{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T00:34:14Z","timestamp":1772066054261,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":29,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642240003","type":"print"},{"value":"9783642240010","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-24001-0_11","type":"book-chapter","created":{"date-parts":[[2011,9,24]],"date-time":"2011-09-24T08:20:15Z","timestamp":1316852415000},"page":"103-112","source":"Crossref","is-referenced-by-count":14,"title":["A Characterization Theorem for t-Representable n-Dimensional Triangular Norms"],"prefix":"10.1007","author":[{"given":"Benjam\u00edn","family":"Bedregal","sequence":"first","affiliation":[]},{"given":"Gleb","family":"Beliakov","sequence":"additional","affiliation":[]},{"given":"Humberto","family":"Bustince","sequence":"additional","affiliation":[]},{"given":"Tomasa","family":"Calvo","sequence":"additional","affiliation":[]},{"given":"Javier","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[]},{"given":"Radko","family":"Mesiar","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"11_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K.T. Atanassov","year":"1986","unstructured":"Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems\u00a020, 87\u201396 (1986)","journal-title":"Fuzzy Sets and Systems"},{"key":"11_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7908-1870-3","volume-title":"Intuitionistic Fuzzy Sets. Theory and Applications","author":"K.T. Atanassov","year":"1999","unstructured":"Atanassov, K.T.: Intuitionistic Fuzzy Sets. Theory and Applications. Physica-Verlag, Heidelberg (1999)"},{"key":"11_CR3","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","volume":"31","author":"K.T. Atanassov","year":"1989","unstructured":"Atanassov, K.T., Gargov, G.: Interval Valued Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems\u00a031, 343\u2013349 (1989)","journal-title":"Fuzzy Sets and Systems"},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"Bedregal, B.C., Takahashi, A.: Interval t-norms as interval representations of t-norms. In: Proc. of IEEE International Conference on Fuzzy Systems (Fuzz-IEEE), Reno, Nevada, May 22\u201325, pp. 909\u2013914 (2005)","DOI":"10.1109\/FUZZY.2005.1452515"},{"key":"11_CR5","doi-asserted-by":"crossref","unstructured":"Bedregal, B., Beliakov, G., Bustince, H., Calvo, T., Mesiar, R., Paternain, D.: A class of fuzzy multisets with a fixed number of memberships. Information Sciences (submitted)","DOI":"10.1016\/j.ins.2011.11.040"},{"key":"11_CR6","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1016\/j.ins.2009.11.035","volume":"180","author":"B.C. Bedregal","year":"2010","unstructured":"Bedregal, B.C., Dimuro, G.P., Santiago, R.H.N., Reiser, R.H.S.: On interval fuzzy S-implications. Information Sciences\u00a0180, 1373\u20131389 (2010)","journal-title":"Information Sciences"},{"key":"11_CR7","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1002\/int.20292","volume":"23","author":"H. Bustince","year":"2008","unstructured":"Bustince, H., Barrenechea, E., Pagola, M.: Generation of interval-valued fuzzy and Atanassov\u2019s intuitionistic fuzzy connectives from fuzzy connectives and from K\n                  \n                    \u03b1\n                   operators: Laws for conjunctions and disjunctions, amplitude. Int. J. of Intelligent Systems\u00a023, 680\u2013714 (2008)","journal-title":"Int. J. of Intelligent Systems"},{"key":"11_CR8","first-page":"5","volume":"1","author":"H. Bustince","year":"1995","unstructured":"Bustince, H., Burillo, P.: A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets\u00a01, 5\u201316 (1995)","journal-title":"Notes on Intuitionistic Fuzzy Sets"},{"key":"11_CR9","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/S0165-0114(02)00214-2","volume":"134","author":"H. Bustince","year":"2003","unstructured":"Bustince, H., Burillo, P., Soria, F.: Automorphism, negations and implication operators. Fuzzy Sets and Systems\u00a0134, 209\u2013229 (2003)","journal-title":"Fuzzy Sets and Systems"},{"key":"11_CR10","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0888-613X(03)00072-0","volume":"35","author":"C. Cornelis","year":"2004","unstructured":"Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. Int. J. of Approximate Reasoning\u00a035, 55\u201395 (2004)","journal-title":"Int. J. of Approximate Reasoning"},{"issue":"4","key":"11_CR11","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1016\/j.ijar.2010.11.004","volume":"52","author":"C.G. Costa Da","year":"2011","unstructured":"Da Costa, C.G., Bedregal, B.C., Doria Neto, A.D.: Relating De Morgan triples with Atanassov\u2019s intuitionistic De Morgan triples via automorphisms. Int. J. Approximate Reasoning\u00a052(4), 473\u2013487 (2011)","journal-title":"Int. J. Approximate Reasoning"},{"key":"11_CR12","doi-asserted-by":"publisher","first-page":"1597","DOI":"10.1016\/j.fss.2007.09.017","volume":"159","author":"G. Deschrijver","year":"2008","unstructured":"Deschrijver, G.: A representation of t-norms in interval-valued L-fuzzy set theory. Fuzzy Sets and Systems\u00a0159, 1597\u20131618 (2008)","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"11_CR13","first-page":"345","volume":"15","author":"G. Deschrijver","year":"2007","unstructured":"Deschrijver, G., Cornelis, C.: Representability in interval-valued fuzzy set theory. Int. J.\u00a015(3), 345\u2013361 (2007)","journal-title":"Int. J."},{"key":"11_CR14","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/S0165-0114(02)00127-6","volume":"133","author":"G. Deschrijver","year":"2003","unstructured":"Deschrijver, G., Kerre, E.E.: On the relation between some extensions of fuzzy set theory. Fuzzy Sets and Systems\u00a0133, 227\u2013235 (2003)","journal-title":"Fuzzy Sets and Systems"},{"key":"11_CR15","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1002\/(SICI)1098-111X(199610)11:10<733::AID-INT2>3.0.CO;2-#","volume":"11","author":"M. Gehrke","year":"1996","unstructured":"Gehrke, M., Walker, C., Walker, E.: De Morgan systems on the unit interval. Int. J. on Intelligent Systems\u00a011, 733\u2013750 (1996)","journal-title":"Int. J. on Intelligent Systems"},{"key":"11_CR16","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0022-247X(67)90189-8","volume":"18","author":"J. Goguen","year":"1967","unstructured":"Goguen, J.: L-fuzzy sets. Journal of Mathematics Analisys Applied\u00a018, 145\u2013167 (1967)","journal-title":"Journal of Mathematics Analisys Applied"},{"key":"11_CR17","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/S0165-0114(96)00135-2","volume":"90","author":"S. Jenei","year":"1997","unstructured":"Jenei, S.: A more efficient method for defining fuzzy connectives. Fuzzy Sets and Systems\u00a090, 25\u201335 (1997)","journal-title":"Fuzzy Sets and Systems"},{"key":"11_CR18","doi-asserted-by":"crossref","unstructured":"Jur\u00edo, A., Pagola, M., Mesiar, R., Beliakov, G., Bustince, H.: Image magnification using interval information. IEEE Trans. on Image Processing; doi:10.1109\/TIP.2011.2158227","DOI":"10.1109\/TIP.2011.2158227"},{"key":"11_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9540-7","volume-title":"Triangular Norms","author":"E.P. Klement","year":"2000","unstructured":"Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)"},{"key":"11_CR20","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/978-4-431-67907-3_2","volume-title":"Soft Computing and Human-Centered Machines","author":"S. Miyamoto","year":"2000","unstructured":"Miyamoto, S.: Multisets and fuzzy multisets. In: Liu, Z.-Q., Miyamoto, S. (eds.) Soft Computing and Human-Centered Machines, pp. 9\u201333. Springer, Berlin (2000)"},{"key":"11_CR21","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717716","volume-title":"Introduction to Interval Analysis","author":"R.E. Moore","year":"2009","unstructured":"Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)"},{"key":"11_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/978-3-540-73445-1_22","volume-title":"Logic, Language, Information and Computation","author":"R.H.S. Reiser","year":"2007","unstructured":"Reiser, R.H.S., Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N.: Interval Valued QL-Implications. In: Leivant, D., de Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol.\u00a04576, pp. 307\u2013321. Springer, Heidelberg (2007)"},{"key":"11_CR23","unstructured":"Sambuc, R.: Fonctions \u03c6-floues. Application \u00e1 l\u2019aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Universit\u00e9 de Marseille, France (1975)"},{"key":"11_CR24","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/BFb0073967","volume":"274","author":"D.S. Scott","year":"1972","unstructured":"Scott, D.S.: Continuous Lattices. Lecture Notes in Mathematics\u00a0274, 97\u2013136 (1972)","journal-title":"Lecture Notes in Mathematics"},{"key":"11_CR25","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1016\/j.camwa.2010.04.044","volume":"60","author":"Y. Shang","year":"2010","unstructured":"Shang, Y., Yuan, X., Lee, E.S.: The n-dimensional fuzzy sets and Zadeh fuzzy sets based on the finite valued fuzzy sets. Computers and Mathematics with Applications\u00a060, 442\u2013463 (2010)","journal-title":"Computers and Mathematics with Applications"},{"key":"11_CR26","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/03081078608934952","volume":"13","author":"R.R. Yager","year":"1986","unstructured":"Yager, R.R.: On the theory of bags. Int. J. General Systems\u00a013, 23\u201337 (1986)","journal-title":"Int. J. General Systems"},{"key":"11_CR27","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"L.A. Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Information and Control\u00a08, 338\u2013353 (1965)","journal-title":"Information and Control"},{"key":"11_CR28","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"6","author":"L.A. Zadeh","year":"1975","unstructured":"Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Information Sciences\u00a06, 199\u2013249 (1975)","journal-title":"Information Sciences"},{"key":"11_CR29","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.ins.2003.05.010","volume":"165","author":"W.R. Zhang","year":"2004","unstructured":"Zhang, W.R., Zhang, L.: Yin Yang bipolar logic and bipolar fuzzy logic. Information Sciences\u00a0165, 265\u2013287 (2004)","journal-title":"Information Sciences"}],"container-title":["Advances in Intelligent and Soft Computing","Eurofuse 2011"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-24001-0_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T20:19:53Z","timestamp":1554668393000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-24001-0_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642240003","9783642240010"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-24001-0_11","relation":{},"ISSN":["1867-5662","1867-5670"],"issn-type":[{"value":"1867-5662","type":"print"},{"value":"1867-5670","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}