Abstract: The use of incomplete probabilistic linguistic term sets (InPLTSs) can enrich the flexibility of qualitative decision-making information expression, especially in decision-making situations with high time pressure and insufficient knowledge. In this study, a method for group decision-making (GDM) with incomplete probabilistic linguistic preference relations (InPLPRs), considering consistency and consensus simultaneously, is developed. First, to fully explore the ability of InPLTSs to express uncertain information, InPLTSs are specifically classified. Then, an expected multiplicative consistency of InPLPRs is introduced, which is conductive to estimating the missing information more accurately and effectively. Subsequently, considering the consensus of GDM problems, a consensus index, which considers the principle of majority and minority, is developed to measure the agreement degree among multiple individuals. Because individual InPLPRs may not all meet acceptable consistency after reaching consensus, a consistency- and consensus-improving mathematical programing model considering information distortion is presented. Then, to aggregate all individual preference relationships into a collective one, a reliability induced ordered weighted geometric operator is introduced, whose induced variable reliability is determined by the confidence degree and consistency index of individual preference relationships. Furthermore, a multi-phase algorithm with InPLPRs is developed to solve GDM problems. Finally, a numerical example is presented to illustrate the applicability of the proposed method, and some detailed validity test and comparative analysis are conducted to highlight the advantages of the proposed method.

Biography: Prof. Liu worked at School of Management Science and Engineering in Shandong University of Finance and Economics. He obtained his Doctor degree in Management Science and Engineering in the Beijing Jiaotong University in 2010, obtained his Master degree in Signal and Information Processing in the Southeast University in 1991, and obtained his Bachelor degree in Signal and Information Processing in the Southeast University in 1988.
He was engaged in the technology development and the technical management in the Inspur Group Ltd. from 1991 to 2004, and had been Senior Engineer (1997-2005). Since February 2004, he has been with the School of Management Science and engineering of the Shandong University of Finance and Economics, and now he is a full professor in Shandong University of Finance and Economics (SDUFE) since 2005. At the same time, he is also (1) Dean of Management Science and Engineering, SDUFE; (2) Director of Decision Science Research Institute of SDUFE; (2) Vice chairman of Professor Committee of SDUFE; (3) the Assistant Director of the Enterprise’s Electronic-commerce Engineering Research Center of Shandong Province.
In addition, he is the standing director of China Information Economics Society (CIES), the standing director of China Quantitative Economics Society (CQES), the standing director of China Branch of International Electronic Commerce Federation, Executive vice president of Shandong Electronic Society, and the standing director of Shandong Economic Management Association. He is also the Associate Editors of Information sciences, International Journal of Fuzzy Systems, Journal of Intelligent and Fuzzy Systems, Technological and Economic Development of Economy, and also is a member of editorial board of Mathematical Problems in Engineering, Journal of Applied Mathematics, etc.. Besides, he has been an active reviewer for many journals and conferences such as IEEE TFS, IEEE TCYB, Information Sciences, Expert Systems With Applications, Knowledge-Based Systems, European Journal of Operational Research, Information Fusion, Applied Soft Computing, etc.
Prof. Liu has authored or coauthored more than 280 publications in IEEE Transactions on Fuzzy systems, IEEE Transactions on Cybernetics, IEEE Transactions on Systems, Man, and Cybernetics: Systems, Information Sciences, Expert Systems with Applications, Knowledge-Based Systems, Applied Soft Computing, International Journal of Approximate Reasoning, etc.

Research fields: decision analysis and decision support, applied mathematics, expert systems, technology and information management, electronic-commerce, intelligent information processing.