The X-mu approach: Fuzzy quantities, fuzzy arithmetic and fuzzy association rules

The use of so-called fuzzy numbers for approximate calculations leads to significant problems, because the underlying mathematical structure is weaker than ordinary arithmetic. Many of these problems arise from the fact that the fuzzy quantities are actually fuzzy intervals. Gradual numbers were recently proposed as a better representation for fuzzy quantities. In this paper, we describe the X-μ approach, a new method of visualizing and calculating functions of fuzzy quantities. In particular, we illustrate the calculation of fuzzy association confidence in cases where membership can be represented by a function or a table of values.