On a new distance measure of three-parameter interval numbers and its application to pattern recognition

Abstract

In this paper, a new distance measure of three-parameter interval numbers is proposed, which considers not only the particularity of the center of gravity in a three-parameter interval number but also the influence of risk attitudes of decision makers. Some properties of the proposed distance measure are also proved from the perspective of metric spaces. Based on the proposed distance measure of three-parameter interval numbers, a new type of distance measure of LR-type fuzzy numbers is introduced. By considering different left and right shape functions in the proposed distance measure of LR-type fuzzy numbers, some new distance measures of triangular fuzzy numbers and normal fuzzy numbers are obtained. It is shown from some examples that the proposed distance measures of triangular fuzzy numbers and normal fuzzy numbers may overcome drawbacks of some existing similarity measures of triangular fuzzy numbers and normal fuzzy numbers.