{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:47:26Z","timestamp":1761896846459,"version":"3.37.3"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T00:00:00Z","timestamp":1531267200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018,7,11]]},"abstract":"We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. This new method uses a decomposition technique to convert a fully fuzzy linear system into two types of decomposition in the form of interval matrices. It finds the solution of a fully fuzzy linear system by using interval operations. This new method uses interval arithmetic and two new interval operations \u2296<\/mml:mo><\/mml:mrow><\/mml:math> and \u2298<\/mml:mo><\/mml:mrow><\/mml:math>. These new operations, which are inverses of basic interval operations +<\/mml:mo><\/mml:mrow><\/mml:math> and \u00d7<\/mml:mo><\/mml:mrow><\/mml:math>, will be presented in the middle of this paper. Some numerical examples are given to illustrate the ability of proposed methods.<\/jats:p>","DOI":"10.1155\/2018\/2104343","type":"journal-article","created":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T19:33:10Z","timestamp":1531337590000},"page":"1-10","source":"Crossref","is-referenced-by-count":10,"title":["An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7903-9244","authenticated-orcid":true,"given":"Esmaeil","family":"Siahlooei","sequence":"first","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3724-8689","authenticated-orcid":true,"given":"Seyed Abolfazl","family":"Shahzadeh Fazeli","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran"},{"name":"Processing Laboratory, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00270-9"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00793-8"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.12.085"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.02.018"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.11.124"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-009-9039-9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s12543-009-0024-y"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.043"},{"issue":"3","key":"9","first-page":"140","volume":"2","year":"2008","journal-title":"International Journal of Computational and Mathematical Sciences"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.03.085"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/593274"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-0986-x"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-1037-3"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2197-8"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-015-9283-0"},{"issue":"2","key":"17","doi-asserted-by":"crossref","first-page":"921","DOI":"10.3233\/IFS-151813","volume":"30","year":"2016","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"18","first-page":"55","volume":"1-3","year":"2017","journal-title":"Fuzzy Systems: Concepts, Methodologies, Tools, and Applications"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-016-2294-8"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.876743"},{"issue":"1","key":"22","first-page":"99","volume":"2","year":"2011","journal-title":"International Journal of Latest Trends in Computing"},{"issue":"10","key":"23","first-page":"14","volume":"112","year":"2015","journal-title":"International Journal of Computer Applications"},{"year":"1980","series-title":"chapter 4","key":"24"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011470131086"},{"year":"1979","key":"26"},{"first-page":"225","volume-title":"Extended interval arithmetics: new results and applications","year":"1992","key":"27"},{"year":"2013","key":"28"},{"year":"2015","key":"29"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/2104343.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/2104343.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2018\/2104343.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,7,11]],"date-time":"2018-07-11T19:33:13Z","timestamp":1531337593000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2018\/2104343\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,11]]},"references-count":27,"alternative-id":["2104343","2104343"],"URL":"https:\/\/doi.org\/10.1155\/2018\/2104343","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"type":"print","value":"1687-7101"},{"type":"electronic","value":"1687-711X"}],"subject":[],"published":{"date-parts":[[2018,7,11]]}}}