{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T13:10:43Z","timestamp":1711372243788},"reference-count":60,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,27]],"date-time":"2009-02-27T00:00:00Z","timestamp":1235692800000},"content-version":"unspecified","delay-in-days":5020,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIEDAM"],"published-print":{"date-parts":[[1995,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Interval arithmetic has been extensively applied to systems of linear equations by the interval matrix arithmetic community. This paper demonstrates through simple examples that some of this work can be viewed as particular instantiations of an abstract \u201cdesign operation,\u201d the RANGE operation of the Labeled Interval Calculus formalism for inference about sets of possibilities in design. These particular operations promise to solve a variety of design problems that lay beyond the reach of the original Labeled Interval Calculus. However, the abstract view also leads to a new operation, apparently overlooked by the matrix mathematics community, that should also be useful in design; the paper provides an algorithm for computing it.<\/jats:p>","DOI":"10.1017\/s0890060400002420","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T13:46:29Z","timestamp":1270043189000},"page":"183-196","source":"Crossref","is-referenced-by-count":4,"title":["The RANGE family of propagation operations for intervals on simultaneous linear equations"],"prefix":"10.1017","volume":"9","author":[{"given":"R.","family":"Chen","sequence":"first","affiliation":[]},{"given":"A.C.","family":"Ward","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,2,27]]},"reference":[{"key":"S0890060400002420_ref060","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90031-X"},{"key":"S0890060400002420_ref059","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919197"},{"key":"S0890060400002420_ref058","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919320"},{"key":"S0890060400002420_ref056","unstructured":"Ward A. , Liker J. , Sobek D. , & Cristiano J. The second Toyota paradox: How delaying decisions can make better cars faster. Sloan Management Review (in press)."},{"key":"S0890060400002420_ref055","volume-title":"Matrix Iterative Analysis","author":"Varga","year":"1962"},{"key":"S0890060400002420_ref054","doi-asserted-by":"crossref","unstructured":"Sarma E.S. , & Rinderle J.R. (1991). Quiescence in internal propagation. Proceedings of the ASME Design Theory and Methodology Conference, pp. 257\u2013263.","DOI":"10.1115\/DETC1991-0057"},{"key":"S0890060400002420_ref002","unstructured":"Bains N. , & Ward A. Multiple-type interval propagations through non-monotonic equations. ASME Journal of Mechanical Design (in press)."},{"key":"S0890060400002420_ref035","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386090"},{"key":"S0890060400002420_ref051","doi-asserted-by":"publisher","DOI":"10.1007\/BF02243809"},{"key":"S0890060400002420_ref003","doi-asserted-by":"publisher","DOI":"10.1109\/20.106439"},{"key":"S0890060400002420_ref049","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90004-9"},{"key":"S0890060400002420_ref057","first-page":"47","article-title":"Extending the constraint propagation of intervals","volume":"4","author":"Ward","year":"1990","journal-title":"AI EDAM"},{"key":"S0890060400002420_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(87)90091-9"},{"key":"S0890060400002420_ref036","doi-asserted-by":"publisher","DOI":"10.1109\/31.7573"},{"key":"S0890060400002420_ref040","doi-asserted-by":"crossref","unstructured":"Rinderle J.R. , & Krishnan V. (1990). Constraint reasoning in concurrent design. Proceedings of the 1990 ASME Design Theory and Methodology Conference, pp. 53\u201362.","DOI":"10.1115\/DETC1990-0108"},{"key":"S0890060400002420_ref006","unstructured":"Chen R. (1992). Generalizing Interval Matrix Operations for Design: Fusing the Labeled Interval Calculus and Interval Matrix Arithmetic. Ph.D. Thesis, University of Michigan."},{"key":"S0890060400002420_ref033","volume-title":"Interval Methods for Systems of Equations","author":"Neumaier","year":"1990"},{"key":"S0890060400002420_ref017","first-page":"308","article-title":"Interval arithmetic in matrix computations, Part I","volume":"2","author":"Hansen","year":"1965","journal-title":"SIAM J. Numerical Analysis"},{"key":"S0890060400002420_ref007","doi-asserted-by":"publisher","DOI":"10.1137\/0716070"},{"key":"S0890060400002420_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238739"},{"key":"S0890060400002420_ref001","volume-title":"Introduction to Interval Computation","author":"Alefeld","year":"1983"},{"key":"S0890060400002420_ref025","doi-asserted-by":"publisher","DOI":"10.1109\/59.49103"},{"key":"S0890060400002420_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02241224"},{"key":"S0890060400002420_ref026","volume-title":"Interval Analysis","author":"Moore","year":"1966"},{"key":"S0890060400002420_ref050","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238736"},{"key":"S0890060400002420_ref053","doi-asserted-by":"publisher","DOI":"10.1007\/BF01932142"},{"key":"S0890060400002420_ref015","first-page":"279","volume-title":"ASME Design Theory and Methodology Conference","author":"Habib","year":"1991"},{"key":"S0890060400002420_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02259840"},{"key":"S0890060400002420_ref005","unstructured":"Chang T.-S. , Ward A. , Lee J. , & Jacox E. Conceptual robustness in simultaneous engineering: An extension of Taguchi\u2019s parameter design. Research in Engineering Design (in press)."},{"key":"S0890060400002420_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82739-6"},{"key":"S0890060400002420_ref012","unstructured":"Finch W. , & Ward A. Extending generalized interval propagation to monotonic relations among more than three variables (in preparation)."},{"key":"S0890060400002420_ref029","first-page":"107","volume-title":"Interval Mathematics, Proceedings of the International Symposium","author":"Neumaier","year":"1985"},{"key":"S0890060400002420_ref018","doi-asserted-by":"publisher","DOI":"10.1137\/0704001"},{"key":"S0890060400002420_ref028","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(84)90217-9"},{"key":"S0890060400002420_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(69)90024-X"},{"key":"S0890060400002420_ref030","first-page":"37","article-title":"Further results on linear interval equations","volume":"4","author":"Neumaier","year":"1985","journal-title":"Freiburger Intervall-Berichte"},{"key":"S0890060400002420_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396417"},{"key":"S0890060400002420_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/BF02262219"},{"key":"S0890060400002420_ref031","first-page":"5","article-title":"Tolerance analysis with interval arithmetic","volume":"9","author":"Neumaier","year":"1986","journal-title":"Freiburger Intervall-Berichte"},{"key":"S0890060400002420_ref023","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238301"},{"key":"S0890060400002420_ref013","doi-asserted-by":"publisher","DOI":"10.1137\/0719062"},{"key":"S0890060400002420_ref043","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-07170-9_6"},{"key":"S0890060400002420_ref024","unstructured":"Ly T.E.A. , & Girczyc E.F. (1988). Constraint propagation in the object-oriented IC design environment. 25th ACM\/IEEE Design Automation Conference, pp. 628\u2013633."},{"key":"S0890060400002420_ref052","doi-asserted-by":"publisher","DOI":"10.1007\/BF01952693"},{"key":"S0890060400002420_ref032","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90164-9"},{"key":"S0890060400002420_ref034","first-page":"115","article-title":"On the solution set of linear systems with inaccurate coefficients","volume":"2","author":"Oettli","year":"1965","journal-title":"SIAM J. Numerical Analysis"},{"key":"S0890060400002420_ref004","doi-asserted-by":"publisher","DOI":"10.1145\/321556.321564"},{"key":"S0890060400002420_ref041","doi-asserted-by":"publisher","DOI":"10.1007\/BF02241817"},{"key":"S0890060400002420_ref038","doi-asserted-by":"publisher","DOI":"10.1109\/31.7599"},{"key":"S0890060400002420_ref039","article-title":"The Edinburgh designer system as a framework for robotics: The design of behavior","volume":"1","author":"Popplestone","year":"1987","journal-title":"AI EDAM"},{"key":"S0890060400002420_ref014","doi-asserted-by":"publisher","DOI":"10.1137\/0611006"},{"key":"S0890060400002420_ref042","unstructured":"Ris F.N. (1972). Interval Analysis and Applications to Linear Algebra. Ph.D. Thesis, Oxford."},{"key":"S0890060400002420_ref045","doi-asserted-by":"publisher","DOI":"10.1007\/BF02243426"},{"key":"S0890060400002420_ref037","doi-asserted-by":"publisher","DOI":"10.1109\/31.7598"},{"key":"S0890060400002420_ref044","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(81)90298-6"},{"key":"S0890060400002420_ref027","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970906"},{"key":"S0890060400002420_ref046","first-page":"23","article-title":"An algorithm for solving interval linear systems and inverting interval matrices","volume":"82","author":"Rohn","year":"1982","journal-title":"Freiburger Intervall-Ber"},{"key":"S0890060400002420_ref047","first-page":"157","volume-title":"Interval Mathematics, Proceedings of the International Symposium","author":"Rohn","year":"1985"},{"key":"S0890060400002420_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF02251836"},{"key":"S0890060400002420_ref048","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-505630-4.50015-8"}],"container-title":["Artificial Intelligence for Engineering Design, Analysis and Manufacturing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0890060400002420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,25]],"date-time":"2024-03-25T12:52:42Z","timestamp":1711371162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0890060400002420\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":60,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S0890060400002420"],"URL":"https:\/\/doi.org\/10.1017\/s0890060400002420","relation":{},"ISSN":["0890-0604","1469-1760"],"issn-type":[{"value":"0890-0604","type":"print"},{"value":"1469-1760","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}