Decision making based on AND-logical quantification of uncertainty in pairwise comparisons

When pairwisely comparing alternatives of a decision making problem, the decision maker (DM) could provide some discrete values to express her/his opinions. The existing uncertainty in pairwise comparisons should be quantified for establishing a decision making model with applications. In this paper, we propose a novel multi-criteria decision making (MCDM) model called AND-logical analytic hierarchy process (AND-AHP). The AND logic is used to quantify uncertainty such that the preference information of the DM is expressed as an AND-logical number. The concept of AND pairwise comparison matrix (AND-PCM) is developed and used as the mathematical tool of the proposed MCDM model. The consistency of AND-PCM is defined and acceptable consistency is discussed. The priority vector is elicited from an AND-PCM by proposing an AND-weighting (AND-W) model. The observation reveals that the proposed model provides an alternative way to effectively investigate MCDM problems with discrete comparisons of alternatives.