{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T19:06:28Z","timestamp":1777921588450,"version":"3.51.4"},"reference-count":32,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"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":[[1998,1]]},"DOI":"10.1016\/s0165-0114(96)00144-3","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T13:25:26Z","timestamp":1049721926000},"page":"125-135","source":"Crossref","is-referenced-by-count":277,"title":["On a canonical representation of fuzzy numbers"],"prefix":"10.1016","volume":"93","author":[{"given":"M.","family":"Delgado","sequence":"first","affiliation":[]},{"given":"M.A.","family":"Vila","sequence":"additional","affiliation":[]},{"given":"W.","family":"Voxman","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0165-0114(96)00144-3_BIB1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0005-1098(77)90008-5","article-title":"Rating and ranking of multiple aspect alternatives using fuzzy sets","volume":"3","author":"Baas","year":"1977","journal-title":"Automatica"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB2","article-title":"Selecting uncertainty calculi and granularity: an experiment in trading-off precision and complexity","author":"Bonissone","year":"1985"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB3","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0020-7373(85)80001-8","article-title":"Editorial: reasoning with uncertainty in expert systems","volume":"22","author":"Bonissone","year":"1985","journal-title":"Int. J. Man-Machine Studies"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0165-0114(84)90072-1","article-title":"Associative monotonic operations in fuzzy sets theory","volume":"12","author":"Czogala","year":"1984","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB5","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0165-0114(88)90005-X","article-title":"Ranking fuzzy numbers using fuzzy relations","volume":"26","author":"Delgado","year":"1988","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB6","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0888-613X(88)90105-3","article-title":"The problem of linguistic approximation in clinical decision making","volume":"2","author":"Degani","year":"1988","journal-title":"Int. J. Approximate Reasoning"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB7","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","article-title":"Operations of fuzzy numbers","volume":"9","author":"Dubois","year":"1978","journal-title":"Int. J. Systems Sci."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0165-0114(79)90005-8","article-title":"Fuzzy real algebra: some results","volume":"2","author":"Dubois","year":"1979","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB9","series-title":"Fuzzy Sets and Systems, Theory and Applications","author":"Dubois","year":"1980"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB10","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1109\/TAC.1981.1102744","article-title":"Addition of interactive fuzzy numbers","volume":"26","author":"Dubois","year":"1981","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB11","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/0022-247X(78)90148-8","article-title":"Compactness in fuzzy topological spaces","volume":"62","author":"Gantner","year":"1978","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB12","first-page":"9","article-title":"On subjective order relations between fuzzy numbers","volume":"33","author":"Gonzalez","year":"1987","journal-title":"BUSEFAL"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB13","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/0022-247X(75)90039-6","article-title":"Normality in fuzzy topological spaces","volume":"50","author":"Hutton","year":"1975","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB14","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1080\/00207727608942013","article-title":"Tolerance analysis using fuzzy sets","volume":"12","author":"Jain","year":"1976","journal-title":"J. Systems Sci."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB15","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/0165-0114(84)90073-3","article-title":"Generalizing the L-fuzzy unit interval","volume":"12","author":"Klein","year":"1984","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB16","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S0165-0114(83)80115-8","article-title":"On R(L)+","volume":"10","author":"Lowen","year":"1983","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB17","first-page":"23","article-title":"How to handle fuzzy quantities","volume":"13","author":"Mares","year":"1977","journal-title":"Kybernetika"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB18","first-page":"41","article-title":"On fuzzy quantities with real and integer values","volume":"13","author":"Mares","year":"1977","journal-title":"Kybernetika"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB19","series-title":"Int. Conf. Cybernetic Soc.","article-title":"Algebraic properties of fuzzy numbers","author":"Mizumoto","year":"1976"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB20","series-title":"Advances in Fuzzy Sets Theory and Applications","first-page":"153","article-title":"Some properties of fuzzy numbers","author":"Mizumoto","year":"1979"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB21","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0165-0114(78)90011-8","article-title":"Fuzzy variables","volume":"1","author":"Nahmias","year":"1978","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB22","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0165-0114(82)90028-8","article-title":"Fuzzy addition in the L-fuzzy real line","volume":"8","author":"Rodabaugh","year":"1982","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB23","series-title":"Fuzzy Sets and Possibility Theory","first-page":"402","article-title":"The fuzzy real line and its subspaces","author":"Rodabaugh","year":"1982"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB24","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/S0165-0114(83)80077-3","article-title":"Separation axioms and the fuzzy real lines","volume":"11","author":"Rodabaugh","year":"1983","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB25","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0165-0114(84)90071-X","article-title":"Solution of fuzzy equations with extended operations","volume":"12","author":"Sanchez","year":"1984","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB26","article-title":"Non standard fuzzy arithmetics","author":"Sanchez","year":"1985"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB27","first-page":"323","article-title":"Linguistic solutions to fuzzy decision problems","volume":"20","author":"Tong","year":"1984","journal-title":"TIMS\/Studies Management Sci."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB28","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0165-0114(80)90065-2","article-title":"On the lack of inverses in fuzzy arithmetic","author":"Yager","year":"1980","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB29","series-title":"Cone convexity, cone extreme points and nondominated solutions in decision problems with multiobjectives","author":"Yu","year":"1974"},{"key":"10.1016\/S0165-0114(96)00144-3_BIB30_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of linguistic variable and its applications to approximate reasoning, Part I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inform. Sci."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB30_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","article-title":"The concept of linguistic variable and its applications to approximate reasoning, Part II","volume":"8","author":"Zadeh","year":"1976","journal-title":"Inform. Sci."},{"key":"10.1016\/S0165-0114(96)00144-3_BIB30_3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/0020-0255(75)90017-1","article-title":"The concept of linguistic variable and its applications to approximate reasoning, Part III","volume":"9","author":"Zadeh","year":"1976","journal-title":"Inform. Sci."}],"container-title":["Fuzzy Sets and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011496001443?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0165011496001443?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T13:54:49Z","timestamp":1556632489000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0165011496001443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["S0165011496001443"],"URL":"https:\/\/doi.org\/10.1016\/s0165-0114(96)00144-3","relation":{},"ISSN":["0165-0114"],"issn-type":[{"value":"0165-0114","type":"print"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}