Increasing growth and development of building industry and civil engineering motivates enterprises to advance bid evaluation process in an effort to ameliorate building quality and diminish construction cost. The selection of qualified construction contractor has been generally formulated and addressed as a multi-attribute group decision-making problem. However, few existing studies have taken the reasoning logic pattern in human cognition process and the compensatory among attributes into account. Therefore, a two-stage logic scoring of preference-ELECTRE III-based approach is established for the management and manipulation of bidder selection. In a bid to facilitate expert evaluation articulation, alternative-attribute assessments in this approach take the form of generalized comparative linguistic expressions, which are subsequently converted into possibility-distribution-based hesitant fuzzy linguistic term set via the similarity measure-based generation approach to enhance information quality and reliability. Then, nonlinear optimization-based direction rules are introduced to advance the automatic minimum-distance-based consensus reaching model and based on which, the individual semantic-embedded assessments are algorithmically adjusted to reach acceptable consensus. Furthermore, the expert and attribute importance degrees are extracted from both semantic and formal logic aspects, and the modified individual assessments are gathered by integrating the two-stage logic scoring of preference aggregation structure and the ELECTRE III method. The present approach provides a solution to bid evaluation problems considering the reasoning logic pattern in human cognition process and the compensatory among attributes. A practical case study and a comparative analysis are performed to demonstrate the feasibility and effectiveness of the established multi-attribute group decision-making approach.