Proof the Positive Definiteness for the Jaccard Index Matrix Based on Fuzzy Sets. Issue 3 (October 2020)

• Record Type: Journal Article
• Authors: Sun, Linge; Song, Yafei; Lei, Lei
• Is Part Of: Journal of physics. Volume 1650:Issue 3(2020)
• Publication Date: 2020-10
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1650/3/032206
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: This paper addresses the proof process of the positive definiteness property for the Jaccard index matrix, which is applied to define a metric distance measure between belief functions. Our proof is implemented in the framework of fuzzy sets. Based on the decomposition theorem of Jaccard index matrix proposed by M. Bouchard et al, and the transformation between crisp sets and fuzzy sets, the positive definiteness of the Jaccard index matrix can be proved in a concise way.