The measurement of membership by subjective ratio estimation

When we perform algebraic operations on membership degrees, we must be sure that they are compatible with the kind of scale on which these degrees are measured. For example, we will not add (in a weighted average) membership degrees that are measured on an ordinal scale. An important question is therefore how to determine on which kind of scale we measure the membership. There are several techniques for measuring membership. In this paper, we present some of them, based on Stevens’ technique of ratio estimation, and we characterize them, thereby providing a sound way to determine the level of measurement. We also discuss the problem of the representation of the union or intersection by a t-conorm or t-norm.