eprintid: 4847 rev_number: 12 eprint_status: archive userid: 351 dir: disk0/00/00/48/47 datestamp: 2016-01-15 02:07:25 lastmod: 2021-08-27 17:15:33 status_changed: 2016-01-15 02:07:25 type: monograph 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 these experiment, we conclude that 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 date_type: published publisher: RR-97-012. Reprinted from Computers & Operations Research, 23(12) [December 1996]. iiasapubid: RP-97-012 iiasa_bibref: Reprinted from Computers & Operations Research; 23(12) [December 1996] price: 10 creators_browse_id: 1588 creators_browse_id: 1305 full_text_status: public monograph_type: research_reprint publication: Computers & Operations Research volume: 23 number: 12 place_of_pub: IIASA, Laxenburg, Austria pages: 18 refereed: TRUE coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Stam, A. , Sun, M., & Haines, M. (1996). Artificial Neural Network Representations for Hierarchical Preference Structures. IIASA Research Report (Reprint). IIASA, Laxenburg, Austria: RR-97-012. Reprinted from Computers & Operations Research, 23(12) [December 1996]. document_url: https://pure.iiasa.ac.at/id/eprint/4847/1/RR-97-12.pdf