How to treat strict preference information in multicriteria decision analysis

Abstract

This paper addresses the use of incomplete information on both multi-criteria alternative values and importance weights in evaluating decision alternatives. Incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds. En route to prioritizing alternatives, the majority of previous studies have replaced these strict inequalities with weak inequalities, by employing a small positive number. As this replacement closes the feasible region of decision parameters, it circumvents certain troubling questions that arise when utilizing a mathematical programming approach to evaluate alternatives. However, there are no hard and fast rules for selecting the factual small value and, even if the choice is possible, the resultant prioritizations depend profoundly on that choice. The method developed herein addresses and overcomes this drawback, and allows for dominance and potential optimality among alternatives, without selecting any small value for the strict preference information. Given strict information on criterion weights alone, we form a linear program and solve it via a two-stage method. When both alternative values and weights are provided in the form of strict inequalities, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve this linear program via the same two-stage method. One application of this methodology to a market entry decision, a salient subject in the area of international marketing, is demonstrated in detail herein.