Fuzzy least-squares priority method in the analytic hierarchy process

The least-squares priority method is an effective priority method in the analytic hierarchy process. But it is not appropriate under fuzziness. This paper. is concerned with the question of estimation of weights of factors by least squares from a fuzzy judgment matrix. First, the expression form of least squares under fuzziness is given. Then the associated system of equation is developed. After some properties of the system are investigated, the explicit solution is derived. Finally, it is shown that the solution of the system is the solution of the fuzzy least-squares. In this paper, an example is also given to illustrate the procedure. (C) 2000 Elsevier Science B.V. All rights reserved.