Dissimilarity measure of logical expressions

The concept of label semantics proposed by Lawry is a random set framework for modeling with words. It proposes two fundamental and inter-related measures of the a appropriateness of labels as descriptions of an object or value. In this paper, based on an introduction of logical expressions based on label semantics, we present a new measure to evaluate the distance between two logical expressions of fuzzy labels. Two fundamental and important properties of this distance are discussed. It is theoretically proved and tested by experiments that the new measure can explain the dissimilarity of linguistic rules well.