{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T21:44:44Z","timestamp":1785966284634,"version":"3.56.0"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts\u2019 inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing TL-transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology\u2019s logic and effectiveness.<\/jats:p>","DOI":"10.3390\/sym13040609","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T06:05:43Z","timestamp":1617689143000},"page":"609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["On the Analytic Hierarchy Process Structure in Group Decision-Making Using Incomplete Fuzzy Information with Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3199-3346","authenticated-orcid":false,"given":"Atiq ur","family":"Rehman","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Punjab 53710, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0834-2019","authenticated-orcid":false,"given":"Andrii","family":"Shekhovtsov","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nighat","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Lahore, Lahore 53710, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shahzad","family":"Faizi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Virtual University of Pakistan, Lahore 54000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7076-2519","authenticated-orcid":false,"given":"Wojciech","family":"Sa\u0142abun","sequence":"additional","affiliation":[{"name":"Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. \u017bo\u0142nierska 49, 71-210 Szczecin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"34","DOI":"10.31181\/rme200101034c","article-title":"Sustainable supplier selection using combined FUCOM\u2014Rough SAW model","volume":"1","author":"Chatterjee","year":"2020","journal-title":"Rep. 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