{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:35:12Z","timestamp":1781109312717,"version":"3.54.1"},"reference-count":29,"publisher":"IGI Global Scientific Publishing","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p>In the view of significant exposure of multifarious interval-valued fuzzy numbers in neoteric studies, different measures of interval-valued generalized hexagonal fuzzy numbers (IVGHFN) associated with assorted membership functions (MF) are explored in this article. Considering the symmetricity and asymmetricity of the hexagonal fuzzy structures, the idea of MF is generalized a bit more, to nonlinear membership functions. The construction of level sets, accordingly for each case of linear and nonlinear MF are also carried out. In addition, the concepts of generalized Hukuhara (gH) differentiability for the interval-valued generalized hexagonal fuzzy functions (IVGHFF) are also the main features of this framework. Illustratively, the developed intellects are implemented on a logistic population growth problem, by taking ecological functions as IVGHFFs. For the further numerical demonstrations of the model, artificial neural network with simulated annealing (ANNSA) algorithm is utilized.<\/jats:p>","DOI":"10.4018\/ijfsa.2020100102","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T08:39:09Z","timestamp":1596703149000},"page":"21-60","source":"Crossref","is-referenced-by-count":0,"title":["Measures of Linear and Nonlinear Interval-Valued Hexagonal Fuzzy Number"],"prefix":"10.4018","volume":"9","author":[{"given":"Najeeb Alam","family":"Khan","sequence":"first","affiliation":[{"name":"University of Karachi, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oyoon Abdul","family":"Razzaq","sequence":"additional","affiliation":[{"name":"Bahria University, Karachi, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Avishek","family":"Chakraborty","sequence":"additional","affiliation":[{"name":"Department of Basic Sicence, Narula Institute of Technology, Kolkata, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sankar Parsad","family":"Mondal","sequence":"additional","affiliation":[{"name":"Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shariful","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2432","reference":[{"issue":"1","key":"IJFSA.2020100102-0","first-page":"3","article-title":"A single layer functional link artificial neural network based on Chebyshev polynomials for neural evaluations of nonlinear nth order fuzzy differential equations.","volume":"56","author":"A.Ara","year":"2018","journal-title":"Analele Universit\u04d1\u021bii de Vest Timi\u0219oara Seria Matematic\u04d1-Informati\u04d1"},{"key":"IJFSA.2020100102-1","unstructured":"Christi, M. S. A., & Priyadharshini, N. (2017). Stability of the queuing model using DSW model with hexagonal fuzzy number. Mathematical Sciences International Research Journal, 6(7)."},{"issue":"6","key":"IJFSA.2020100102-2","article-title":"A new ranking technique of hexagonal fuzzy numbers.","volume":"5","author":"K.Dhurai","year":"2016","journal-title":"International Journal of Science and Research"},{"key":"IJFSA.2020100102-3","unstructured":"Dinagar, D. S., & Narayanan, U. H. (2017). A study on rank of hexagonal fuzzy number matrices. International Journal of Advances in Mathematics, (6), 82-100."},{"key":"IJFSA.2020100102-4","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2018.1523903"},{"key":"IJFSA.2020100102-5","doi-asserted-by":"publisher","DOI":"10.18488\/journal.24\/2016.5.2\/24.2.131.137"},{"issue":"1","key":"IJFSA.2020100102-6","article-title":"On the convergence speed of artificial neural networks in the solving of linear systems.","volume":"7","author":"A.Jafarian","year":"2015","journal-title":"International Journal of Industrial Mathematics"},{"key":"IJFSA.2020100102-7","doi-asserted-by":"publisher","DOI":"10.1016\/j.joems.2013.07.002"},{"key":"IJFSA.2020100102-8","doi-asserted-by":"publisher","DOI":"10.1515\/nleng-2013-0029"},{"key":"IJFSA.2020100102-9","doi-asserted-by":"publisher","DOI":"10.5772\/64151"},{"issue":"3","key":"IJFSA.2020100102-10","first-page":"384","article-title":"An interval-valued fuzzy number approach for supplier selection.","volume":"24","author":"C. S.Lee","year":"2016","journal-title":"Journal of Marine Science and Technology"},{"key":"IJFSA.2020100102-11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48476-0"},{"key":"IJFSA.2020100102-12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-28998-4"},{"key":"IJFSA.2020100102-13","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2014.2333065"},{"key":"IJFSA.2020100102-14","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2013.06.019"},{"key":"IJFSA.2020100102-15","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2013.10.036"},{"key":"IJFSA.2020100102-16","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2018185"},{"issue":"6","key":"IJFSA.2020100102-17","first-page":"41","article-title":"A new multi-objective optimization approach for sustainable project portfolio selection: A real-world application under interval-valued fuzzy environment.","volume":"13","author":"V.Mohagheghi","year":"2016","journal-title":"Iranian Journal of Fuzzy System"},{"key":"IJFSA.2020100102-18","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161898"},{"key":"IJFSA.2020100102-19","doi-asserted-by":"crossref","unstructured":"Paul, S., Mondal, S. P., & Bhattacharya, P. (2016). Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach. Modeling Earth Systems and Environment, 2(2), 70.","DOI":"10.1007\/s40808-016-0113-y"},{"key":"IJFSA.2020100102-20","doi-asserted-by":"publisher","DOI":"10.1007\/s40096-016-0192-y"},{"issue":"1","key":"IJFSA.2020100102-21","first-page":"52","article-title":"A new approach for ranking of fuzzy numbers using the incentre of centroids.","volume":"4","author":"P.Rajarajeswari","year":"2014","journal-title":"International Journal of Fuzzy Mathematical Archive"},{"issue":"6","key":"IJFSA.2020100102-22","first-page":"925","article-title":"Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees. Omega: The International Journal of management","volume":"41","author":"S. P.Wan","year":"2013","journal-title":"Science"},{"key":"IJFSA.2020100102-23","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2013.2253107"},{"key":"IJFSA.2020100102-24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.07.014"},{"key":"IJFSA.2020100102-25","doi-asserted-by":"crossref","unstructured":"Ye, J., Cui, W., & Lu, Z. (2018). Neutrosophic number nonlinear programming problems and their general solution methods under neutrosophic number environments. Axioms, 7(1).","DOI":"10.3390\/axioms7010013"},{"key":"IJFSA.2020100102-26","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"IJFSA.2020100102-27","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2015.08.023"},{"key":"IJFSA.2020100102-28","doi-asserted-by":"publisher","DOI":"10.11113\/mjfas.v13n2.564"}],"container-title":["International Journal of Fuzzy System Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.igi-global.com\/viewtitle.aspx?TitleId=259936","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,5]],"date-time":"2022-05-05T20:18:35Z","timestamp":1651781915000},"score":1,"resource":{"primary":{"URL":"http:\/\/services.igi-global.com\/resolvedoi\/resolve.aspx?doi=10.4018\/IJFSA.2020100102"}},"subtitle":[""],"short-title":[],"issued":{"date-parts":[[2020,10]]},"references-count":29,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.4018\/ijfsa.2020100102","relation":{},"ISSN":["2156-177X","2156-1761"],"issn-type":[{"value":"2156-177X","type":"print"},{"value":"2156-1761","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10]]}}}