{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:35:46Z","timestamp":1761597346451},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"S1","license":[{"start":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T00:00:00Z","timestamp":1333584000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s00521-012-0913-6","type":"journal-article","created":{"date-parts":[[2012,4,4]],"date-time":"2012-04-04T08:06:46Z","timestamp":1333526806000},"page":"329-336","source":"Crossref","is-referenced-by-count":9,"title":["Minimal solution of fuzzy linear system of differential equations"],"prefix":"10.1007","volume":"21","author":[{"given":"Maryam","family":"Mosleh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahmood","family":"Otadi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"913_CR1","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1016\/j.amc.2005.01.110","volume":"171","author":"S Abbasbandy","year":"2005","unstructured":"Abbasbandy S, Jafarian A, Ezzati R (2005) Conjugate gradient method for fuzzy symmetric positive definite system of linear equations. Appl Math Comput 171:1184\u20131191","journal-title":"Appl Math Comput"},{"key":"913_CR2","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1016\/j.chaos.2005.03.018","volume":"26","author":"S Abbasbandy","year":"2005","unstructured":"Abbasbandy S, Nieto JJ, Alavi M (2005) Tuning of reachable set in one dimensional fuzzy differential inclusions. Chaos Solitons Fractals 26:1337\u20131341","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR3","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.amc.2005.02.018","volume":"172","author":"S Abbasbandy","year":"2006","unstructured":"Abbasbandy S, Ezzati R, Jafarian A (2006) LU decomposition method for solving fuzzy system of linear equations. Appl Math Comput 172:633\u2013643","journal-title":"Appl Math Comput"},{"key":"913_CR4","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1016\/j.chaos.2006.10.045","volume":"37","author":"S Abbasbandy","year":"2008","unstructured":"Abbasbandy S, Otadi M, Mosleh M (2008) Minimal solution of general dual fuzzy linear systems. Chaos Solitons Fractals 37:1113\u20131124","journal-title":"Chaos Solitons & Fractals"},{"key":"913_CR5","first-page":"1633","volume":"177","author":"T Allahviranloo","year":"2007","unstructured":"Allahviranloo T, Ahmadi N, Ahmadi E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Sciences 177:1633\u20131647","journal-title":"Sciences"},{"key":"913_CR6","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1016\/j.ins.2007.10.013","volume":"178","author":"T Allahviranloo","year":"2008","unstructured":"Allahviranloo T, Ahmadi E, Ahmadi N (2008) Nth-order fuzzy linear differential equations. Inf Sci 178:1309\u20131324","journal-title":"Information scinces"},{"key":"913_CR7","doi-asserted-by":"crossref","first-page":"956","DOI":"10.1016\/j.ins.2008.11.016","volume":"179","author":"T Allahviranloo","year":"2009","unstructured":"Allahviranloo T, Kiani NA, Motamedi N (2009) Solving fuzzy differential equations by differential transformation. Inf Sci 179:956\u2013966","journal-title":"Information scinces"},{"key":"913_CR8","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s00500-008-0397-6","volume":"14","author":"T Allahviranloo","year":"2010","unstructured":"Allahviranloo T, Barkhordari Ahmadi M (2010) Fuzzy Laplace transforms. Soft Comput 14:235\u2013243","journal-title":"Soft Comput"},{"key":"913_CR9","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.amc.2004.10.042","volume":"169","author":"B Asady","year":"2005","unstructured":"Asady B, Abbasbandy S, Alavi M (2005) Fuzzy general linear systems. Appl Math Comput 169:34\u201340","journal-title":"Appl Math Comput"},{"key":"913_CR10","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198596653.001.0001","volume-title":"Matrix Methods and Applications","author":"S Barnet","year":"1990","unstructured":"Barnet S (1990) Matrix methods and applications. Clarendon Press, Oxford"},{"key":"913_CR11","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/S0165-0114(98)00150-X","volume":"110","author":"JJ Buckley","year":"2000","unstructured":"Buckley JJ, Feuring T (2000) Fuzzy differential equations. Fuzzy Sets Syst 110:69\u201377","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR12","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.chaos.2004.11.018","volume":"25","author":"M Caldas","year":"2005","unstructured":"Caldas M, Jafari S (2005) \u03b8-Compact fuzzy topological spaces. Chaos Solitons Fractals 25:229\u2013232","journal-title":"Chaos Solitons & Fractals"},{"key":"913_CR13","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/TSMC.1972.5408553","volume":"2","author":"SL Chang","year":"1972","unstructured":"Chang SL, Zadeh SL (1972) On fuzzy mapping and control. IEEE Trans Syst Man Cybem 2:30\u201334","journal-title":"IEEE Trans. Systems Man Cybemet"},{"key":"913_CR14","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","volume":"9","author":"D Dubois","year":"1978","unstructured":"Dubois D, Prade H (1978) Operations on fuzzy numbers. J Syst Sci 9:613\u2013626","journal-title":"J Systems Sci"},{"key":"913_CR15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0165-0114(82)80001-8","volume":"8","author":"D Dubois","year":"1982","unstructured":"Dubois D, Prade H (1982) Towards fuzzy differential calculus: part3, differentiation. Fuzzy Sets Syst 8:225\u2013233","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0960-0779(03)00278-9","volume":"19","author":"MS Elnaschie","year":"2004","unstructured":"Elnaschie MS (2004) A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos Solitons Fractals 19:209\u2013236","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR17","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.chaos.2004.02.028","volume":"22","author":"MS Elnaschie","year":"2004","unstructured":"Elnaschie MS (2004) The concepts of E infinity: an elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos Solitons Fractals 22:495\u2013511","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR18","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1515\/IJNSNS.2005.6.2.95","volume":"6","author":"MS Elnaschie","year":"2005","unstructured":"Elnaschie MS (2005) On a fuzzy K\u00e3hler manifold which is consistent with the two slit experiment. Int J Nonlinear Sci Numer Simul 6:95\u201398","journal-title":"Int J Nonlinear Science and Numerical Simulation"},{"key":"913_CR19","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.chaos.2005.04.116","volume":"27","author":"MS Elnaschie","year":"2006","unstructured":"Elnaschie MS (2006) Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos Solitons Fractals 27:297\u2013330","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR20","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.chaos.2005.11.032","volume":"29","author":"MS Elnaschie","year":"2006","unstructured":"Elnaschie MS (2006) Superstrings, entropy and the elementary particles content of the standard model. Chaos Solitons Fractals 29:48\u201354","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR21","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.chaos.2004.04.013","volume":"23","author":"G Feng","year":"2005","unstructured":"Feng G, Chen G (2005) Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos Solitons Fractals 23:459\u2013467","journal-title":"Chaos Solitons & Fractals"},{"key":"913_CR22","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0165-0114(96)00270-9","volume":"96","author":"M Friedman","year":"1998","unstructured":"Friedman M, Ming M, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96:201\u2013209","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR23","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0165-0114(98)00102-X","volume":"109","author":"M Friedman","year":"2000","unstructured":"Friedman M, Ming M, Kandel A (2000) Duality in fuzzy linear systems. Fuzzy Sets Syst 109:55\u201358","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR24","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0165-0114(86)90026-6","volume":"18","author":"R Goetschel","year":"1986","unstructured":"Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18:31\u201343","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR25","doi-asserted-by":"crossref","unstructured":"Jiang W, Guo-Dong Q, Bin D (2005) $$H_\\infty$$ variable universe adaptive fuzzy control for chaotic system. Chaos Solitons Fractals 24:1075\u20131086","DOI":"10.1016\/j.chaos.2004.09.056"},{"key":"913_CR26","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0165-0114(87)90029-7","volume":"24","author":"O Kaleva","year":"1987","unstructured":"Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301\u2013317","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR27","volume-title":"Introduction Fuzzy Arithmetic","author":"A Kaufmann","year":"1985","unstructured":"Kaufmann A, Gupta MM (1985) Introduction fuzzy arithmetic. Van Nostrand Reinhold, New York"},{"key":"913_CR28","volume-title":"Numerical Analysis, Mathematics of scientific computing","author":"D Kincaid","year":"1996","unstructured":"Kincaid D, Cheney W (1996) Numerical analysis, mathematics of scientific computing, 2nd edn. Brooks\/Cole Publishing Co., Pacific Grove"},{"key":"913_CR29","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0165-0114(97)00310-2","volume":"108","author":"Ma Ming","year":"1999","unstructured":"Ming M, Friedman M, Kandel A (1999) A new fuzzy arithmetic. Fuzzy Sets Syst 108:83\u201390","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0165-0114(97)00233-9","volume":"105","author":"Ma Ming","year":"1999","unstructured":"Ming M, Friedman M, Kandel A (1999) Numerical solutions of fuzzy differential equations. Fuzzy Sets Syst 105:133\u2013138","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR31","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.chaos.2006.03.066","volume":"34","author":"K Nozari","year":"2007","unstructured":"Nozari K, Fazlpour B (2007) Some consequences of spacetime fuzziness. Chaos Solitons Fractals 34:224\u2013234","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR32","doi-asserted-by":"crossref","first-page":"5026","DOI":"10.1016\/j.apm.2011.04.008","volume":"35","author":"M Otadi","year":"2011","unstructured":"Otadi M, Mosleh M (2011) Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network. Appl Math Model 35:5026\u20135039","journal-title":"Applied mathematical modeling"},{"key":"913_CR33","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1007\/s00500-010-0685-9","volume":"15","author":"M Otadi","year":"2011","unstructured":"Otadi M, Mosleh M, Abbasbandy S (2011) Numerical solution of fully fuzzy linear systems by fuzzy neural network. Soft Comput 15:1513\u20131522","journal-title":"Soft computing"},{"key":"913_CR34","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/j.chaos.2004.02.051","volume":"22","author":"JH Park","year":"2004","unstructured":"Park JH (2004) Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 22:1039\u20131046","journal-title":"Chaos Solitons & Fractals"},{"key":"913_CR35","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0893-9659(97)00043-8","volume":"10","author":"DW Pearson","year":"1997","unstructured":"Pearson DW (1997) A property of linear fuzzy differential equations. Appl Math Lett 10:99\u2013103","journal-title":"Appl Math Lett"},{"key":"913_CR36","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1016\/0022-247X(83)90169-5","volume":"91","author":"ML Puri","year":"1983","unstructured":"Puri ML, Ralescu DA (1983) Differentials of fuzzy functions. J Math Anal Appl 91:552\u2013558","journal-title":"J Math Anal Appl"},{"key":"913_CR37","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0165-0114(87)90030-3","volume":"24","author":"S Seikkala","year":"1987","unstructured":"Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24:319\u2013330","journal-title":"Fuzzy Sets Syst"},{"key":"913_CR38","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.chaos.2004.09.034","volume":"24","author":"Y Tanaka","year":"2005","unstructured":"Tanaka Y, Mizuno Y, Kado T (2005) Chaotic dynamics in the Friedman equation. Chaos Solitons Fractals 24:407\u2013422","journal-title":"Chaos, Solitons & Fractals"},{"key":"913_CR39","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199\u2013249","journal-title":"Inform Sci"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-0913-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-012-0913-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-0913-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T19:26:05Z","timestamp":1713813965000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-012-0913-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,5]]},"references-count":39,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["913"],"URL":"https:\/\/doi.org\/10.1007\/s00521-012-0913-6","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,5]]}}}