Ordered weighted geometric averaging operators for basic uncertain information

Basic Uncertain Information (BUI) was proposed as an information granule that simultaneously accounts for both the value of the input and the certainty about that value. To aggregate BUI granules using Ordered Weighted Averaging (OWA) operators with bi-polar optimism-pessimism preferences, the ordered weighted averaging (BUIOWA) operators have been proposed recently. As weighted geometric mean is an alternative aggregation operator to weighted mean, the ordered weighted geometric averaging operator (OWGA) is the alternative to the OWA operator. Therefore, this study proposes basic uncertain information ordered weighted geometric averaging (BUIOWGA) operators to serve as the alternative aggregation choice to BUIOWA operators. Unlike BUIOWA operators, BUIOWGA operators have three different types, BUIOWGA type I, BUIOWGA type II, and BUIOWGA type III, with an increasing order relation. Several monotonicities, properties, and relations are proposed for the three different BUIOWGA operators and the BUIOWA operator. Finally, we present comparative analysis, numerical examples, and applications.