{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T18:20:47Z","timestamp":1769710847455,"version":"3.49.0"},"reference-count":34,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,8,1]]},"abstract":"<jats:p>Due to the importance of the multi-level fully rough interval linear programming (MLFRILP) problem to address a wide range of management and optimization challenges in practical applications, such as policymaking, supply chain management, energy management, and so on, few researchers have specifically discussed this point. This paper presents an easy and systematic roadmap of studies of the currently available literature on rough multi-level programming problems and improvements related to group procedures in seven basic categories for future researchers and also introduces the concept of multi-level fully rough interval optimization. We start remodeling the problem into its sixteen crisp linear programming LP problems using the interval method and slice sum method. All crisp LPs can be reduced to four crisp LPs. In addition, three different optimization techniques were used to solve the complex multi-level linear programming issues. A numerical example is also provided to further clarify each strategy. Finally, we have a comparison of the methods used for solving the MLFRILP problem.<\/jats:p>","DOI":"10.3233\/jifs-230057","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T13:20:20Z","timestamp":1685107220000},"page":"2593-2610","source":"Crossref","is-referenced-by-count":1,"title":["Three different optimization techniques for solving the fully rough interval multi-level linear programming problem"],"prefix":"10.1177","volume":"45","author":[{"given":"E.","family":"Fathy","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Helwan University, Egypt"}]},{"given":"E.","family":"Ammar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Egypt"}]},{"given":"M.A.","family":"Helmy","sequence":"additional","affiliation":[{"name":"Planning Techniques Center, Institute of National Planning, Egypt"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-230057_ref1","doi-asserted-by":"crossref","first-page":"2428","DOI":"10.1002\/int.22779","article-title":"A new approach to three way decisions making based on fractional fuzzy decision theoretical rough set","volume":"37","author":"Abdullah","year":"2022","journal-title":"International Journal of Intelligent Systems"},{"issue":"4","key":"10.3233\/JIFS-230057_ref2","first-page":"137","article-title":"A Novel Approach for Solving a Fully Rough Multi-Level Quadratic Programming Problem and Its Application","volume":"11","author":"Abohany","year":"2020","journal-title":"International Journal of Service Science, Management, Engineering, and Technology (IJSSMET)"},{"key":"10.3233\/JIFS-230057_ref3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.cor.2013.06.009","article-title":"A trilevel programming approach for electric grid defense planning","volume":"41","author":"Alguacil","year":"2014","journal-title":"Computers & Operations Research"},{"issue":"1","key":"10.3233\/JIFS-230057_ref5","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/S0377-2217(98)00336-1","article-title":"Determining optimal pollution control policies: An application of bilevel programming","volume":"119","author":"Amouzegar","year":"1999","journal-title":"European Journal of Operational Research"},{"key":"10.3233\/JIFS-230057_ref6","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jclepro.2014.09.069","article-title":"A bi-level optimization model for aid distribution after the occurrence of a disaster","volume":"105","author":"Camacho-Vallejo","year":"2015","journal-title":"Journal of Cleaner Production"},{"key":"10.3233\/JIFS-230057_ref7","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.dss.2014.12.004","article-title":"A bi-level decision support system for uncertain network design with equilibrium flow","volume":"69","author":"Chiou","year":"2015","journal-title":"Decision Support Systems"},{"issue":"1","key":"10.3233\/JIFS-230057_ref8","first-page":"012008","article-title":"Application of Pattern Matching in Heating Furnace\u2013Rough Rolling Process","volume":"2261","author":"Cui","year":"2022","journal-title":"In Journal of Physics: Conference Series"},{"issue":"4","key":"10.3233\/JIFS-230057_ref9","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1016\/j.aej.2019.12.002","article-title":"Fuzzy rough bi-level multi-objective nonlinear programming problems","volume":"58","author":"Elsisy","year":"2019","journal-title":"Alexandria Engineering Journal"},{"issue":"65","key":"10.3233\/JIFS-230057_ref10","first-page":"3221","article-title":"Interactive bi-level multi-objective integer non-linear programming problem","volume":"5","author":"Emam","year":"2011","journal-title":"Applied Mathematical Sciences"},{"key":"10.3233\/JIFS-230057_ref11","doi-asserted-by":"crossref","first-page":"305","DOI":"10.18576\/jsap\/060206","article-title":"On Rough Interval Three Level Large Scale Quadratic Integer Programming Problem","volume":"2","author":"Emam","year":"2017","journal-title":"Journal of Statistics Applications & Probability"},{"issue":"7","key":"10.3233\/JIFS-230057_ref12","doi-asserted-by":"crossref","first-page":"18","DOI":"10.5120\/ijca2016912287","article-title":"Fully fuzzy multi-level linear programming problem","volume":"155","author":"Emam","year":"2016","journal-title":"International Journal of Computer Applications"},{"key":"10.3233\/JIFS-230057_ref13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.9734\/JAMCS\/2017\/34811","article-title":"An Interactive Model for Fully Fuzzy Multi-Level Linear Programming Problem based on Multi-objective Linear Programming Technique","volume":"23","author":"Emam","year":"2017","journal-title":"Journal of Advances in Mathematics and Computer Science"},{"issue":"2","key":"10.3233\/JIFS-230057_ref14","doi-asserted-by":"crossref","first-page":"2727","DOI":"10.3233\/JIFS-182952","article-title":"A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique","volume":"37","author":"Fathy","year":"2019","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-230057_ref15","first-page":"139","article-title":"Building fuzzy approach with linearization technique for fully rough multi-objective multi-level linear fractional programming problem","volume":"18","author":"Fathy","year":"2021","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-230057_ref16","doi-asserted-by":"crossref","first-page":"3011","DOI":"10.3233\/JIFS-210694","article-title":"On solving the multilevel rough interval linear programming problem","volume":"42","author":"Fathy","year":"2022","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-230057_ref17","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1080\/00207543.2019.1584415","article-title":"The collaborative multi-level lot-sizing problem with cost synergies","volume":"58","author":"Gansterer","year":"2020","journal-title":"International Journal of Production Research"},{"key":"10.3233\/JIFS-230057_ref18","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.ijar.2022.01.007","article-title":"Three-way decision based on confidence level change in rough set","volume":"143","author":"Guo","year":"2022","journal-title":"International Journal of Approximate Reasoning"},{"issue":"3","key":"10.3233\/JIFS-230057_ref19","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.3233\/IFS-130804","article-title":"Linear programming with rough interval coefficients","volume":"26","author":"Hamzehee","year":"2014","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"10.3233\/JIFS-230057_ref20","first-page":"253","article-title":"Malware Evolution and Detection Based on the Variable Precision Rough Set Model","volume":"30","author":"Jerbi","year":"2022","journal-title":"Conference on Computer Science and Intelligence Systems (FedCSIS)"},{"issue":"1","key":"10.3233\/JIFS-230057_ref21","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1002\/er.6162","article-title":"Three-level interactive energy management strategy for optimal operation of multiple virtual power plants considering different time scales","volume":"45","author":"Li","year":"2021","journal-title":"International Journal of Energy Research"},{"issue":"1","key":"10.3233\/JIFS-230057_ref22","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/07408170600729192","article-title":"Algorithms for discrete and continuous multicommodity flow network interdiction problems","volume":"39","author":"Lim","year":"2007","journal-title":"IIE Transactions"},{"issue":"8","key":"10.3233\/JIFS-230057_ref23","doi-asserted-by":"crossref","first-page":"25","DOI":"10.5120\/ijca2017912790","article-title":"Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function","volume":"157","author":"Omran","year":"2017","journal-title":"International Journal of Computer Applications"},{"key":"10.3233\/JIFS-230057_ref24","doi-asserted-by":"crossref","first-page":"115","DOI":"10.18576\/jsap\/070111","article-title":"Solving fully rough interval multi-level multi-objective linear fractional programming problems via FGP","volume":"7","author":"Osman","year":"2018","journal-title":"Journal of Statistics Applications and Probability Letters"},{"issue":"2","key":"10.3233\/JIFS-230057_ref25","first-page":"13866","article-title":"Fully rough integer interval transportation problems","volume":"8","author":"Pandian","year":"2016","journal-title":"International Journal of Pharmacy and Technology"},{"key":"10.3233\/JIFS-230057_ref26","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cie.2017.02.007","article-title":"A supply chain with variable demand under three level trade credit policy","volume":"106","author":"Pramanik","year":"2017","journal-title":"Computers & Industrial Engineering"},{"issue":"4","key":"10.3233\/JIFS-230057_ref27","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1111\/itor.12645","article-title":"Multi-level, multi-stage lot-sizing and scheduling in the flexible flow shop with demand information updating","volume":"28","author":"Rehman","year":"2021","journal-title":"International Transactions in Operational Research"},{"issue":"12","key":"10.3233\/JIFS-230057_ref28","doi-asserted-by":"crossref","first-page":"2034","DOI":"10.1080\/1369183X.2017.1341708","article-title":"Multi-level governance of an intractable policy problem: Migrants with irregular status in Europe","volume":"44","author":"Spencer","year":"2018","journal-title":"Journal of Ethnic and Migration Studies"},{"issue":"1","key":"10.3233\/JIFS-230057_ref29","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/TPWRS.2013.2278700","article-title":"Energy and reserve scheduling under a joint generation and transmission security criterion: An adjustable robust optimization approach","volume":"29","author":"Street","year":"2013","journal-title":"IEEE Transactions on Power Systems"},{"key":"10.3233\/JIFS-230057_ref30","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.cor.2012.11.010","article-title":"Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints","volume":"41","author":"Wang","year":"2014","journal-title":"Computers & Operations Research"},{"issue":"2","key":"10.3233\/JIFS-230057_ref31","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.cie.2013.07.012","article-title":"A tri-level programming model based on conditional value-at-risk for three-stage supply chain management","volume":"66","author":"Xu","year":"2013","journal-title":"Computers & Industrial Engineering"},{"key":"10.3233\/JIFS-230057_ref32","doi-asserted-by":"crossref","first-page":"102848","DOI":"10.1016\/j.agsy.2020.102848","article-title":"Towards sustainable water management in an arid agricultural region: A multi-level multi-objective stochastic approach","volume":"182","author":"Zhang","year":"2020","journal-title":"Agricultural Systems"},{"key":"10.3233\/JIFS-230057_ref33","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1016\/j.ins.2022.05.122","article-title":"Measurement, modeling, reduction of decision-theoretic multigranulation fuzzy rough sets based on three-way decisions","volume":"607","author":"Zhang","year":"2022","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-230057_ref34","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.ijar.2021.09.017","article-title":"AMG-DTRS: Adaptive multi-granulation decision-theoretic rough sets","volume":"140","author":"Zhang","year":"2022","journal-title":"International Journal of Approximate Reasoning"},{"key":"10.3233\/JIFS-230057_ref35","doi-asserted-by":"crossref","first-page":"116187","DOI":"10.1016\/j.eswa.2021.116187","article-title":"Tri-level attribute reduction in rough set theory","volume":"190","author":"Zhang","year":"2022","journal-title":"Expert Systems with Applications"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-230057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T07:19:44Z","timestamp":1769671184000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-230057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,1]]},"references-count":34,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/jifs-230057","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,1]]}}}