Unbalanced probabilistic linguistic decision-making method for multi-attribute group decision-making problems with heterogeneous relationships and incomplete information

摘要

In group decision-making problems, decision makers prefer to use several linguistic terms to describe their own perception and knowledge, and give their preference intensity of each possible linguistic terms based on their own understanding and interpretation. Due to the nonlinearity of decision maker’s cognition, the gaps between adjacent linguistic terms are unbalanced. The unbalanced probabilistic linguistic term set (UPLTS) is proposed to present such situation. To this phenomenon, a resolution framework is constructed to analyze multiple attribute group decision-making problems under unbalanced probabilistic linguistic environment. Firstly, the integration model based on evidential reasoning theory is proposed to aggregate UPLTSs from different groups in view of incomplete probabilistic distributions in UPLTS. Secondly, the transformation function based on proportional 2 tuple is developed to transform UPLTS into probabilistic linguistic term set, making it easier for subsequent analysis and processing. Thirdly, Based on the multiple types of partitioned structure relationship among attributes, partitioned fuzzy measure is developed to globally capture these interactions among attributes. Then the probabilistic linguistic Choquet integral operator with partitioned fuzzy measure is proposed to obtain the comprehensive performances of alternatives. Lastly, the effectiveness and practicability of the proposed method is demonstrated using three numerical examples and comparing with other methods.