A linguistic distribution behavioral multi-criteria group decision making model integrating extended generalized TODIM and quantum decision theory

Abstract

In most existing multi-criteria group decision making (MCGDM) problems, the decision makers (DMs) are usually regarded as independent and DMs’ psychological behaviors are rarely considered. However, in many cases, the opinions of DMs are likely to influence each other and the DMs often hold subjective bounded rationality in the decision making process. To address this issue, a linguistic distribution behavioral MCGDM model integrating extended generalized TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method and quantum decision theory is developed. First, linguistic distribution assessments considering the sample size information are used to gather the group linguistic evaluations, which can integrally depict the quantitative distribution and qualitative vagueness. Second, an extended generalized linguistic distribution TODIM method is presented to reflect the DMs’ bounded rational behaviors. It is used to calculate the dominance of each alternative. Third, a quantum possibilistic aggregation framework is constructed to explore the interference effects among DMs’ opinions. In this process, DMs’ opinions are viewed as synchronously occurred wave functions that interfere with each other and influence the aggregated result. Finally, a case study is examined to recommend the optimal automobile for customers based on distributed online reviews in newcar.xcar.com and autohome.com. Three separate scenarios with conjunctive, neural, and disjunctive modes are considered respectively. The sensitivity analysis is given to show the effect of risk factors and interference factors. The parameters show to be dominant in the final best automobile recommendation. The comparisons with some existing methods confirm the validity and stability of the proposed MCGDM method.