Computing with Words -- When Results Do Not Depend on the Selection of the Membership Function

Often, we need to transform natural-language expert knowledge into computer-understandable numerical form. One of the most successful ways to do it is to use fuzzy logic and membership functions. The problem is that membership functions are subjective. It is therefore desirable to look for cases when the results do not depend on this subjective choice. In this paper, after describing a known example of such a situation, we list several other examples where the results do not depend on the subjective choice of a membership function. 1 Formulation of the Problem Often, we need to transform natural-language expert knowledge into computerunderstandable numerical form. One of the most successful ways to do it is to use fuzzy logic; see, e.g., [1, 2, 3, 4, 5, 6]. In fuzzy logic, each imprecise property like “small” is described by a membership function that assigns, to each possible value x, a degree μ(x) to which x is, e.g., small.