Cognitive Consistency in Uncertain and Preference Involved Weights Determination

In uncertain information environment, bi-polar preferences can be elicited from experts and processed to be exerted over some weights determination for multiple-agents evaluation. Recently, some weighting methodologies and models in uncertain and preference involved environment with multiple opinions from multiple experts are proposed in some literature. However, in that existing method, when collecting different types of preferences from a single expert, sometimes some subtle cognitive inconsistency may occur. To eliminate such inconsistency, this work elaborately analyzes the possible reasons and proposes some amendment together with a new distinguishable set of formulations for modeling. In addition, we further consider two situations of the weighting models for the problem, with one only considering the situation of single expert with no risk of cognitive inconsistency and the other considering the case of multiple experts wherein some inconsistency might occur. Numerical example and comparison are also presented accordingly.