| As a practical and effective multi-criterion decision analysis method, analytic hierarchy process (AHP) has been widely applied to society, economy, management and engineering systems. With the development of AHP theory and the actual requirements of applications, the fuzzy idea and fuzzy method are introduced to AHP, so the fuzzy analytic hierarchy process (FAHP) has been forming. The research of FAHP based on fuzzy judgement matrices is an important problem for discussion in recently years.This paper studies the consistency problems and ranking methods for three sorts of fuzzy judgement matrices in FAHP, i.e. fuzzy complementary judgement matrices, fuzzy number judgement matrices and linguistic judgement matrices. The main content and research results are as followed.(1) A new index is given to test the degree of multiplicative consistency for the fuzzy complementary judgement matrix and an improved approach is presented for the sake of adjusting additive consistency of fuzzy complementary judgement matrix.(2) The ranking methods based on the fuzzy complementary judgement matrix are summarized simply. Comparing and analyzing to these methods are made and the properties of some priority methods are proved supplementarily.(3) Based on the concept of possibility degree in comparing two fuzzy numbers, an improved method is presented for reciprocal judgement matrix composed of fuzzy number. Based on the concept that two fuzzy numbers are equal approximately, additive consistency of complementary judgement matrix with fuzzy num- ber is defined. By constucting a multi-objective optimization model, a new rangking method is presented for complementary judgement matrix with triangular fuzzy number.(4) The consistency problem and ranking method are discussed for linguistic judgement matrix. Conven- tional two-tuple linguistic symbol is extended to the case of fuzziness and a priority method is given for the judgement matrix which is composed of fuzzy two-tuple linguistic symbol.
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