Affiliations: School of Economics and Management, Southeast University, Nanjing, Jiangsu, China | School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, China
Note: [] Corresponding author. Zeshui Xu, School of Economics and Management, Southeast University, Nanjing, Jiangsu, China. Tel./Fax: +86 25 84483382; E-mails: xuzeshui@263.net (Z. Xu); chenna_njue@163.com (N. Chen).
Abstract: Interval-valued hesitant fuzzy sets (IVHFSs), as an extension of hesitant fuzzy sets, can account for the membership degrees of an element to a given set having a few different interval values, which provides an intuitionistic description on the differences among decision makers. We derive the properties and relationships of fundamental operations on IVHFSs for Algebraic t-norm and t-conorm. Furthermore, we present the operations based on Archimedean t-norm and t-conorm and investigate their properties. The results obtained using the two types of t-norms and t-conorms could be useful for applications of IVHFSs in information aggregation and decision making.
Keywords: Interval-valued hesitant fuzzy set, interval-valued hesitant fuzzy element, Algebraic and Archimedean t-norms and t-conorms
