Sains Malaysiana 48(12)(2019): 2787–2796

http://dx.doi.org/10.17576/jsm-2019-4812-20

A Distance Measure of Interval-valued Belief Structures

(Suatu Jarak Pengukuran Nilai Selang Struktur Kepercayaan)

JUNQIN CAO^1,2, XUEYING ZHANG²* & JIAPENG FENG³

¹College of Information and Computer, Taiyuan University of Technology, Taiyuan, 030024, China

²School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

³Tai Yuan Institute of China Coal Technology and Engineering Group, Taiyuan, 030024, China

Received: 21 February 2019/Accepted: 23 December 2019

ABSTRACT

Interval-valued belief structures are generalized from belief function theory, in terms of basic belief assignments from crisp to interval numbers. The distance measure has long been an essential tool in belief function theory, such as conflict evidence combinations, clustering analysis, belief function and approximation. Researchers have paid much attention and proposed many kinds of distance measures. However, few works have addressed distance measures of interval-valued belief structures up. In this paper, we propose a method to measure the distance of interval belief functions. The method is based on an interval-valued one-dimensional Hausdorff distance and Jaccard similarity coefficient. We show and prove its properties of non-negativity, non-degeneracy, symmetry and triangle inequality. Numerical examples illustrate the validity of the proposed distance.

Keywords: Distance; Hausdorff distance; interval-valued belief structures; Jaccard similarity coefficient

ABSTRAK

Nilai selang struktur kepercayaan digeneralisasi daripada teori fungsi kepercayaan, dari sudut tugasan kepercayaan asas nombor krisp kepada selang. Jarak pengukuran telah menjadi alat yang penting dalam teori fungsi kepercayaan, seperti gabungan bukti konflik, analisis berkelompok, fungsi kepercayaan dan penganggaran. Penyelidik telah memberi banyak perhatian dan mencadangkan pelbagai jenis jarak pengukuran. Walau bagaimanapun, beberapa kajian telah membincangkan jarak pengukuran nilai selang struktur kepercayaan. Dalam kertas ini, kami mencadangkan kaedah untuk mengukur jarak fungsi selang kepercayaan. Kaedah ini berdasarkan jarak nilai selang satu dimensi Hausdorff dan pekali kesamaan Jaccard. Kami tunjuk dan buktikan sifatnya yang tidak negatif, tidak merosot, simetri dan ketidaksamaan segitiga. Contoh berangka menunjukkan kesahan jarak yang dicadangkan.

Kata kunci: Jarak; jarak Hausdorff; nilai selang struktur kepercayaan; pekali kesamaan Jaccard

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*Corresponding author; email: tyzhangxy@163.com