{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:33:34Z","timestamp":1771659214361,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T00:00:00Z","timestamp":1628553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad Autonoma de Zacatecas, Mexico","award":["Universidad Autonoma de Zacatecas, Mexico"],"award-info":[{"award-number":["Universidad Autonoma de Zacatecas, Mexico"]}]},{"name":"CONACyT, Mexico","award":["CONACyT, Mexico"],"award-info":[{"award-number":["CONACyT, Mexico"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this research work, a soft computing optimization operating approach is developed for a multi-objective aspirational level fractional transportation problem. In the proposed technique, a mathematical model is formulated for the multi-objective aspirational level fractional transportation problem (MOFTP) based on the highest value of one and all objectives of the model. We also used the symmetry concept over our model to identify the best optimum solution based on symmetrical data. We constructed the membership grades for the set of fetched parameters having symmetry. In this work, we also used the concept of ranking function in our mathematical model to obtain the optimum solution of the fuzzy multi-objective fractional transportation. In this proposed algorithm, the aspiration levels are also associated with the objective function of MOFTP. We are also proposing a new approach for the optimization of fractional problems in which the objectives are being optimized by using the numerator function and denominator function simultaneously. Further, a methodology is also developed to find the average cost for each fractional objective of the model. After that, we will find the ranking function for each parameter by using the defuzzification method. By this methodology, we will be able to convert the MOFTP into a bi-objective transportation problem. The provided technique is elaborated with the help of numerical computations to prove the beauty and power of the proposed technique.<\/jats:p>","DOI":"10.3390\/sym13081465","type":"journal-article","created":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T08:57:14Z","timestamp":1628585834000},"page":"1465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Fuzzy Optimization Technique for Multi-Objective Aspirational Level Fractional Transportation Problem"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3071-5931","authenticated-orcid":false,"given":"Mukesh Kumar","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics, C. C. S. University Meerut, Meerut 250004, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Kamini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, C. C. S. University Meerut, Meerut 250004, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nitesh","family":"Dhiman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, C. C. S. University Meerut, Meerut 250004, Uttar Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2159-7710","authenticated-orcid":false,"given":"Vishnu Narayan","family":"Mishra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indra Gandhi National Tribal University, Lalpur, Amarkantak 484887, Madhya Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9498-6602","authenticated-orcid":false,"given":"Hamurabi Gamboa","family":"Rosales","sequence":"additional","affiliation":[{"name":"Center for Research and Innovation in Information and Communication Technologies (INFOTEC-CONACyT), Ciudad de M\u00e9xico 14050, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arvind","family":"Dhaka","sequence":"additional","affiliation":[{"name":"Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amita","family":"Nandal","sequence":"additional","affiliation":[{"name":"Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur 303007, Rajasthan, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1176-2057","authenticated-orcid":false,"given":"Edgar Gonz\u00e1lez","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Center for Research and Innovation in Information and Communication Technologies (INFOTEC-CONACyT), Ciudad de M\u00e9xico 14050, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1638-5086","authenticated-orcid":false,"given":"Tania A.","family":"Ramirez-delReal","sequence":"additional","affiliation":[{"name":"CONACyT-CentroGeo Centro de Investigaci\u00f3n en Ciencias de Informaci\u00f3n Geoespacial, Aguascalientes 20313, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lakshmi Narayan","family":"Mishra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632014, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1002\/sapm1941201224","article-title":"The Distribution of a Product from Several Sources to Numerous Localities","volume":"20","author":"Hitchcock","year":"1941","journal-title":"J. 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