Incomplete fuzzy preference relations and the consistency

A well-known method of decision problems is the Analytic Hierarchy Process (AHP). Most decision processes are known to be based on preference relations. Because of decision makers having limited attention spans and information processing capabilities, as well as some decision alternatives being incomparable, decision makers may develop incomplete preference relations in which some elements cannot be provided. The method proposed by Herrera et al. [11] devises a consistent preference relation that is restricted by the set of n - 1 values {p12, p23,, pn-1n}. Therefore, for convenience and flexibility, the following uses the incomplete fuzzy preference relation with the least judgments (that is, n - 1 judgments) to develop a simple and practical method for constructing a consistent complete fuzzy preference relation in which experts can compare any row, column or diagonal. The proposed method is more convenient and flexible than that of Herrera et al.