{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T14:08:20Z","timestamp":1780582100388,"version":"3.54.1"},"reference-count":47,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T00:00:00Z","timestamp":1702944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Analytic Hierarchy Process (AHP) has been a widely used multi-criteria decision-making (MCDM) method since the 1980s because of its simplicity and rationality. However, the conventional AHP assumes criteria independence, which is not always accurate in realistic scenarios where interdependencies between criteria exist. Several methods have been proposed to relax the postulation of the independent criteria in the AHP, e.g., the Analytic Network Process (ANP). However, these methods usually need a number of pairwise comparison matrices (PCMs) and make it hard to apply to a complicated and large-scale problem. This paper presents a groundbreaking approach to address this issue by incorporating discrete Markov Random Fields (MRFs) into the AHP framework. Our method enhances decision making by effectively and sensibly capturing interdependencies among criteria, reflecting actual weights. Moreover, we showcase a numerical example to illustrate the proposed method and compare the results with the conventional AHP and Fuzzy Cognitive Map (FCM). The findings highlight our method\u2019s ability to influence global priority values and the ranking of alternatives when considering interdependencies between criteria. These results suggest that the introduced method provides a flexible and adaptable framework for modeling interdependencies between criteria, ultimately leading to more accurate and reliable decision-making outcomes.<\/jats:p>","DOI":"10.3390\/a17010001","type":"journal-article","created":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T06:03:11Z","timestamp":1702965791000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Using Markov Random Field and Analytic Hierarchy Process to Account for Interdependent Criteria"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7965-7165","authenticated-orcid":false,"given":"Jih-Jeng","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Computer Science & Information Management, SooChow University, No. 56 Kueiyang Street, Section 1, Taipei 100, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chin-Yi","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Business Administration, Chung Yuan Christian University, No. 200 Chung Pei Road, Chung Li District, Taoyuan 320, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Saaty, T.L. 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