{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:45:45Z","timestamp":1760237145384,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,5]],"date-time":"2020-03-05T00:00:00Z","timestamp":1583366400000},"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 Pythagorean fuzzy models deal with graphical and algebraic structures in case of vague information related to membership and non-membership grades. Here, we use Pythagorean fuzzy sets to generalize the concept of vector spaces and discuss their basis and dimensions. We also highlight the concept of Pythagorean fuzzy matroids and examine some of their fundamental characteristics like circuits, basis, dimensions, and rank functions. Additionally, we explore the concept of Pythagorean fuzzy matroids in linear algebra, graph theory, and combinatorics. Finally, we demonstrate the use of Pythagorean fuzzy matroids for minimizing the time taken by a salesman in delivering given products.<\/jats:p>","DOI":"10.3390\/sym12030423","type":"journal-article","created":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T09:26:41Z","timestamp":1583486801000},"page":"423","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Pythagorean Fuzzy Matroids with Application"],"prefix":"10.3390","volume":"12","author":[{"given":"Muhammad","family":"Asif","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Xiamen University, Xiamen 361005, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7217-7962","authenticated-orcid":false,"given":"Muhammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8393-994X","authenticated-orcid":false,"given":"Ghous","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.2307\/2371182","article-title":"On the abstract properties of linear dependence","volume":"57","author":"Whitney","year":"1935","journal-title":"Am. 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