{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T15:14:13Z","timestamp":1784733253743,"version":"3.55.0"},"reference-count":45,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2003,4,1]],"date-time":"2003-04-01T00:00:00Z","timestamp":1049155200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fuzzy Sets and Systems"],"published-print":{"date-parts":[[2003,4]]},"DOI":"10.1016\/s0165-0114(02)00246-4","type":"journal-article","created":{"date-parts":[[2003,3,25]],"date-time":"2003-03-25T10:44:53Z","timestamp":1048589093000},"page":"5-9","source":"Crossref","is-referenced-by-count":246,"title":["Interval analysis and fuzzy set theory"],"prefix":"10.1016","volume":"135","author":[{"given":"Ramon","family":"Moore","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weldon","family":"Lodwick","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0165-0114(02)00246-4_BIB1","series-title":"Proc. ICANNGA\u201999\u2014Portoroz April 6\u20139, 1999","first-page":"1","article-title":"Topological approach to fuzzy sets and fuzzy logic","author":"Albrecht","year":"1999"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB2","series-title":"Proc. Internat. Conf. Computational Intelligence","first-page":"1","article-title":"Topological theory of fuzziness","author":"Albrecht","year":"1999"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB3","series-title":"Symbolic Algebra Methods and Verification Methods","first-page":"1","article-title":"Topological concepts for hierachies of variables, types and controls","author":"Albrecht","year":"2000"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB4","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0165-0114(94)00355-B","article-title":"Implementing fuzzy arithmetic","volume":"72","author":"Anile","year":"1995","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB5","first-page":"48","article-title":"Automatically verified reasoning with both intervals and probability density functions","volume":"2","author":"Berleant","year":"1993","journal-title":"Interval Comput."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB6","series-title":"Applications of Interval Analysis","first-page":"227","article-title":"Automatically verified arithmetic on probability distributions and intervals","author":"Berleant","year":"1996"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1023\/A:1009933109326","article-title":"Bounding the results of arithmetic operations on random variables of unknown dependency using intervals","volume":"4","author":"Berleant","year":"1998","journal-title":"Reliable Comput."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB8","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0377-2217(86)90266-3","article-title":"Fuzzy sets and statistical data","volume":"25","author":"Dubois","year":"1986","journal-title":"European J. Oper. Res."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB9","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0165-0114(91)90091-4","article-title":"Random sets and fuzzy interval analysis","volume":"42","author":"Dubois","year":"1991","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB10","series-title":"The Handbook of Fuzzy Sets","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/978-1-4615-4429-6_11","article-title":"Fuzzy interval analysis","author":"Dubois","year":"2000"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB11","first-page":"135","article-title":"The VPI software package for variable precision interval arithmetic","volume":"2","author":"Ely","year":"1993","journal-title":"Interval Comput."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB12","doi-asserted-by":"crossref","unstructured":"S. Ferson, Quality assurance for Monte Carlo risk assessment, Proc. ISUMA-NAFIPS\u201995, 1995, pp. 14\u201319.","DOI":"10.1109\/ISUMA.1995.527662"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB13","unstructured":"S. Ferson, Probability bounds analysis software, in: Computing in Environmental Resource Management: Proc. Special Conf., Research Triangle Park, NC, Air and Waste Management Association, Pittsburgh, PA, December 2\u20134, 1996, pp. 669\u2013678."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB14","doi-asserted-by":"crossref","unstructured":"S. Ferson, L. Ginzburg, Hybrid arithmetic, Proc. ISUMA-NAFIPS\u201995, 1995, pp. 619\u2013623.","DOI":"10.1109\/ISUMA.1995.527766"},{"issue":"2","key":"10.1016\/S0165-0114(02)00246-4_BIB15","article-title":"Fuzzy Arithmetic\u2014Special Issue","volume":"91","year":"1997","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB16","series-title":"Interval Mathematics","first-page":"7","article-title":"A generalized interval arithmetic","author":"Hansen","year":"1975"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB17","doi-asserted-by":"crossref","unstructured":"M. Hanss, A nearly strict fuzzy arithmetic for solving problems with uncertainties, in: T. Whalen (Ed.), Proc. North American Fuzzy Information Processing Society, NAFIPS\u201900, 2000, pp. 439\u2013443.","DOI":"10.1109\/NAFIPS.2000.877469"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB18","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0165-0114(81)90035-X","article-title":"Representation theorems for L-fuzzy quantities","volume":"5","author":"Hoehle","year":"1981","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB19","series-title":"Applied Interval Analysis","year":"2001"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB20","series-title":"Introduction to Fuzzy Arithmetic\u2014Theory and Applications","author":"Kaufmann","year":"1985"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB21","series-title":"Applications of Interval Analysis","first-page":"227","year":"1996"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01398455","article-title":"An axiomatic approach to rounded computation","volume":"18","author":"Kulisch","year":"1971","journal-title":"Numer. Math."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB23","series-title":"A New Approach to Scientific Computation","first-page":"1","article-title":"A new arithmetic for scientific computing","author":"Kulisch","year":"1983"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB24","series-title":"Computer Arithmetic","author":"Kulisch","year":"1982"},{"issue":"1","key":"10.1016\/S0165-0114(02)00246-4_BIB25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/1028001","article-title":"The arithmetic of the digital computer","volume":"28","author":"Kulisch","year":"1986","journal-title":"SIAM Rev."},{"issue":"3","key":"10.1016\/S0165-0114(02)00246-4_BIB26","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1142\/S0218488597000221","article-title":"Interval methods and fuzzy optimization","volume":"5","author":"Lodwick","year":"1997","journal-title":"Internat. J. Uncertainty Fuzziness Knowledge-Based Reasoning"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB27","doi-asserted-by":"crossref","unstructured":"W.A. Lodwick, K.D. Jamison, F.D. Newman, Extension of interval validation methods to fuzzy set theory, Proc. North American Fuzzy Information Processing Society, NAFIPS\u201901, 2001.","DOI":"10.1109\/NAFIPS.2001.943801"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB28","series-title":"Developments in Reliable Computing","first-page":"167","article-title":"The contribution of T. Sunaga to interval analysis and reliable computing","author":"Markov","year":"1999"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB29","unstructured":"R.E. Moore, Interval analysis and automatic error analysis in digital computing, Ph.D. Thesis, Stanford, University, 1962."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB30","series-title":"Interval Analysis","author":"Moore","year":"1966"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB31","series-title":"Methods and Applications of Interval Analysis","author":"Moore","year":"1979"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB32","first-page":"1","article-title":"Risk analysis without Monte Carlo methods","volume":"84\/1","author":"Moore","year":"1984","journal-title":"Freiburger Intervall-Berichte"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB33","first-page":"23","article-title":"Interval risk analysis of real estate investment","volume":"85\/3","author":"Moore","year":"1985","journal-title":"Frieburger Intervall-Berichte"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB34","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1108\/eb005392","article-title":"Representation theorems for fuzzy concepts","volume":"4","author":"Negoita","year":"1975","journal-title":"Kybernetes"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB35","series-title":"Applications of Interval Analysis","first-page":"245","article-title":"Nested intervals and sets","author":"Nguyen","year":"1996"},{"issue":"3","key":"10.1016\/S0165-0114(02)00246-4_BIB36","first-page":"44","article-title":"Interval statistics","volume":"1","author":"Orlov","year":"1992","journal-title":"Interval Comput."},{"issue":"2","key":"10.1016\/S0165-0114(02)00246-4_BIB37","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02425918","article-title":"Interval approach challenges Monte Carlo simulation","volume":"2","author":"Pesonen","year":"1996","journal-title":"Reliable Comput."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB38","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0165-0114(92)90021-U","article-title":"A generalization of the representation theorem","volume":"51","author":"Ralescu","year":"1992","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB39","series-title":"Applications of Interval Analysis","first-page":"337","article-title":"Computing uncertainty in interval based sets","author":"Rocha","year":"1996"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB40","unstructured":"J. Stolfi, M.V.A. Andrade, J.L.D. Comba, R. Van Iwaarden, Affine arithmetic: a correlation-sensitive variant of interval arithmetic, http:\/\/www.dcc.unicamp.br\/~stolfi\/E...\/projects\/affine-arith"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB41","first-page":"28","article-title":"Theory of an interval algebra and its application to numerical analysis","volume":"2","author":"Sunaga","year":"1958","journal-title":"RAAG Mem."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB42","unstructured":"J.A. Tupper, Graphing equations with generalized interval arithmetic, Masters Thesis, Graduate Department of Computer Science, University of Toronto, 1996."},{"issue":"5","key":"10.1016\/S0165-0114(02)00246-4_BIB43","first-page":"253","article-title":"Calculus of approximations","volume":"Cl. III-15","author":"Warmus","year":"1956","journal-title":"Bull. Sci. L'Acad. Pol. Sci."},{"key":"10.1016\/S0165-0114(02)00246-4_BIB44","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0888-613X(90)90022-T","article-title":"Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds","volume":"4","author":"Williamson","year":"1990","journal-title":"Internat. J. Approximate Reasoning"},{"key":"10.1016\/S0165-0114(02)00246-4_BIB45","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1007\/BF01457934","article-title":"The algebra of many-valued quantities","volume":"31","author":"Young","year":"1931","journal-title":"Math. Ann."}],"container-title":["Fuzzy Sets and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011402002464?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011402002464?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T05:20:49Z","timestamp":1554960049000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165011402002464"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,4]]}},"alternative-id":["S0165011402002464"],"URL":"https:\/\/doi.org\/10.1016\/s0165-0114(02)00246-4","relation":{},"ISSN":["0165-0114"],"issn-type":[{"value":"0165-0114","type":"print"}],"subject":[],"published":{"date-parts":[[2003,4]]}}}