{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:32:12Z","timestamp":1777703532798,"version":"3.51.4"},"reference-count":63,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T00:00:00Z","timestamp":1564704000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,9,9]]},"abstract":"<jats:p>\u00a0Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated.<\/jats:p>","DOI":"10.3233\/jifs-182579","type":"journal-article","created":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:20:00Z","timestamp":1565094000000},"page":"2289-2307","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Cubic bipolar fuzzy graphs with applications"],"prefix":"10.1177","volume":"37","author":[{"given":"Naeem","family":"Jan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistic, International Islamic University Islamabad, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lemnaouar","family":"Zedam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Laboratory of Pure and Applied Mathematics, Med Boudiaf University of Msila, Msila, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tahir","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistic, International Islamic University Islamabad, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kifayat","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistic, International Islamic University Islamabad, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,8,2]]},"reference":[{"issue":"1","key":"e_1_3_1_2_2","first-page":"83","article-title":"Cubic sets","volume":"4","author":"Jun Y.B.","year":"2012","unstructured":"JunY.B., KimC.S. and YangK.O., Cubic sets, Annals of fuzzy Mathematics and Informatics 4(1) (2012), 83\u201398.","journal-title":"Annals of fuzzy Mathematics and Informatics"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793005717500041"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151906"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141377"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/935905"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym9070121"},{"key":"e_1_3_1_8_2","first-page":"291","article-title":"Cubic soft sets with applications in BCK\/BCI-algebras","volume":"8","author":"Muhiuddin G.","year":"2014","unstructured":"MuhiuddinG. and Al-RoqiA.M., Cubic soft sets with applications in BCK\/BCI-algebras, Annals of Fuzzy Mathematics and Informatics 8 (2014)291\u2013304.","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/458638"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.5831\/HMJ.2013.35.4.607"},{"issue":"1","key":"e_1_3_1_11_2","first-page":"105","article-title":"Cubic G-subalgebras of G-algebras","volume":"10","author":"Jana C.","year":"2015","unstructured":"JanaC. and SenapatiT., Cubic G-subalgebras of G-algebras, Annals of Pure and Applied Mathematics 10(1) (2015), 105\u2013115.","journal-title":"Annals of Pure and Applied Mathematics"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms7010007"},{"issue":"2","key":"e_1_3_1_13_2","article-title":"Some Operations and Properties of Neutrosophic Cubic Soft Set","volume":"4","author":"Pramanik S.","year":"2017","unstructured":"PramanikS., DalapatiS., AlamS. and RoyT.K., Some Operations and Properties of Neutrosophic Cubic Soft Set, Global Journal of Research and Review 4(2), 2017.","journal-title":"Global Journal of Research and Review"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.20454\/ijas.2016.1055"},{"issue":"1","key":"e_1_3_1_15_2","first-page":"31","article-title":"Some Generalized Aggregation Operators for Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making","volume":"49","author":"Mahmood T.","year":"2017","unstructured":"MahmoodT., MehmoodF. and KhanQ., Some Generalized Aggregation Operators for Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making, Journal of Mathematics 49(1) (2017), 31\u201349.","journal-title":"Journal of Mathematics"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_1_17_2","doi-asserted-by":"crossref","unstructured":"RosenfeldA. Fuzzy graphs in Fuzzy sets and their applications to cognitive and decision processes. (1975) Elsevier pp. 77\u201395.","DOI":"10.1016\/B978-0-12-775260-0.50008-6"},{"key":"e_1_3_1_18_2","unstructured":"KaufmannA. Introduction \u00e1 la th\u00e9orie des sous-ensembles flous \u00e1 l\u2019usage des ing\u00e9nieurs: \u00c9l\u00e9ments th\u00e9oriques de base. Vol. 1. 1973: Masson."},{"issue":"9","key":"e_1_3_1_19_2","first-page":"1451","article-title":"Complement of a fuzzy graph","volume":"33","author":"Sunitha M.","year":"2002","unstructured":"SunithaM. and VijayakumarA., Complement of a fuzzy graph, Indian Journal of Pure and Applied Mathematics 33(9) (2002), 1451\u20131464.","journal-title":"Indian Journal of Pure and Applied Mathematics"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.01.003"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(87)90012-2"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(89)90049-4"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.01.006"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.10.006"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(98)00064-6"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(02)00411-5"},{"key":"e_1_3_1_27_2","unstructured":"GaniA.N. and RadhaK. On regular fuzzy graphs 2008."},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(93)90115-T"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.14569\/IJARAI.2014.030108"},{"issue":"11","key":"e_1_3_1_30_2","first-page":"517","article-title":"On irregular fuzzy graphs","volume":"6","author":"Gani A.N.","year":"2012","unstructured":"GaniA.N. and LathaS., On irregular fuzzy graphs, Applied Mathematical Sciences 6(11) (2012), 517\u2013523.","journal-title":"Applied Mathematical Sciences"},{"key":"e_1_3_1_31_2","doi-asserted-by":"crossref","unstructured":"YehR.T. and BangS. Fuzzy relations fuzzy graphs and their applications to clustering analysis in Fuzzy sets and their applications to Cognitive and Decision Processes. 1975 Elsevier. pp. 125\u2013149.","DOI":"10.1016\/B978-0-12-775260-0.50010-4"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3800(89)90075-6"},{"issue":"1","key":"e_1_3_1_33_2","first-page":"145","article-title":"Order, Size in Fuzzy Graphs","volume":"22","author":"Gani A.N.","year":"2003","unstructured":"GaniA.N. and AhamedM.B., Order, Size in Fuzzy Graphs, Bulletin of Pure and Applied Sciences 22(1) (2003), 145\u2013148.","journal-title":"Bulletin of Pure and Applied Sciences"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(85)90232-2"},{"issue":"1","key":"e_1_3_1_35_2","first-page":"92","article-title":"Fuzzy graph theory: A survey","volume":"4","author":"Sunitha M.","year":"2013","unstructured":"SunithaM. and MathewS., Fuzzy graph theory: A survey, Annals of Pure and Applied mathematics 4(1) (2013), 92\u2013110.","journal-title":"Annals of Pure and Applied mathematics"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.11.004"},{"issue":"3","key":"e_1_3_1_38_2","first-page":"677","article-title":"Complete interval-valued fuzzy graphs","volume":"6","author":"Rashmanlou H.","year":"2013","unstructured":"RashmanlouH. and JunY.B., Complete interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 6(3) (2013), 677\u2013687.","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"e_1_3_1_39_2","article-title":"Irregular.Interval valued fuzzy graphs","author":"Pal M.","year":"2014","unstructured":"PalM. and RashmanlouH., Irregular.Interval valued fuzzy graphs. arXiv preprint arXiv:: 1407.6190, 2014.","journal-title":"arXiv preprint arXiv:"},{"key":"e_1_3_1_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0733-0"},{"key":"e_1_3_1_41_2","doi-asserted-by":"crossref","unstructured":"RashmanlouH. and PalM. Balanced interval-valued fuzzy graphs 2013.","DOI":"10.1155\/2013\/857070"},{"key":"e_1_3_1_42_2","article-title":"Isometry on interval-valued fuzzy graphs","author":"Rashmanlou H.","year":"2014","unstructured":"RashmanlouH. and PalM., Isometry on interval-valued fuzzy graphs. arXiv preprint arXiv: 2014. 1405.6003.","journal-title":"arXiv preprint arXiv"},{"issue":"1","key":"e_1_3_1_43_2","first-page":"47","article-title":"Isomorphism on interval-valued fuzzy graphs","volume":"6","author":"Talebi A.","year":"2013","unstructured":"TalebiA. and RashmanlouH., Isomorphism on interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics 6(1) (2013), 47\u201358.","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"e_1_3_1_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-014-0284-7"},{"key":"e_1_3_1_45_2","doi-asserted-by":"publisher","DOI":"10.3390\/math7010072"},{"key":"e_1_3_1_46_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-181123"},{"key":"e_1_3_1_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-019-00634-w"},{"key":"e_1_3_1_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-019-00643-9"},{"key":"e_1_3_1_49_2","doi-asserted-by":"publisher","DOI":"10.71330\/thenucleus.2018.417"},{"key":"e_1_3_1_50_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym10060193"},{"key":"e_1_3_1_51_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym11030357"},{"issue":"2","key":"e_1_3_1_52_2","article-title":"A Note on Geometric Aggregation Operators in Spherical Fuzzy Environment and its Application in Multi-Attribute Decision Making","volume":"37","author":"Ullah K.","year":"2018","unstructured":"UllahK., MahmoodT., JanN. and AliZ., A Note on Geometric Aggregation Operators in Spherical Fuzzy Environment and its Application in Multi-Attribute Decision Making, Journal of Engineering and Applied Sciences 37(2) 2018. https:\/\/doi.org\/10.25211\/jeas.v37i2.2871","journal-title":"Journal of Engineering and Applied Sciences"},{"key":"e_1_3_1_53_2","article-title":"Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making","author":"Ullah K.","year":"2019","unstructured":"UllahK., GargH., MahmoodT., JanN. and AliZ., Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making, Soft Computing, 2019, https:\/\/doi.org\/10.1007\/s00500-019-03993-6.","journal-title":"Soft Computing"},{"key":"e_1_3_1_54_2","article-title":"An Approach Towards Decision Making and Medical Diagnosis Problems Using the Concept of Spherical Fuzzy Sets","author":"Mahmood T.","year":"2018","unstructured":"MahmoodT., UllahK., KhanQ. and JanN., An Approach Towards Decision Making and Medical Diagnosis Problems Using the Concept of Spherical Fuzzy Sets, Neural Computing and Applications, 2018, https:\/\/doi.org\/10.1007\/s00521-018-3521-2.","journal-title":"Neural Computing and Applications"},{"key":"e_1_3_1_55_2","unstructured":"ZhangW.R. Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis. In Fuzzy Information Processing Society Biannual Conference 1994. Industrial Fuzzy Control and Intelligent Systems Conference and the NASA Joint Technology Workshop on Neural Networks and Fuzzy Logic IEEE (1994) pp. 305\u2013309."},{"key":"e_1_3_1_56_2","doi-asserted-by":"crossref","unstructured":"ZhangW.R. (Yin)(Yang) bipolar fuzzy sets. In Fuzzy Systems Proceedings 1998. IEEE World Congress on Computational Intelligence The 1998 IEEE International Conference 1 (1998) pp. 835\u2013840.","DOI":"10.1109\/FUZZY.1998.687599"},{"key":"e_1_3_1_57_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.07.037"},{"key":"e_1_3_1_58_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.08.022"},{"key":"e_1_3_1_59_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141333"},{"key":"e_1_3_1_60_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0772-6"},{"key":"e_1_3_1_61_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.03.049"},{"key":"e_1_3_1_62_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.07.038"},{"issue":"5","key":"e_1_3_1_63_2","first-page":"733","article-title":"Cubic graphs with application","volume":"16","author":"Rashid S.","year":"2018","unstructured":"RashidS., YaqoobN., AkramM. and GulistanM., Cubic graphs with application, International Journal of Analysis and Applications 16(5) (2018), 733\u2013750.","journal-title":"International Journal of Analysis and Applications"},{"issue":"7","key":"e_1_3_1_64_2","first-page":"51","article-title":"Some Generalized Distance and Similarity Measures for Picture Hesitant Fuzzy Sets and Their Applications in Building Material Recognition and Multi-Attribute Decision Making","volume":"51","author":"Jan N.","year":"2019","unstructured":"JanN., AliZ., MahmoodT. and UllahK., Some Generalized Distance and Similarity Measures for Picture Hesitant Fuzzy Sets and Their Applications in Building Material Recognition and Multi-Attribute Decision Making, Punjab University Journal of Mathematics 51(7) (2019), 51\u201370.","journal-title":"Punjab University Journal of Mathematics"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182579","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-182579","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182579","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:56Z","timestamp":1777455536000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-182579"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,2]]},"references-count":63,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,9,9]]}},"alternative-id":["10.3233\/JIFS-182579"],"URL":"https:\/\/doi.org\/10.3233\/jifs-182579","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,2]]}}}