Publication Date



Technical Report: UTEP-CS-18-57


In many design problems, it is important to take into account expert knowledge. Expert often describe their knowledge by using imprecise ("fuzzy") natural-language words like "small". To describe this imprecise knowledge in computer-understandable terms, Zadeh came up with special fuzzy methodology -- techniques that have been successful in many applications. This methodology starts with eliciting, from the expert, a membership function corresponding to each imprecise term -- a function that assigns, to each possible value of the corresponding quantity, a degree to which this value satisfies the relevant property (e.g., a degree to which, in the expert's opinion, this value is small). In principle, we can have complex membership functions. However, somewhat surprisingly, in many applications, the simplest membership functions -- of triangular or trapezoid shape -- turned out to be most efficient. There exist some explanations for this surprising empirical phenomenon, but these explanations only work when we use the simplest possible "and"-operation -- minimum. In this paper, we provide a new, more general explanation which is applicable for all possible "and"-operations.