Some consistency issues in multi-criteria decision making

The complexity of decision-making problems included under the multi-criteria decision-making (MCDM) paradigm has favored the proliferation of many schools of thought and varied methodologies. It has not yet been possible to prove the supremacy of any of these approaches. Moreover, in some cases it is difficult to combine the theoretical validity of the approximations with their practical appropriateness. It seems that rigor and applicability are two opposing concepts, something that should not be so. It is our responsibility to bridge the gap. To reduce the gap between theory and practice and use effective methodological approaches, it is necessary to combine the rigor and objectivity of traditional science with the realism and subjectivity of human behavior. The analytic hierarchy process (AHP) perfectly combines a classical axiomatic foundation, and offers the objectivity of the traditional scientific method, with an excellent adaptation to the real behavior of individuals and systems in decision making (which connects with behavioral subjectivity). To help achieve this harmony between theoretical foundation and applicability, in this work we consider a framework built within the AHP that provides a mechanism for improving consistency based on a process of linearization developed by the authors. This provides the rigorous counterpart of our scheme. Its applicability hinges on the fact that it is a simple approach that can simultaneously deal with a wide number of applications. Finally, various case studies within the industrial field are presented that support the use of the linearization process to help bridge the gap between theoretical validity and applicability in MCDM