A short primer on fuzzy regression

Traditional statistical tools for performing regression cannot handle the large uncertainties present in a fuzzy number dataset. Therefore we will have to rely on techniques developed for interval analysis (Moore 1966; Moore 1979). A useful property of algorithms that handle fuzzy numbers is that they can be rewritten in terms of intervals allowing the powerful mathematical tools of interval analysis to be applied. Every fuzzy number problem can be approached as a level-wise interval problem. The only data requirement is that the fuzzy numbers have the same number of nested intervals. See: Kaufmann & Gupta (1991) for a formal definition of fuzzy numbers. This primer will focus on estimating bounds on coefficients for a linear model when the dependent variable is composed of measurements which are fuzzy numbers and the independent variable is measured exactly. The feasibility of computing bounds on the coefficients when the independent variable is also inexact will be explored.