Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions

• We define the linguistic distribution assessments and their operations.
• We propose the transformations in the multi-granular unbalanced context.
• We discuss the application of this proposal in the MAGDM.

Linguistic distribution assessments with exact symbolic proportions have been recently presented. Due to various subjective and objective conditions, it is often difficult for decision makers to provide exact symbolic proportions in linguistic distribution assessments. In some situations, decision makers will express their preferences in multi-granular unbalanced linguistic contexts. Therefore, in this study, we propose the concept of linguistic distribution assessments with interval symbolic proportions under multi-granular unbalanced linguistic contexts. First, the weighted averaging operator and the ordered weighted averaging operator for the linguistic distribution assessments with interval symbolic proportions are presented. Then, we develop the transformation functions among the multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions. Finally, we present the application of the proposed linguistic distribution assessments in multiple attribute group decision making.