Comparison of fuzzy and crisp analytic hierarchy process (AHP) methods for spatial multicriteria decision analysis in GIS

Abstract: There are a number of decision making problems in which Geographical Information System (GIS) has employed to organize and facilitate the procedure of analyzing the problem. These GIS-based decision problems which typically include a number of different criteria and alternatives are generally analyzed by Multicriteria Decision Analysis (MCDA).Different locations within a geographical area represent the alternatives by which the overall goal of the project is achieved. The quality of achieving the goal is evaluated by a set of criteria which should be considered in the work. Analytic Hierarchy Process (AHP) which is a powerful method of MCDA generally can organize spatial problems and decides which alternatives are most suitable for the defined problems. However due to some intrinsic uncertainty in the method, a number of authors suggest fuzzifying the method while others are against fuzzification of the AHP. The debate over fuzzifying AHP is going on and attempt for finding that was mostly in theory, and little, if any; practical comparison between the AHP and fuzzified AHP has done. This work presents a practical comparison of AHP and fuzzy AHP in a GIS-based problem, case study, for locating a dam in Costa Rica, considering different criteria. In order to perform the AHP and fuzzy AHP in the GIS-based problem and calculating weights of the criteria by the methods, some computer codes have written and developed in MATLAB. The comparisons between the AHP and fuzzy AHP methods are done on result weights and on the result final maps. The comparison between the weights is repeated on different levels of uncertainty in fuzzy AHP then all the results are compared with the result of AHP method. Also this study for checking the effect of fuzzification on results is suggested Chi-Square test as a suitable tool. Comparisons between the resulting weights of the AHP and fuzzy AHP methods show some differences between the methods. Furthermore, the Chi-Square test shows that the higher level of uncertainty in the fuzzy AHP, the greater the difference in results between the AHP and fuzzy AHP methods.