effective. Preliminary tests are performed using different types of input data: a Gaussian function, a Sigmoidal function, three datasets of synthetic discrete data, and an histogram obtained from a colour satellite image.