{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T10:21:09Z","timestamp":1778926869411,"version":"3.51.4"},"reference-count":50,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"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 paradigm shift prompted by Zadeh\u2019s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.<\/jats:p>","DOI":"10.3390\/sym11111381","type":"journal-article","created":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T11:17:25Z","timestamp":1573125445000},"page":"1381","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["A Study on Hypergraph Representations of Complex Fuzzy Information"],"prefix":"10.3390","volume":"11","author":[{"given":"Anam","family":"Luqman","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5559-5951","authenticated-orcid":false,"given":"Ahmad N.","family":"Al-Kenani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-9281","authenticated-orcid":false,"given":"Jos\u00e9 Carlos R.","family":"Alcantud","sequence":"additional","affiliation":[{"name":"BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,7]]},"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","doi-asserted-by":"crossref","first-page":"171186","DOI":"10.1109\/91.995119","article-title":"Complex fuzzy sets","volume":"10","author":"Ramot","year":"2002","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2017.01.010","article-title":"A systematic review of complex fuzzy sets and logic","volume":"338","author":"Yazdanbakhsh","year":"2018","journal-title":"Fuzzy Sets. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1983","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liu, X., Kim, H., Feng, F., and Alcantud, J.C.R. (2018). Centroid transformations of intuitionistic fuzzy values based on aggregation operators. Mathematics, 6.","DOI":"10.3390\/math6110215"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/TFUZZ.2018.2860967","article-title":"Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods","volume":"27","author":"Feng","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Akram, M., Al-Kenani, A.N., and Alcantud, J.C.R. (2019). Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry, 11.","DOI":"10.3390\/sym11101313"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s10726-018-9606-6","article-title":"A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making","volume":"28","author":"Akram","year":"2019","journal-title":"Group Decis. Negot."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.fss.2018.01.015","article-title":"Fuzzy politics I: The genesis of parties","volume":"349","author":"Alcantud","year":"2018","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.inffus.2018.05.005","article-title":"Necessary and possible hesitant fuzzy sets: A novel model for group decision-making","volume":"46","author":"Alcantud","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1002\/int.21584","article-title":"Pythagorean membership grades, complex numbers and dcision making","volume":"28","author":"Yager","year":"2013","journal-title":"Int. J. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean membership grades in multi-criteria decision making","volume":"22","author":"Yager","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","article-title":"Generalized orthopair fuzzy sets","volume":"25","author":"Yager","year":"2017","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1002\/int.21927","article-title":"Some q-rung orthopair fuzzy aggregation operators and their applications to multi-attribute decision making","volume":"33","author":"Liu","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Alcantud, J.C.R., and Mu\u00f1oz Torrecillas, M.J. (2018). Intertemporal choice of fuzzy soft sets. Symmetry, 10.","DOI":"10.3390\/sym10090371"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1111\/meca.12012","article-title":"Evaluations of infinite utility streams: Pareto efficient and egalitarian axiomatics","volume":"64","author":"Alcantud","year":"2013","journal-title":"Metroeconomica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.econlet.2009.11.021","article-title":"Paretian evaluation of infinite utility streams: An egalitarian criterion","volume":"106","author":"Alcantud","year":"2010","journal-title":"Econ. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1002\/int.21985","article-title":"Some q-rung orthopair fuzzy heronian mean operators in multiple attribute decision making","volume":"33","author":"Wei","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bai, K., Zhu, X., Wang, J., and Zhang, R. (2018). Some partitioned maclaurin symmetric mean based on q-rung orthopair fuzzy information for dealing with multi-attribute group decision making. Symmetry, 10.","DOI":"10.3390\/sym10090383"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, L., Zhang, R., Wang, J., Shang, X., and Bai, K. (2018). A novel approach to multi-attribute group decision-making with q-rung picture linguistic information. Symmetry, 10.","DOI":"10.3390\/sym10050172"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1063\/1.4757515","article-title":"Complex intuitionistic fuzzy sets","volume":"14","author":"Alkouri","year":"2012","journal-title":"AIP Conf. Proc."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ullah, K., Mahmood, T., Ali, Z., and Jan, N. (2019). On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst., forthcoming.","DOI":"10.1007\/s40747-019-0103-6"},{"key":"ref_23","unstructured":"Zadeh, L.A., Fu, K.S., and Shimura, M. (1975). Fuzzy graphs. Fuzzy Sets and Their Applications, Academic Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0167-8655(87)90012-2","article-title":"Some remarks on fuzzy graphs","volume":"6","author":"Bhattacharya","year":"1987","journal-title":"Pattern Recognit. Lett."},{"key":"ref_25","first-page":"243","article-title":"Energy of a complex fuzzy graph","volume":"10","author":"Thirunavukarasu","year":"2016","journal-title":"Int. J. Math. Sci. Eng. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Reusch, B. (2006). Intuitionistic fuzzy graphs. Computational Intelligence, Theory and Applications, Springer.","DOI":"10.1007\/3-540-34783-6"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Akram, M., and Naz, S. (2018). Energy of Pythagorean fuzzy graphs with applications. Mathematics, 6.","DOI":"10.3390\/math6080136"},{"key":"ref_28","first-page":"91","article-title":"q-Rung orthopair fuzzy competition graphs with application in the soil ecosystem","volume":"7","author":"Akram","year":"2018","journal-title":"Mathematics"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Akram, M., Habib, A., and Koam, A.N. (2019). A novel description on edge-regular q-rung picture fuzzy graphs with application. Symmetry, 11.","DOI":"10.3390\/sym11040489"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yaqoob, N., Gulistan, M., Kadry, S., and Wahab, H. (2019). Complex intuitionistic fuzzy graphs with application in cellular network provider companies. Mathematics, 7.","DOI":"10.3390\/math7010035"},{"key":"ref_31","first-page":"85","article-title":"Complex neutrosophic graphs","volume":"6","author":"Yaqoob","year":"2018","journal-title":"Bull. Comput. Appl. Math."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Akram, M., and Naz, S. (2019). A novel decision-making approach under complex Pythagorean fuzzy environment. Math. Comput. Appl., 24.","DOI":"10.3390\/mca24030073"},{"key":"ref_33","unstructured":"Berge, C. (1973). Graphs and Hypergraphs, North-Holland Publishing Company."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Boulet, R., Lajaunie, C., and Mazzega, P. (2019). Environmental and Trade Regimes: Comparison of Hypergraphs Modeling the Ratifications of UN Multilateral Treaties. Law, Public Policies and Complex Systems, Springer. Chapter 11.","DOI":"10.1007\/978-3-030-11506-7_11"},{"key":"ref_35","first-page":"389","article-title":"Modelling and simulation of utility service provision for sustainable communities","volume":"58","author":"Strzelecka","year":"2012","journal-title":"Int. J. Elect. Tel."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Han, Y., Zhou, B., Pei, J., and Jia, Y. (May, January 30). Understanding importance of collaborations in co-authorship networks: A supportiveness analysis approach. Proceedings of the 2009 SIAM International Conference on Data Mining, Sparks, NV, USA.","DOI":"10.1137\/1.9781611972795.95"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"10005","DOI":"10.1088\/1742-5468\/2010\/10\/P10005","article-title":"A hypergraph model of social tagging networks","volume":"10","author":"Zhang","year":"2010","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_38","unstructured":"Ouvrard, X., Goff, J.M.L., and Marchand-Maillet, S. (2017). Networks of collaborations: Hypergraph modeling and visualisation. arXiv."},{"key":"ref_39","unstructured":"Kaufmann, A. (1977). Introduction a la Theorie des Sous-Ensemble Flous 1, Masson."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1109\/21.362951","article-title":"Fuzzy hypergraph and fuzzy partition","volume":"25","author":"Lee","year":"1995","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_41","unstructured":"Mordeson, J.N., and Nair, P.S. (1998). Fuzzy Graphs and Fuzzy Hypergraphs, Physica Verlag. [2nd ed.]."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0165-0114(95)00327-4","article-title":"Fuzzy transversals of fuzzy hypergraphs","volume":"84","author":"Goetschel","year":"1996","journal-title":"Fuzzy Sets. Syst."},{"key":"ref_43","first-page":"46","article-title":"Intuitionistic fuzzy hypergraphs","volume":"9","author":"Parvathi","year":"2009","journal-title":"Cyber. Inf. Tech."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.ins.2012.06.024","article-title":"Intuitionistic fuzzy hypergraphs with applications","volume":"218","author":"Akram","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.ipl.2013.05.004","article-title":"Intuitionistic fuzzy shortest hyperpath in a network","volume":"113","author":"Parvathi","year":"2013","journal-title":"Inf. Process. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.3233\/JIFS-17228","article-title":"Bipolar neutrosophic hypergraphs with applications","volume":"33","author":"Akram","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"351","DOI":"10.3233\/JIFS-161668","article-title":"Transversals of m-polar fuzzy hypergraphs with applications","volume":"33","author":"Akram","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Luqman, A., Akram, M., and Al-Kenani, A.N. (2019). q-Rung orthopair fuzzy hypergraphs with applications. Mathematics, 7.","DOI":"10.3390\/math7030260"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Luqman, A., Akram, M., and Koam, A.N. (2019). An m-polar fuzzy hypergraph model of granular computing. Symmetry, 11.","DOI":"10.3390\/sym11040483"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Luqman, A., Akram, M., and Koam, A.N. (2019). Granulation of hypernetwork models under the q-rung picture fuzzy environment. Mathematics, 7.","DOI":"10.3390\/math7060496"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1381\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:32:40Z","timestamp":1760189560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/11\/1381"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,7]]},"references-count":50,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["sym11111381"],"URL":"https:\/\/doi.org\/10.3390\/sym11111381","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,7]]}}}