An alternative solution to the analytic hierarchy process

Let us consider the Analytic Hierarchy Process in which the labels are structured as graded numbers. To obtain the scoring that corresponds to the best alternative, or the ranking of the alternatives, we need to use a total order for the graded numbers involved in the problem. In this article, we consider a definition of such a total order, which is based upon two subjective aspects: the degree of optimism/pessimism and the liking for risk /safety. As several operations, such as product, quotient, and so forth, of fuzzy numbers do not preserve the triangularity, we also use the graded numbers that are analogous to the fuzzy numbers; however, the operations with graded numbers are carried out as a simple extension of operations with real intervals. © 2006 Wiley Periodicals, Inc.