{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:44:20Z","timestamp":1760031860896,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"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 bipolar fuzzy model is a rapidly evolving research area that provides a robust framework for addressing real-world problems, with wide-ranging applications in scientific and technical domains. Within this framework, bipolar fuzzy graphs play a significant role in decision-making and problem-solving, particularly through domination theory, which helps tackle practical challenges. This study explores various operations on product bipolar fuzzy graphs, including union (\u222a), join (+), intersection (\u2229), Cartesian product (\u00d7), composition (\u2218), and complement, leading to the generation of new graph structures. Several important results related to complete product bipolar fuzzy graphs under these operations are established. Additionally, we introduce key concepts such as dominating sets, minimal dominating sets, and the domination number \u22ce(H), supported by illustrative examples. This study further investigates the properties of domination in the context of these operations. To demonstrate practical applicability, we present a decision-making problem involving the optimization of bus routes and the strategic placement of bus stations using domination principles. This research contributes to the advancement of bipolar fuzzy graph theory and its practical applications in real-world scenarios.<\/jats:p>","DOI":"10.3390\/sym17040479","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T13:48:20Z","timestamp":1742824100000},"page":"479","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing Decision-Making Using Domination Theory in Product Bipolar Fuzzy Graphs"],"prefix":"10.3390","volume":"17","author":[{"given":"Wei","family":"Ming","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Areen","family":"Rasool","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of the Education, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sundas","family":"Shahzadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of the Education, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mubariz","family":"Garayev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh P.O. Box 2455, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_2","unstructured":"Zhang, W.R. (1994, January 18\u201321). 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