The inclusion of logical interaction between criteria in FAHP

Abstract

This chapter presents a methodology that allows modeling of logical interaction between criteria in multicriteria decision-making (MCDM). We propose a hybrid model for supporting the selection of suppliers in the telecommunications sector, combining the fuzzy analytic hierarchy process (FAHP) and interpolative Boolean algebra (IBA). The baseline model will be FAHP where each criterion is supposed to be independent, and the aggregation function is supposed to be linear, that is, a weighted sum of criteria is a good aggregation function for ranking. The competing approach is the application of IBA in order to establish the logical interactions than can be expressed by decision makers. Once the logical functions are set, they are translated into a generalized Boolean polynomial (GBP), after which the GBP is reduced to a numerical value through logical aggregation (LA). What makes IBA more exible and efcient is that all the structural transformations-that is, the logical dependencies among criteria-are established before the introduction of a numerical value, which is not the case with conventional fuzzy multicriteria decision-making (FMCDM) methods. In this way, one can overcome the complex matrix for a large number of criteria, subcriteria, and alternatives that are inherent in fuzzy logic, thereby simplifying the computational effort. In addition, the proposed approach treats contradiction differently than other FMCDM methods (i.e., the negated variable is not transformed immediately into a value) and respects the law of the excluded middle.