Some interval-valued hesitant uncertain linguistic Bonferroni mean operators and their application in multiple attribute group decision making

Abstract

The aim of this paper is to propose some novel multiple attribute group decision making (MAGDM) methods to deal with MAGDM problems in which the attributes are interactive in the form of interval-valued hesitant uncertain linguistic numbers (IVHULNs). Firstly, some new aggregation operators for IVHULNs based on Bonferroni mean (BM) are proposed, which are the interval-valued hesitant uncertain linguistic BM (IVHULBM) operator, the normalized weighted IVHULBM (NWIVHULBM) operator, the interval-valued hesitant uncertain linguistic geometric BM (IVHULGBM) operator and the normalized weighted IVHULGBM (NWIVHULGBM) operator. The advantages of the proposed operators are that it cannot only effectively aggregate IVHULNs, but it can also consider the interactive characteristics among attributes. At the same time, some special cases of these operators are discussed. Then, this paper demonstrates that these presented operators are able to meet four desirable properties, which are reducibility, idempotency, monotonicity, and boundedness. Moreover, to solve MAGDM problems, two approaches on the basis of the NWIVHULBM and NWIVHULGBM operators are put forward. Finally, the proposed methods are applied to a decision making problem regarding online service quality evaluation. It provides us with a useful way for MAGDM with IVHULNs.