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Analytic Hierarchy process (AHP) is a powerful method belonging to the full aggregation family of multi-criteria decision-making methods based on pairwise comparisons of objects. Since the information about the problem is usually not complete in real decision-making problems, it is difficult to express precisely the preferences on pairs of compared objects. This problem has been handled in the literature by introducing fuzziness into AHP. However, neither AHP nor its fuzzy extensions can deal with sorting decision-making problems, which form a significant part of decision-making problems. This paper presents the FAHPSort method — a fuzzy extension of the AHPSort method, which is an adaptation of the AHP method for sorting decision-making problems. The FAHPSort method handles the vagueness in the meaning of linguistic terms expressing the intensity of preference of one object over another one. Key properties of the FAHPSort method are described in the paper, and the method is illustrated in a decision-making problem. [ABSTRACT FROM AUTHOR]

In the last 30 years, several distinguished researchers have proposed and discussed different fuzzy versions of well-known Saaty's Analytic Hierarchy Process (AHP). The paper recently published by K. Zhü in the European Journal of Operational Research heavily criticizes the fuzzy approaches to AHP, claiming the fallacy of all of them. Therefore, it seems to be necessary to clarify whether the criticisms are well-founded or not. The present paper aims to rebut Zhü's claims by showing that the evidences and the reasonings in his paper are very poor and far from proving the fallacy of fuzzy AHP. [ABSTRACT FROM AUTHOR]