Some Muirhead mean operators for probabilistic linguistic term sets and their applications to multiple attribute decision-making

Abstract Archimedean t-conorm and t-norm (ATT) consists of t-conorm (TC) and t-norm (TN) families, which can develop the general operational laws for some fuzzy sets (FSs). Linguistic scale functions (LSFs) generate different semantic values for the linguistic terms (LTs) based on the different usage environments. Muirhead mean (MM) aggregation operators have a prominent advantage of capturing interrelationship among any number of arguments. So it is essential to combine MM operators with probabilistic linguistic term sets (PLTSs) on the basis of the ATT and LSFs. In this paper, we firstly propose the general operational laws for PLTSs by ATT and LSFs. Then, we develop the probabilistic linguistic Archimedean MM (PLAMM) operator, probabilistic linguistic Archimedean weighted MM (PLAWMM) operator, probabilistic linguistic Archimedean dual MM (PLADMM) operator and probabilistic linguistic Archimedean dual weighted MM (PLADWMM) operator, and further explore their special examples. Moreover, we provide two multiple attribute decision-making (MADM) methods built on the proposed operators. Finally, some numerical examples are proposed to validate the proposed methods, which are compared with other existing methods to denote their effectiveness.