{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T18:34:17Z","timestamp":1778092457971,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,4]],"date-time":"2023-02-04T00:00:00Z","timestamp":1675468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Fahd University of Petroleum and Minerals","award":["SB191005"],"award-info":[{"award-number":["SB191005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The article provides an \u03b1-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using \u03b1-cut of fuzzy numbers wherein the \u03b1- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r\u2208(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.<\/jats:p>","DOI":"10.3390\/sym15020419","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T04:08:07Z","timestamp":1675656487000},"page":"419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Fuzzy Linear Fractional Programming Problems via \u03b1-Cut-Based Method with Application in Transportation Sector"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0226-4395","authenticated-orcid":false,"given":"Abhishek","family":"Chauhan","sequence":"first","affiliation":[{"name":"Department of Applied Sciences, Punjab Engineering College, Chandigarh 160012, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8815-1190","authenticated-orcid":false,"given":"Sumati","family":"Mahajan","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, Punjab Engineering College, Chandigarh 160012, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3482-8634","authenticated-orcid":false,"given":"Izhar","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"},{"name":"Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5998-0635","authenticated-orcid":false,"given":"Suliman","family":"Al-Homidan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"},{"name":"Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nav.3800090303","article-title":"Programming with linear fractional functionals","volume":"9","author":"Charnes","year":"1962","journal-title":"Nav. 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