In this paper, the concept of linguistic cubic number (LCN) is introduced which further extends the concept of linguistic intuitionistic fuzzy number (LIFN). More specifically, the notions of internal (external) developed and (P-)R-order for LCN are studied. For a given LCN, some basic operational laws, score and accuracy function are proposed. Also, some generalized aggregation operators based on the operational rules are developed and their related properties are investigated. As application, a multi-attribute decision-making (MADM) method is established based in the environment of LCNs and with the help of defined aggregation operators. Finally, an illustrative example is provided to show the effectiveness of the proposed MADM method.
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