{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:06:32Z","timestamp":1777705592816,"version":"3.51.4"},"reference-count":52,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,2,2]]},"abstract":"<jats:p>The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control of randomness, fuzziness, and outliers in the data obtained from uncertain environments. In the present study, we propose a new two-stage fuzzy linear regression model based on a new interval type-2 (IT2) fuzzy least absolute deviation (FLAD) method so that regression coefficients and dependent variables are trapezoidal IT2 fuzzy numbers and independent variables are crisp. In the first stage, to estimate the IT2 fuzzy regression coefficients and provide an initial model (by original dataset), we introduce two new distance measures for comparison of IT2 fuzzy numbers and propose a novel framework for solving fuzzy mathematical programming problems. In the second stage, we introduce a new procedure to determine the mild and extreme fuzzy outlier cutoffs and apply them to remove the outliers, and then provide the final model based on a clean dataset. Furthermore, to evaluate the performance of the proposed methodology, we introduce and employ suitable goodness of fit indices. Finally, to illustrate the theoretical results of the proposed method and explain how it can be used to derive the regression model with IT2 trapezoidal fuzzy data, as well as compare the performance of the proposed model with some well-known models using training data designed by Tanaka et\u00a0al. [55], we provide two numerical examples.<\/jats:p>","DOI":"10.3233\/jifs-210340","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T11:53:19Z","timestamp":1639137199000},"page":"1381-1403","source":"Crossref","is-referenced-by-count":2,"title":["Introducing a trapezoidal interval type-2 fuzzy regression model"],"prefix":"10.1177","volume":"42","author":[{"given":"Mikaeel","family":"Mokhtari","sequence":"first","affiliation":[{"name":"Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tofigh","family":"Allahviranloo","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey"},{"name":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Hassan","family":"Behzadi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farhad Hoseinzadeh","family":"Lotfi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-210340_ref2","first-page":"151","article-title":"The nearest symmetric fuzzy solution for a symmetric fuzzy linear system","volume":"20","author":"Allahviranloo","year":"2012","journal-title":"An. St. Univ. Ovidius Constanta"},{"key":"10.3233\/JIFS-210340_ref3","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00500-019-04424-2","article-title":"Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters","volume":"24","author":"Arefi","year":"2020","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-210340_ref4","first-page":"12","article-title":"Linguistic questionnaire evaluation an application of the signed distance defuzzification method on different fuzzy numbers, the impact on the skewness of the output distributions","volume":"3","author":"Berkachy","year":"2018","journal-title":"International Journal of Fuzzy Systems and Advanced Applications"},{"key":"10.3233\/JIFS-210340_ref5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1142\/S1793005720500040","article-title":"Interval-valued intuitionistic fuzzy linear programming problem","volume":"16","author":"Bhartia","year":"2020","journal-title":"New Mathematics and Natural Computation"},{"key":"10.3233\/JIFS-210340_ref6","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0165-0114(94)90228-3","article-title":"Fuzzy genetic algorithm and applications","volume":"61","author":"Buckley","year":"1994","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-210340_ref7","first-page":"63","article-title":"Multiple fuzzy regression model for fuzzy input-output data","volume":"13","author":"Chachi","year":"2016","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-210340_ref8","first-page":"23","article-title":"An intelligent fuzzy regression approach for affective product design that captures nonlinearity and fuzziness","volume":"225","author":"Chan","year":"2011","journal-title":"Journal of Engineering Design"},{"key":"10.3233\/JIFS-210340_ref9","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1109\/TSMCB.2006.889609","article-title":"A mathematical programming method for formulating a fuzzy regression model based on distance criterion","volume":"37","author":"Chen","year":"2007","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"},{"key":"10.3233\/JIFS-210340_ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.asoc.2019.105915","article-title":"A new approach to formulate fuzzy regression models","volume":"86","author":"Chen","year":"2020","journal-title":"Applied Soft Computing"},{"key":"10.3233\/JIFS-210340_ref11","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s00500-007-0198-3","article-title":"Fuzzy regression using least absolutedeviation estimators","volume":"12","author":"Choi","year":"2007","journal-title":"Soft Compute"},{"key":"10.3233\/JIFS-210340_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105708"},{"key":"10.3233\/JIFS-210340_ref13","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s40300-013-0025-9","article-title":"Weighted least squares and least median squares estimation for the fuzzy linear regression analysis","volume":"71","author":"D\u2019Urso","year":"2013","journal-title":"METRON"},{"key":"10.3233\/JIFS-210340_ref14","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s10489-016-0779-x","article-title":"A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers","volume":"46","author":"Das","year":"2017","journal-title":"Appl Intell"},{"key":"10.3233\/JIFS-210340_ref15","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0020-0255(88)90047-3","article-title":"Fuzzy least squares","volume":"46","author":"Diamond","year":"1988","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-210340_ref18","doi-asserted-by":"crossref","unstructured":"Farhadinia B. , Sensitivity analysis in interval valued trapezoidal fuzzy number linear programming problems, Applied Mathematical Modeling, 38 (2014), 50\u201362.","DOI":"10.1016\/j.apm.2013.05.033"},{"key":"10.3233\/JIFS-210340_ref19","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/978-3-319-04280-0_4","article-title":"Linear programming with interval type -2 fuzzy constraints","volume":"539","author":"Figueroa-Garcia","year":"2014","journal-title":"Constraint Programming and Decision Making"},{"key":"10.3233\/JIFS-210340_ref20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/sym12081295","article-title":"The use of fuzzy linear regression and ANFIS methods to predict the compressive strength of cement","volume":"12","author":"Gkountakou","year":"2020","journal-title":"Symmetry"},{"key":"10.3233\/JIFS-210340_ref21","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1007\/s00500-010-0688-6","article-title":"A goal programming approach to fuzzy linear regression with fuzzy input-output data","volume":"15","author":"Hassanpour","year":"2011","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-210340_ref22","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/j.eswa.2018.10.026","article-title":"Fuzzy quantile linear regression model adopted with a semi-parametric technique based on fuzzy predictors and fuzzy responses","volume":"118","author":"Hesamian","year":"2019","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/JIFS-210340_ref24","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.ejor.2004.01.039","article-title":"A simple method for computation of fuzzy linear regression","volume":"166","author":"Hojati","year":"2005","journal-title":"European Journal of Operational Research"},{"key":"10.3233\/JIFS-210340_ref25","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0165-0114(02)00514-6","article-title":"Support vector fuzzy regression machines","volume":"138","author":"Hong","year":"2003","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-210340_ref26","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/11881599_23","article-title":"Fuzzy nonlinear regression model based on LS-SV min features space, Fuzzy Systems and Knowledge Discovery","volume":"4223","author":"Hong","year":"2006","journal-title":"Lecture Notes in Computer Science"},{"key":"10.3233\/JIFS-210340_ref27","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1007\/s00500-014-1328-3","article-title":"A weighted goal programming approach to fuzzy linear regression with crisp inputs and type-2 fuzzy outputs","volume":"19","author":"Hosseinzadeh","year":"2015","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-210340_ref28","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.3233\/IFS-152046","article-title":"A weighted goalprogramming approach to estimate the linear regression model in fullquasi type-2 fuzzy environment","volume":"30","author":"Hosseinzadeh","year":"2016","journal-title":"Journal of Intelligent & FuzzySystems"},{"key":"10.3233\/JIFS-210340_ref29","first-page":"192","article-title":"A weighted goal programming approach to fuzzy linear regression with quasi type-2 input-output data","volume":"6","author":"Hosseinzadeh","year":"2016","journal-title":"TWMS Journal of Applied and Engineering Mathematics"},{"key":"10.3233\/JIFS-210340_ref30","doi-asserted-by":"crossref","first-page":"3109","DOI":"10.1016\/j.fss.2006.08.004","article-title":"An omission approach for detecting outliers in fuzzy regression models","volume":"157","author":"Hung","year":"2006","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-210340_ref31","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.eswa.2019.04.033","article-title":"A multi-objective evolutionary approach for fuzzy regression analysis","volume":"130","author":"Jiang","year":"2019","journal-title":"Expert Systems with Applications"},{"key":"10.3233\/JIFS-210340_ref32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ins.2012.04.017","article-title":"Fuzzy least-absolutes regression using shape-preserving operations","volume":"214","author":"Kelkinnama","year":"2012","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-210340_ref33","first-page":"105","article-title":"A robust least squares fuzzy regression model based on kernel function","volume":"17","author":"Khammar","year":"2020","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-210340_ref34","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0165-0114(97)00100-0","article-title":"Evaluation of fuzzy linear regression models by comparing membership functions","volume":"100","author":"Kim","year":"1998","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-210340_ref35","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1080\/03081079008935108","article-title":"Fuzziness vs. probability","volume":"17","author":"Kosko","year":"1990","journal-title":"Int J General Systems"},{"key":"10.3233\/JIFS-210340_ref36","doi-asserted-by":"crossref","first-page":"1822","DOI":"10.1016\/j.camwa.2013.07.021","article-title":"Uncertainty degree and modeling of interval type-2 fuzzy sets: Definition, method and application","volume":"66","author":"Li","year":"2013","journal-title":"Computers and Mathematics with Applications"},{"key":"10.3233\/JIFS-210340_ref37","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.engappai.2016.02.009","article-title":"A new fuzzy regression model based on least absolute deviation","volume":"52","author":"Li","year":"2016","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10.3233\/JIFS-210340_ref38","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-018-0119-0"},{"key":"10.3233\/JIFS-210340_ref40","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.3233\/IFS-152044","article-title":"TOPSIS and Choquet integral hybrid technique for solving MAGDM problems with interval type 2 fuzzy numbers","volume":"30","author":"Mishmast Nehi","year":"2016","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"10.3233\/JIFS-210340_ref41","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0165-0114(96)00100-5","article-title":"The relationship between goal programming and fuzzy programming","volume":"89","author":"Mohamed","year":"1997","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-210340_ref42","first-page":"45","article-title":"Pedomodels fitting with fuzzy least squares regression","volume":"1","author":"Mohammadi","year":"2004","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-210340_ref43","doi-asserted-by":"crossref","unstructured":"P\u00e9rez-Ca\u00f1edo B. and Concepci\u00f3n-Morales E.R. , A method tofind the unique optimal fuzzy value of fully fuzzy linearprogramming problems with inequality constraints having unrestrictedL-R fuzzy parameters and decision variables, Expert Systems WithApplications, 123 (2019), 256\u2013269.","DOI":"10.1016\/j.eswa.2019.01.041"},{"key":"10.3233\/JIFS-210340_ref44","first-page":"677","article-title":"A fuzzygoal programming approach to fully fuzzy linear regression","volume":"1238","author":"P\u00e9rez-Ca\u00f1edo","year":"2020","journal-title":"CCIS"},{"key":"10.3233\/JIFS-210340_ref45","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.1007\/s00500-013-1185-5","article-title":"Least-squares approach to regression modeling in full, interval-valued fuzzy environment","volume":"18","author":"Rabiei","year":"2013","journal-title":"Soft Computing"},{"key":"10.3233\/JIFS-210340_ref46","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-1185-5"},{"key":"10.3233\/JIFS-210340_ref47","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1080\/17509653.2012.10671222","article-title":"Symmetric fuzzy linear regression using multi-objective optimization","volume":"6","author":"Rafiei1","year":"2012","journal-title":"International Journal of Management Science and Engineering Management"},{"key":"10.3233\/JIFS-210340_ref48","doi-asserted-by":"crossref","first-page":"946","DOI":"10.20965\/jaciii.2006.p0946","article-title":"New similarity measure between two fuzzy sets","volume":"10","author":"Rezaei","year":"2006","journal-title":"Journal of Advanced Computational Intelligence and Intelligent Informatics"},{"key":"10.3233\/JIFS-210340_ref49","doi-asserted-by":"crossref","first-page":"734","DOI":"10.2991\/ijcis.2017.10.1.49","article-title":"A piecewise type 2 fuzzy regression model","volume":"10","author":"Shafaei Bajestani","year":"2017","journal-title":"International Journal of Computational Intelligence Systems"},{"key":"10.3233\/JIFS-210340_ref51","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1016\/j.asoc.2012.07.001","article-title":"Outlier detection in fuzzy linearregression with crisp input\u2013output by linguistic variableview","volume":"13","author":"Shakouri","year":"2013","journal-title":"Applied Soft Computing"},{"key":"10.3233\/JIFS-210340_ref52","doi-asserted-by":"publisher","DOI":"10.1007\/s42452-019-1825-1"},{"key":"10.3233\/JIFS-210340_ref54","first-page":"121","article-title":"Fuzzy linear regression based on least absolute deviations","volume":"9","author":"Taheri","year":"2012","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-210340_ref55","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/TSMC.1982.4308925","article-title":"Linear regression analysis with fuzzy model","volume":"12","author":"Tanaka","year":"1982","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics"},{"key":"10.3233\/JIFS-210340_ref56","first-page":"348","article-title":"Design of a qualitative classification model through fuzzy support vector machine with type 2 fuzzy expected regression classifier preset","volume":"11","author":"Wei","year":"2016","journal-title":"IEEJ Trans"},{"key":"10.3233\/JIFS-210340_ref58","doi-asserted-by":"crossref","first-page":"263","DOI":"10.5626\/JCSE.2013.7.4.263","article-title":"Robust fuzzy varying coefficient regression analysis with crisp inputs and gaussian fuzzy output","volume":"7","author":"Yang","year":"2013","journal-title":"Journal of Computing Science and Engineering"},{"key":"10.3233\/JIFS-210340_ref59","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1016\/j.asoc.2016.09.029","article-title":"Fuzzy least absolute linear regression","volume":"52","author":"Zeng","year":"2017","journal-title":"Applied Soft Computing"},{"key":"10.3233\/JIFS-210340_ref60","doi-asserted-by":"crossref","first-page":"64","DOI":"10.4236\/jdaip.2016.42006","article-title":"Robust regression analysis with L-R type fuzzy input variables and fuzzy output variable","volume":"4","author":"Zhang","year":"2016","journal-title":"Journal of Data Analysis and Information Processing"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-210340","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:44:21Z","timestamp":1777455861000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-210340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,2]]},"references-count":52,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-210340","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,2]]}}}