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Syst."],"published-print":{"date-parts":[[2022,2]]},"abstract":"Abstract<\/jats:title>In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy $$\\phi $$<\/jats:tex-math>\n \u03d5<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking $$\\phi $$<\/jats:tex-math>\n \u03d5<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy $$\\phi $$<\/jats:tex-math>\n \u03d5<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-tolerance chaingraphs which is the picture fuzzy $$\\phi $$<\/jats:tex-math>\n \u03d5<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs.<\/jats:p>","DOI":"10.1007\/s40747-021-00540-5","type":"journal-article","created":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T12:03:59Z","timestamp":1633003439000},"page":"541-554","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Picture fuzzy tolerance graphs with application"],"prefix":"10.1007","volume":"8","author":[{"given":"Sankar","family":"Das","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3877-8059","authenticated-orcid":false,"given":"Ganesh","family":"Ghorai","sequence":"additional","affiliation":[]},{"given":"Madhumangal","family":"Pal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,30]]},"reference":[{"key":"540_CR1","unstructured":"Al-Hawary T, Mahamood T, Jan N, Ullah K and Hussain A (2018) On intuitionistic fuzzy graphs and some operations on picture fuzzy graphs. 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