An asymmetric trapezoidal cloud-based linguistic group decision-making method under unbalanced linguistic distribution assessments

Linguistic group decision-making issues occur very frequently in practical decision situations. As a kind of information representation, unbalanced linguistic distribution assessments (ULDAs) are commonly utilized in the linguistic group decision-making process. To thoroughly well describe linguistic information, a numerical concept is developed, namely asymmetric trapezoidal cloud (ATC) models. These models overcome the inherent limitation of cloud models, and they are followed by a series of related contents involving a comparison method, distance measure and operational rule. Then, a rational conversion method is proposed to establish a bridge between ULDAs and ATCs. To meet our research requirements, extended linguistic scale functions (LSFs) are introduced to create a map from linguistic terms to numerical values; the map is based on numerical scale (NS) models. Subsequently, two types of decision support models are presented to solve multicriteria group decision-making issues: ATC power average (ATCPA)-based and TODIM-PROMETHEE II-based decision support models. An illustrative case study involving the evaluation of industrial sewage discharge is utilized to validate the feasibility of our decision support models, and it is followed by an analytical comparison and discussion. The findings demonstrate that our work has an excellent performance and some practical implications.