{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:07:18Z","timestamp":1760148438710,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T00:00:00Z","timestamp":1683504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at King Khalid University","award":["R.G.P.1\/109\/44"],"award-info":[{"award-number":["R.G.P.1\/109\/44"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed.<\/jats:p>","DOI":"10.3390\/sym15051044","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T01:06:28Z","timestamp":1683594388000},"page":"1044","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7080-3824","authenticated-orcid":false,"given":"Rashad","family":"Ismail","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, Muhayl Assir, King Khalid University, Abha 61421, Saudi Arabia"},{"name":"Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb 70270, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sami Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samer","family":"Al Ghour","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0418-193X","authenticated-orcid":false,"given":"Esmail Hassan Abdullatif","family":"Al-Sabri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, Muhayl Assir, King Khalid University, Abha 61421, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6416-8097","authenticated-orcid":false,"given":"Maha Mohammed Saeed","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shoukat","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fiaz","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9585-9680","authenticated-orcid":false,"given":"Giorgio","family":"Nordo","sequence":"additional","affiliation":[{"name":"MIFT Department (Mathematics, Computer Science, Physics and Earth Sciences), University of Messina, 98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arif","family":"Mehmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zadeh, L. 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