A Note on Limitations of FAHP

Abstract

Does application of fuzzy AHP improve outcomes? Study reveals that fuzzy AHP brings more complexity and fuzziness in decision-making process and thereby spoil the outcomes. Fuzzy AHP violates fundamental axioms of classical AHP. Three different models of fuzzy AHP are discussed in this regard, namely Van Laarhoven and Pedrycz (Fuzzy Sets Syst 11:229–241, 1983), Buckley (Fuzzy Sets Syst 17:233–247, 1985), and Chang (Eur J Oper Res 95(3):649, 1996). Optimization approaches are also included as an alternative approach to classical AHP to find priorities of criteria and alternatives. Study reveals that fuzziness increases during multiplication of fuzzy numbers with the increase in support of fuzzy membership function. Moreover, very limited research work has been identified on consistency of fuzzy pairwise comparison matrix. In this regard, some of the popular methods are discussed in brief in this chapter, namely method of Triantaphyllou and Lin (1996), Least Square Distance Method (Wang and Parkan, Inf Sci 176:3538–3555, 2006), Defuzzification-based Least Square Method (Wang and Parkan, Inf Sci 176:3538–3555, 2006), Preference Programming (Salo and Hämäläinen, Eur J Oper Res 82:458–475), and Fuzzy Preference Programming (Mikhailov and Singh, IEEE Trans Syst, Man, Cyber Part C 33(1):33–41, 2003). Comparative analysis shows that result obtained from Fuzzy Preference Programming (FPP) is very close to classical AHP.

One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria.

Chiang Kao

Applied Mathematical Modelling (2010), Vol. 34, pp. 1779–1787