Abstract
Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches.
Highlights
Decision making (DM) theory and methods is an important research field [1,2,3,4], while linguisticDM is a critical topic in DM theory and methods since using linguistic terms and arguments, such as “good” and “very good”, for the assessment of the objective world is very fitting for human thinking and expressing habits
Approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of linguistic cubic hesitant variable (LCHV)
Under determinate and indeterminate linguistic situations, the linguistic cubic variable (LCV) that consists of its interval/uncertain linguistic variable (LV) and its certain LV was presented as the linguistic extension of a cubic set in [18] and the weighted aggregation operators of
Summary
Decision making (DM) theory and methods is an important research field [1,2,3,4], while linguistic. This study presents a new linguistic concept based on the combining form of both an LCV and a hesitant LV, which is called a linguistic cubic hesitant variable (LCHV), the operations and ranking method of LCHVs so as to solve MADM problems under the situation of decision makers’ uncertainty and hesitancy. We present the concept of the LCHV, along with internal and external LCHV concepts, the linguistic score function of the LCHV for ranking LCHVs, and the operational relations of LCHVs. Based on the hybrid idea of both an interval/uncertain LV and a hesitant LV, we propose the concept of LCHV, including an internal LCHV and an external LCHV, as below. It is obvious that the above calculational results are still LCHVs
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