Infinite-valued logic based on two-valued logic and probability : part 1.4. the TEE model for grades of membership
Ellen Hisdal · NORA - Norwegian Open Research Archives · 1990
This paper precisates the meaning of numerical membership values and shows that there is no contradiction between a probabilistic interpretation of grades of membership on the one hand, and membership functions of the attribute universe whose ordinates add up to more than 1 on the other. The membership value in a class , e.g., =tall, assigned by a subject to an object of a given attribute value u ex (e.g., u ex =exact height value) is interpreted as the subject's estimate of P (ju ex ) , the probability that this object would be assigned (by herself or another subject) the label in the presence of fuzziness #1, 2 or 3 (in an experimental or natural language LB (labeling) or YN (yes-no) situation in which the subject uses a nonfuzzy threshold criterion in the universe U of estimated attribute values). = l is assumed to be an element of a label set , such as = fsmall, medium, tallg . The probabilistic `summing up to 1 requirement' applies to the sum of P ( l ju ...