A Combined Compromise Decision Method with Large-Scale and Multi-granularity Probabilistic Linguistic Information

The expression forms of existing probabilistic interval linguistic terms are mostly discrete. When the scale of evaluation information is large and the evaluation information is different, using a probabilistic interval linguistic term set that lists linguistic values one by one has certain limitations in expression. This study proposes a new linguistic expression form called multi-granularity log-normal probabilistic interval linguistic value, which not only effectively processes large-scale linguistic information, but also pays attention to the information distribution characteristics within the interval linguistic term. Firstly, the multi-granularity log-normal probabilistic interval linguistic value is defined, and its algorithms and related properties are introduced. Secondly, a consistency conversion method is proposed for dealing with multi-granularity log-normal probabilistic interval linguistic information. Some excellent properties satisfied by the conversion function effectively avoided information loss during the linguistic transformation process. Subsequently, the attribute ratio Analysis method based on indifference threshold (ITARA) considering the log-normal probabilistic interval linguistic features is developed. By establishing a mixed 0–1 integer programming model based on the cross entropy, interval weights and their indifference thresholds are obtained. The shortcomings of the secondary compromise operator in the traditional combined compromise solution (CoCoSo) method are improved, and the unique advantages of the proposed improvement method are demonstrated through comparative examples. Furthermore, an effective fusion and ranking method for log-normal fuzzy numbers is provided. Finally, the applicability and effectiveness of this method are verified through two species abundance evaluation numerical examples.