Probability completion and consensus reaching based on kernel density estimation for incomplete probabilistic linguistic multi-attribute group decision making

Multi-attribute group decision-making is a hot topic in the study of uncertain decision-making processes, particularly when linguistic variables are employed to express evaluative information. However, incomplete information often arises due to cognitive disparities among decision-makers and their diverse evaluation preferences. To address these challenges, this paper proposes a novel multi-attribute group decision-making method that incorporates incomplete probabilistic linguistic term sets and considers nonlinear semantics. First, we introduce an innovative application of kernel density estimation to complete incomplete term sets, employing Gaussian kernel functions to model the nonlinear perceptual variations of decision-makers. The bandwidth and skewness parameters are utilized to reflect perceptual granularity and evaluation bias, respectively. Second, we modify the Kolmogorov-Smirnov distance measure and propose a novel comparison rule tailored to probabilistic linguistic term sets with semantic imbalance, enhancing the computational accuracy of attribute weight determination. Furthermore, two optimization models are developed to determine the bandwidths for completing incomplete information and aggregating individual evaluations. A dynamic adjustment mechanism is introduced to support decision-maker interaction in achieving consensus. The effectiveness of the proposed methods is demonstrated through a case study on gas meter selection. Sensitivity analysis and comparative experiments highlight its superior performance in handling incomplete information and managing uneven semantics.