Some spherical linguistic Muirhead mean operators with their application to multi-attribute decision making

This paper aims to propose a new tool to express decision makers' preference information in multi-attribute decision making (MADM) producers. By taking advantages of spherical fuzzy sets (SFSs) and linguistic variables (LVs), we give the definition of spherical linguistic sets (SLSs) and provide operations of spherical linguistic numbers (SLNs). Based on the proposed operations, we incorporate Muirhead mean (MM) into SLSs and introduce novel spherical linguistic aggregation operators. These proposed operators adsorb the inherent advantages of MM, i.e., taking the interrelationship among any numbers of aggregated inputs into account and producing flexible information fusion process. Furthermore, we apply the proposed method in MADM and present the main steps of a new method. In order to show its effectiveness, we use the method to solve an actual MADM problem. The advantages and superiorities of the proposed method are also studied.