The objective of the paper is to present a new concept named as Cubic q-rung orthopair fuzzy linguistic set (Cq-ROFLS) to quantify the uncertainty in the information. The proposed Cq-ROFLS is qualitative form of cubic q-rung orthopair fuzzy set (Cq-ROFS), where membership degrees (MDs) and non-membership degrees (NMDs) are represented in terms of linguistic variables. The basic notions of Cq-ROFLS have been introduced and study their basic operations and properties. Further, to aggregate the

more »

... ferent pairs of the preferences, we introduce the Cq-ROFL Muirhead mean, weighted Muirhead mean, dual Muirhead mean based operators. The major advantages of considering the Muirhead mean is that it considers the interrelationship between more than two arguments at a time. On the other hand, the Cq-ROFLS has the ability to describe the qualitative information in terms of linguistic variables. Several properties and relation of the derived operators are argued. Besides, we also investigate multi attribute decision making (MADM) problems under the Cq-ROFLS environment and illustrate with a numerical examples. Finally, the effectiveness and advantages of the work are established by comparing with other methods.