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One issue is determining how to compare the LDFNs, i.e., the cost of the edges. The other question is how to calculate the edge addition to determine the cost of the LDF-MST. To overcome these difficulties, the score function representation of LDFNs is utilized and Prim\u2019s method is a well-known approach for solving the minimal spanning tree issue in which uncertainty is ignored, i.e., precise values of arc lengths are supplied. This technique works by providing more energy to nodes dependent on their position in the spanning tree. In addition, an illustrated example is provided to explain the suggested approach. By considering a mobile charger vehicle that travels across the sensor network on a regular basis, charging the batteries of each sensor node.<\/jats:p>","DOI":"10.1007\/s40747-022-00653-5","type":"journal-article","created":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T08:03:24Z","timestamp":1643875404000},"page":"2419-2434","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Lifetime prolongation of a wireless charging sensor network using a mobile robot via linear Diophantine fuzzy graph environment"],"prefix":"10.1007","volume":"8","author":[{"given":"Karthikeyan","family":"Prakash","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1390-2049","authenticated-orcid":false,"given":"Mani","family":"Parimala","sequence":"additional","affiliation":[]},{"given":"Harish","family":"Garg","sequence":"additional","affiliation":[]},{"given":"Muhammad","family":"Riaz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,3]]},"reference":[{"issue":"1","key":"653_CR1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.2298\/FIL1201177A","volume":"26","author":"M Akram","year":"2012","unstructured":"Akram M, Davvaz B (2012) Strong intuitionistic fuzzy graphs. 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