Analytic hierarchy process and fuzzy set theory

The analytic hierarchy process (AHP), introduced by Thomas Saaty (1980), recognized as a modern tool for dealing with complex decision-making may help the decision maker to set priorities to make the best decision. 

Although vast majority of applications of AHP use crisp data, it is quite possible that the data in many real applications are not crisp. Hence, imprecision may arise from a variety of reasons: unquantifiable information, incomplete information, unobtainable information, and partial ignorance. Conventional multiple attribute decision-making methods cannot effectively handle problems with such imprecise information. Hence, fuzzy AHP has been developed dealing with uncertain data and owing to the imprecision in assessing the relative importance of attributes and the performance ratings of alternatives with respect to attributes. 

This chapter provides background information on fuzzy set and fuzzy AHP. We aim to present the research areas that are most influenced by AHP and discuss the use of fuzzy sets in uncertain situation along with AHP. This chapter highlights the major effort involved in handling fuzzy AHP, which has led to several applications that have proven to be very useful when there is a notion of uncertainty in the data.