Additive Consistency of Fuzzy Preference Relations: Characterization and Construction

As it is known, most decision processes are based on preference relations, in the sense that processes are linked to some degree of preference of any alternative over another. The use of preference relations is usual in decision making [1, 5, 10, 14]. Therefore, to establish properties to be verified by such preference relations is very important for designing good decision making models. One of these properties is the so called consistency property. The lack of consistency in decision making can lead to inconsistent conclusions; that is why it is important, if not crucial, to study conditions under which consistency is satisfied [5, 10]. On the other hand, perfect consistency is difficult to obtain in practice, specially when measuring preferences on a set with a large number of alternatives. Clearly, the problem of consistency itself includes two problems [3, 7]: