Aggregation of Basic Uncertain Information With Two-Step Aggregation Frame

There exist various categories of uncertain information, and their corresponding methods of aggregation may also vary. At present, there exists a dearth of specifically tailored techniques for aggregating basic uncertain information (BUI). The present study introduces a two-step aggregation frame that is applicable to inputs of both real-valued and BUI-valued inputs. In the process of constructing such a frame, several novel notions and definitions are introduced. These comprise of extended aggregation operators with respect to a finite set and to a collection of subsets of the set, some certainty independent BUI aggregation and some certainty dependent BUI aggregation, BUI merging operators and BUI aggregation operators, BUI-valued min operator, and BUI-valued Sugeno integral. Some corresponding deductions, necessary reasoning and numerical examples are presented.