A Model for Decision Making with Missing, Imprecise, and Uncertain Evaluations of Multiple Criteria

In real-life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval-valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria’s evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster’s rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret-avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real-life MCDM problems. C ⃝ 2012 Wiley Periodicals, Inc.