Affiliations: Department of Electrical and Information Engineering, Shaoxing University, Shaoxing, Zhejiang Province, P.R. China
Correspondence:
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Corresponding author. Jun Ye, Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang Province 312000, P.R. China. Tel.: +86 575 88327323; E-mail: yejun@usx.edu.cn.
Abstract: To describe both certain linguistic and uncertain linguistic information simultaneously in the real world by a linguistic form, this paper originally proposes the concept of a linguistic cubic variable (LCV) (including internal linguistic cubic variable and external linguistic cubic variable), which is characterized by its uncertain linguistic variable and its certain linguistic variable simultaneously, and the basic operational laws of LCVs. Then, we introduce the distance measures of LCVs and the expected value of LCV for ranking LCVs. Next, we develop a LCV weighted arithmetic averaging (LCVWAA) operator and a LCV weighted geometric averaging (LCVWGA) operator to aggregate linguistic cubic information and prove their desired properties. Further, a multiple attribute decision-making method based on the proposed LCVWAA or LCVWGA operator and the expected value is established under a linguistic cubic environment. Finally, an illustrative example is presented to demonstrate the application and effectiveness of the developed approach.
Keywords: Linguistic cubic variable, distance, expected value, linguistic cubic variable weighted arithmetic averaging (LCVWAA) operator, linguistic cubic variable weighted geometric averaging (LCVWGA) operator, decision making
