{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:30:27Z","timestamp":1761597027174},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2007,6,5]],"date-time":"2007-06-05T00:00:00Z","timestamp":1181001600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2008,3]]},"DOI":"10.1007\/s00500-007-0220-9","type":"journal-article","created":{"date-parts":[[2007,6,4]],"date-time":"2007-06-04T08:45:04Z","timestamp":1180946704000},"page":"469-477","source":"Crossref","is-referenced-by-count":6,"title":["Fuzzy linear regression model based on fuzzy scalar product"],"prefix":"10.1007","volume":"12","author":[{"given":"Hsien-Chung","family":"Wu","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,6,5]]},"reference":[{"key":"220_CR1","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s00500-003-0337-4","volume":"8","author":"R Alex","year":"2004","unstructured":"Alex R (2004) Fuzzy normal regression model and related neural networks. Soft Comput 8:717\u2013721","journal-title":"Soft Comput"},{"key":"220_CR2","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0165-0114(90)90064-D","volume":"65","author":"A B\u00e1rdossy","year":"1990","unstructured":"B\u00e1rdossy A (1990) Note on fuzzy regression. Fuzzy Sets Syst 65:65\u201375","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR3","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/0270-0255(87)90468-4","volume":"9","author":"A Celmin\u0161","year":"1987","unstructured":"Celmin\u0161 A (1987) Multidimensional least-squares fitting of fuzzy models. Math Modell 9:669\u2013690","journal-title":"Math Modell"},{"key":"220_CR4","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1137\/0912029","volume":"12","author":"A Celmin\u0161","year":"1991","unstructured":"Celmin\u0161 A (1991) A practical approach to nonlinear fuzzy regression. SIAM J Sci Stat Comput 12:521\u2013546","journal-title":"SIAM J Sci Stat Comput"},{"key":"220_CR5","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0898-1221(94)00127-8","volume":"28","author":"PT Chang","year":"1994","unstructured":"Chang PT, Lee ES (1994) Fuzzy linear regression with spreads unrestricted in sign. Comput Math Appl 28:61\u201370","journal-title":"Comput Math Appl"},{"key":"220_CR6","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/0165-0114(95)00284-7","volume":"82","author":"PT Chang","year":"1996","unstructured":"Chang PT, Lee ES (1996) A generalized fuzzy weighted least-squares regression. Fuzzy Sets Syst 82:289\u2013298","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR7","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0020-0255(88)90047-3","volume":"46","author":"P Diamond","year":"1988","unstructured":"Diamond P (1988) Fuzzy least squares. Inf Sci 46:141\u2013157","journal-title":"Inf Sci"},{"key":"220_CR8","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0165-0114(97)00393-X","volume":"112","author":"JP Dunyak","year":"2000","unstructured":"Dunyak JP, Wunsch D (2000) Fuzzy regression by fuzzy number neural networks. Fuzzy Sets Syst 112:371\u2013380","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR9","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0167-9473(02)00117-2","volume":"42","author":"P D\u2019Urso","year":"2003","unstructured":"D\u2019Urso P (2003) Linear regression analysis for fuzzy\/crisp input and fuzzy\/crisp output data. Comput Stat Data Anal 42:47\u201372","journal-title":"Comput Stat Data Anal"},{"key":"220_CR10","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/S0167-9473(99)00109-7","volume":"34","author":"P D\u2019Urso","year":"2000","unstructured":"D\u2019Urso P, Gastaldi T (2000) A least-squares approach to fuzzy linear regression analysis. Comput Stat Data Anal 34:427\u2013440","journal-title":"Comput Stat Data Anal"},{"key":"220_CR11","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0165-0114(86)90045-X","volume":"20","author":"K Jajuga","year":"1986","unstructured":"Jajuga K (1986) Linear fuzzy regression. Fuzzy Sets Syst 20:343\u2013353","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR12","volume-title":"Fuzzy regression analysis","year":"1992","unstructured":"Kacprzyk J, Fedrizzi M (eds) (1992) Fuzzy regression analysis. Omnitech Press, Warsaw and Physica-Verlag, Heidelberg"},{"key":"220_CR13","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0165-0114(97)00100-0","volume":"100","author":"B Kim","year":"1998","unstructured":"Kim B, Bishu RR (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 100:343\u2013352","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR14","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/0377-2217(94)00352-1","volume":"92","author":"KJ Kim","year":"1996","unstructured":"Kim KJ, Moskowitz H, Koksalan M (1996) Fuzzy versus statistical linear regression. Eur J Oper Res 92:417\u2013434","journal-title":"Eur J Oper Res"},{"key":"220_CR15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0165-0114(96)00051-6","volume":"88","author":"M Ma","year":"1997","unstructured":"Ma M, Friedman M, Kandel A (1997) General fuzzy least squares. Fuzzy Sets Syst 88:107\u2013118","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR16","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0165-0114(93)90505-C","volume":"58","author":"H Moskowitz","year":"1993","unstructured":"Moskowitz H, Kim K (1993) On assessing the H value in fuzzy linear regression. Fuzzy Sets Syst 58:303\u2013327","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR17","first-page":"873","volume":"155","author":"MM Nasrabadi","year":"2004","unstructured":"Nasrabadi MM, Nasrabadi E (2004) A mathematical programming approach to fuzzy linear regression analysis. Appl Math Comput 155:873\u2013881","journal-title":"Appl Math Comput"},{"key":"220_CR18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0165-0114(94)90144-9","volume":"63","author":"G Peters","year":"1994","unstructured":"Peters G (1994) Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst 63:35\u201343","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR19","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/0165-0114(94)90159-7","volume":"64","author":"DT Redden","year":"1994","unstructured":"Redden DT, Woodall WH (1994) Properties of certain fuzzy linear regression methods. Fuzzy Sets Syst 64:361\u2013375","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0165-0114(92)90175-4","volume":"47","author":"M Sakawa","year":"1992","unstructured":"Sakawa M, Yano H (1992) Multiobjective fuzzy linear regression analysis for fuzzy input\u2013output data. Fuzzy Sets Syst 47:173\u2013181","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR21","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0165-0114(88)90054-1","volume":"27","author":"H Tanaka","year":"1988","unstructured":"Tanaka H, Warada J (1988) Possibilistic linear system and their application to the linear regression model. Fuzzy Sets Syst 27:275\u2013289","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR22","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0165-0114(91)90218-F","volume":"41","author":"H Tanaka","year":"1991","unstructured":"Tanaka H, Ishibuchi H (1991) Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters. Fuzzy Sets Syst 41:145\u2013160","journal-title":"Fuzzy Sets Syst"},{"key":"220_CR23","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1109\/91.728436","volume":"6","author":"H Tanaka","year":"1998","unstructured":"Tanaka H, Lee H (1998) Interval regression analysis by quadratic programming approach. IEEE Trans Fuzzy Syst 6:473\u2013481","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"220_CR24","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1109\/TSMC.1982.4308925","volume":"12","author":"H Tanaka","year":"1982","unstructured":"Tanaka H, Uejima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Man Cyber 12:903\u2013907","journal-title":"IEEE Trans Syst Man Cyber"},{"key":"220_CR25","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0377-2217(89)90431-1","volume":"40","author":"H Tanaka","year":"1989","unstructured":"Tanaka H, Hayashi I, Watada J (1989) Possibilistic linear regression analysis for fuzzy data. Eur J Oper Res 40:389\u2013396","journal-title":"Eur J Oper Res"},{"key":"220_CR26","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1007\/s00500-003-0326-7","volume":"8","author":"Y Toyoura","year":"2004","unstructured":"Toyoura Y, Watada J, Khalid M, Yusof R (2004) Formulation of linguistic regression model based on natural words. Soft Comput 8:681\u2013688","journal-title":"Soft Comput"},{"key":"220_CR27","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/S0377-2217(99)00317-3","volume":"126","author":"HF Wang","year":"2000","unstructured":"Wang HF, Tsaur RC (2000) Resolution of fuzzy regression model. Eur J Oper Res 126:637\u2013650","journal-title":"Eur J Oper Res"},{"key":"220_CR28","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S0167-9473(02)00116-0","volume":"42","author":"HC Wu","year":"2003","unstructured":"Wu HC (2003a) Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data. Comput Stat Data Anal 42:203\u2013217","journal-title":"Comput Stat Data Anal"},{"key":"220_CR29","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1016\/S0898-1221(03)90006-X","volume":"45","author":"HC Wu","year":"2003","unstructured":"Wu HC (2003b) Linear regression analysis for fuzzy input and output data using the extension principle. Comput Math Appl 45:1849\u20131859","journal-title":"Comput Math Appl"},{"key":"220_CR30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0020-0255(82)90043-3","volume":"26","author":"RR Yager","year":"1982","unstructured":"Yager RR (1982) Fuzzy prediction based on regression models. Inf Sci 26:45\u201363","journal-title":"Inf Sci"},{"key":"220_CR31","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"220_CR32","unstructured":"Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning I, II and III. Inf Sci 8:199\u2013249; 8:301\u2013357; 9:43\u201380"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-007-0220-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-007-0220-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-007-0220-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T21:39:52Z","timestamp":1559079592000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-007-0220-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,5]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,3]]}},"alternative-id":["220"],"URL":"https:\/\/doi.org\/10.1007\/s00500-007-0220-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6,5]]}}}