eprintid: 4602 rev_number: 6 eprint_status: archive userid: 351 dir: disk0/00/00/46/02 datestamp: 2016-01-15 02:06:37 lastmod: 2021-08-27 17:15:25 status_changed: 2016-01-15 02:06:37 type: article metadata_visibility: show item_issues_count: 3 creators_name: Stam, A. creators_name: Sun, M. creators_name: Haines, M. creators_id: 1602 creators_id: 7494 title: Artificial neural network representations for hierarchical preference structures ispublished: pub internal_subjects: iis_cmp internal_subjects: iis_met internal_subjects: iis_sys divisions: prog_ins abstract: In this paper, we introduce two artificial neural network formulations that can be used to assess the preference ratings from the pairwise comparison matrices of the Analytic Hierarchy Process. First, we introduce a modified Hopfield network that can determine the vector of preference ratings associated with a positive reciprocal comparison matrix. The dynamics of this network are mathematically equivalent to the power method, a widely used numerical method for computing the principal eigenvectors of square matrices. However, this Hopfield network representation is incapable of generalizing the preference patterns, and consequently is not suitable for approximating the preference ratings if the pairwise comparison judgments are imprecise. Second, we present a feed-forward neural network formulation that does have the ability to accurately approximate the preference ratings. We use a simulation experiment to verify the robustness of the feed-forward neural network formulation with respect to imprecise pairwise judgments. From the results of this experiment, we conclude that the feed-forward neural network formulation appears to be a powerful tool for analyzing discrete alternative multicriteria decision problems with imprecise or fuzzy ratio-scale preference judgments. date: 1996-12 date_type: published publisher: Elsevier id_number: 10.1016/S0305-0548(96)00021-4 iiasapubid: XJ-96-110 iiasa_bibnotes: Available as IIASA Reprint RP-97-012 creators_browse_id: 1588 creators_browse_id: 1305 full_text_status: none publication: Computers & Operations Research volume: 23 number: 12 pagerange: 1191-1201 refereed: TRUE issn: 0305-0548 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Stam, A. , Sun, M., & Haines, M. (1996). Artificial neural network representations for hierarchical preference structures. Computers & Operations Research 23 (12) 1191-1201. 10.1016/S0305-0548(96)00021-4 .