Size relation of uncertain sets with application to clustering

Article type: Research Article

Authors: Yang, Xiangfeng | Ni, Yaodong^{; *}

Affiliations: School of Information Technology & Management, University of International Business & Economics, Beijing, China

Correspondence: [*] Corresponding author. Yaodong Ni, School of Information Technology & Management, University of International Business & Economics, Beijing 100029, China. E-mail: ni@uibe.edu.cn.

Abstract:  Along with increasing and extension of uncertain set theory in decision making, ordering and ranking of uncertain sets have significantly become relevant, that is, an uncertain set needs to be evaluated and compared with the others. This paper introduces the size relation between two uncertain sets. It derives a formula to calculate the uncertain measure that an uncertain set is less than or equal to another one. Moreover, some examples are given to illustrate the size relation of uncertain sets. Finally, clustering is proposed as an application.

Keywords: Uncertainty theory, uncertain set, membership function, size relation, clustering

DOI: 10.3233/JIFS-190342

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 4119-4125, 2020