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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 CAO1,2, 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
Diserahkan: 21
Februari 2019/Diterima: 23 Disember 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; Jaccard similarity coefficient;
interval-valued belief structures
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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*Pengarang untuk surat-menyurat; email:
tyzhangxy@163.com
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