{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:51:45Z","timestamp":1777704705293,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,7,28]],"date-time":"2018-07-28T00:00:00Z","timestamp":1532736000000},"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":[[2019,2,16]]},"abstract":"<jats:p>\n                    In the present study, first, we introduce an iterative method based on quadrature formula for solving two-dimensional nonlinear fuzzy Fredholm integral\n                    <jats:xref ref-type=\"disp-formula\">equations<\/jats:xref>\n                    (2DNFFIE). Then, we present error estimation and the numerical stability analysis for the proposed method. Finally, to show the efficiency of the proposed method, supporting examples are also provided.\n                  <\/jats:p>","DOI":"10.3233\/jifs-171104","type":"journal-article","created":{"date-parts":[[2018,7,31]],"date-time":"2018-07-31T18:11:42Z","timestamp":1533060702000},"page":"661-674","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Numerical solution of two-dimensional nonlinear fuzzy Fredholm integral equations via quadrature iterative method"],"prefix":"10.1177","volume":"36","author":[{"given":"Atiyeh Mashhadi","family":"Gholam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad university, karaj, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reza","family":"Ezzati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad university, karaj, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tofigh","family":"Allahviranloo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,7,28]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.08.005"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.12.008"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151783"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.07.023"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151989"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2038-9"},{"key":"e_1_3_1_8_2","doi-asserted-by":"crossref","unstructured":"G.A.Anastassiou Fuzzy mathematics approximation theory Springer 2010.","DOI":"10.1007\/978-3-642-11220-1"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.12.071"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(03)00182-9"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.10.021"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.08.005"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-015-0389-7"},{"key":"e_1_3_1_14_2","first-page":"2072","article-title":"Numerical solution and error estimation of fuzzy Fredholm integral equation using fuzzy Bernstein polynomials","volume":"5","author":"Ezzati R.","year":"2011","unstructured":"R.Ezzati, S.Ziari, Numerical solution and error estimation of fuzzy Fredholm integral equation using fuzzy Bernstein polynomials, Australian Journal of Basic and Applied Sciences 5 (2011), 2072\u20132082.","journal-title":"Australian Journal of Basic and Applied Sciences"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.09.020"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1316-7"},{"key":"e_1_3_1_17_2","first-page":"375","article-title":"Numerical solution of two-dimensional fuzzy Fredholm integral equations using collocation fuzzy wavelet like operator","volume":"7","author":"Hassasi N.","year":"2015","unstructured":"N.Hassasi, R.Ezzati, Numerical solution of two-dimensional fuzzy Fredholm integral equations using collocation fuzzy wavelet like operator, International Journal of Industrial Mathematics 7 (2015), 375\u2013385.","journal-title":"International Journal of Industrial Mathematics"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2013.12.002"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-016-9534-2"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-016-9490-x"},{"key":"e_1_3_1_21_2","first-page":"46","article-title":"Numerical solution of Fredholm fuzzy integral equations of the second kind via direct method using triangular functions","volume":"1","author":"Mirzaee F.","year":"2012","unstructured":"F.Mirzaee, M.Paripour and Komak YariM., Numerical solution of Fredholm fuzzy integral equations of the second kind via direct method using triangular functions, Journal of Hyperstructures 1 (2012), 46\u201360.","journal-title":"Journal of Hyperstructures"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.bjbas.2015.05.003"},{"issue":"2","key":"e_1_3_1_23_2","first-page":"87","article-title":"Existence and uniqueness of the solution of fuzzy-valude integral equations of mixed type","volume":"12","author":"Mokhtarnejad F.","year":"2015","unstructured":"F.Mokhtarnejad, R.Ezzati, Existence and uniqueness of the solution of fuzzy-valude integral equations of mixed type, Iranian Jornal of Fuzzy Systems 12(2) (2015), 87\u201394.","journal-title":"Iranian Jornal of Fuzzy Systems"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141446"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.034"},{"key":"e_1_3_1_26_2","article-title":"Quadrature iterative method for numerical solution of two-dimensional linear fuzzy Fredholm integral equations","author":"Nouriani H.","unstructured":"H.Nouriani, R.Ezzati, Quadrature iterative method for numerical solution of two-dimensional linear fuzzy Fredholm integral equations, Mathematical Sciences, Accepted.","journal-title":"Mathematical Sciences, Accepted"},{"key":"e_1_3_1_27_2","first-page":"978","article-title":"The approximate solution of linear fuzzy fredholm integral equations of the second kind by using iterative interpolation","volume":"49","author":"Parandin N.","year":"2009","unstructured":"N.Parandin and Fariborzi AraghiM.A., The approximate solution of linear fuzzy fredholm integral equations of the second kind by using iterative interpolation, World Academy of Science, Engineering and Technology 49 (2009), 978\u2013984.","journal-title":"World Academy of Science, Engineering and Technology"},{"key":"e_1_3_1_28_2","first-page":"591","article-title":"Modified homotopy perturbation method for solving two-dimensional fuzzy Fredholm integral equation","volume":"25","author":"Rivaz A.","year":"2012","unstructured":"A.Rivaz, F.Yousefi, Modified homotopy perturbation method for solving two-dimensional fuzzy Fredholm integral equation, International Journal of Applied Mathematics 25 (2012), 591\u2013602.","journal-title":"International Journal of Applied Mathematics"},{"key":"e_1_3_1_29_2","first-page":"571","article-title":"Using block pulse functions for solving two-dimensional fuzzy Fredholm integral equations of the second kind","volume":"25","author":"Rivaz A.","year":"2012","unstructured":"A.Rivaz, F.Yousefi, H.Salehinejad, Using block pulse functions for solving two-dimensional fuzzy Fredholm integral equations of the second kind, International Journal of Applied Mathematics 25 (2012), 571\u2013582.","journal-title":"International Journal of Applied Mathematics"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.5899\/2013\/jfsva-00146"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/413570"},{"key":"e_1_3_1_32_2","first-page":"31","article-title":"Homotopy analysis method to solve two-dimensional fuzzy fredholm integral equation","volume":"22","author":"Vali M.A.","year":"2014","unstructured":"M.A.Vali, M.J.Agheli and Gohari NezhadS., Homotopy analysis method to solve two-dimensional fuzzy fredholm integral equation, Gen Math Notes 22 (2014), 31\u201343.","journal-title":"Gen Math Notes"},{"key":"e_1_3_1_33_2","article-title":"A novel type of soft rough covering and its application multicriteria group decision making","author":"Zhan J.","year":"2018","unstructured":"J.Zhan and AcantudJ.C.R., A novel type of soft rough covering and its application multicriteria group decision making, Artificial Intelligence Review (2018).","journal-title":"Artificial Intelligence Review"},{"key":"e_1_3_1_34_2","doi-asserted-by":"crossref","unstructured":"J.Zhan K.Zhu A novel soft rough set: Z-soft rough fuzzy idealsof hemirings and corresponding decision making 21 (2017) 1923\u20131936.","DOI":"10.1007\/s00500-016-2119-9"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.03.038"},{"key":"e_1_3_1_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.09.012"},{"key":"e_1_3_1_37_2","article-title":"Numerical solution of linear fuzzy Fredholm integral equations of the second kind using fuzzy Haar wavelet","volume":"299","author":"Ziari S.","year":"2012","unstructured":"S.Ziari, R.Ezzati, S.Abbasbandy, Numerical solution of linear fuzzy Fredholm integral equations of the second kind using fuzzy Haar wavelet, In: Advances in Computational Intelligence Communications in Computer and Information Science 299 (2012).","journal-title":"In: Advances in Computational Intelligence Communications in Computer and Information Science"},{"key":"e_1_3_1_38_2","first-page":"821","article-title":"Fuzzy Block-Pulse Functions and Its Application to Solve Linear Fuzzy Fredholm Integral Equations of the Second Kind","author":"Ziari S.","year":"2016","unstructured":"S.Ziari, R.Ezzati, Fuzzy Block-Pulse Functions and Its Application to Solve Linear Fuzzy Fredholm Integral Equations of the Second Kind, Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2016, pp.821\u2013832.","journal-title":"Information Processing and Management of Uncertainty in Knowledge-Based Systems"},{"key":"e_1_3_1_39_2","doi-asserted-by":"publisher","DOI":"10.5899\/2016\/jfsva-00278"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171104","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-171104","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-171104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:49Z","timestamp":1777455709000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-171104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,28]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2,16]]}},"alternative-id":["10.3233\/JIFS-171104"],"URL":"https:\/\/doi.org\/10.3233\/jifs-171104","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,28]]}}}