{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:09:26Z","timestamp":1759032566597},"publisher-location":"Berlin, Heidelberg","reference-count":44,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642166280"},{"type":"electronic","value":"9783642166297"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-16629-7_4","type":"book-chapter","created":{"date-parts":[[2010,10,13]],"date-time":"2010-10-13T12:07:30Z","timestamp":1286971650000},"page":"57-82","source":"Crossref","is-referenced-by-count":3,"title":["Interval-Valued Algebras and Fuzzy Logics"],"prefix":"10.1007","author":[{"given":"Bart","family":"Van Gasse","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chris","family":"Cornelis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Glad","family":"Deschrijver","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.fss.2005.01.006","volume":"153","author":"C. Alcalde","year":"2005","unstructured":"Alcalde, C., Burusco, A., Fuentes-Gonz\u00e1lez, R.: A constructive method for the definition of interval-valued fuzzy implication operators. Fuzzy Sets and Systems\u00a0153, 211\u2013227 (2005)","journal-title":"Fuzzy Sets and Systems"},{"key":"4_CR2","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/S0888-613X(99)00045-6","volume":"23","author":"H. Bustince","year":"2000","unstructured":"Bustince, H.: Indicator of inclusion grade for interval-valued fuzzy sets. application to approximate reasoning based on interval-valued fuzzy sets. International Journal of Approximate Reasoning\u00a023, 137\u2013209 (2000)","journal-title":"International Journal of Approximate Reasoning"},{"issue":"2","key":"4_CR3","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","volume":"88","author":"C. Chang","year":"1958","unstructured":"Chang, C.: Algebraic analysis of many valued logics. Transactions of the American Mathematical Society\u00a088(2), 467\u2013490 (1958)","journal-title":"Transactions of the American Mathematical Society"},{"issue":"1","key":"4_CR4","first-page":"74","volume":"93","author":"C. Chang","year":"1959","unstructured":"Chang, C.: A new proof of the completeness of the lukasiewicz axioms. Transactions of the American Mathematical Society\u00a093(1), 74\u201380 (1959)","journal-title":"Transactions of the American Mathematical Society"},{"key":"4_CR5","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/s005000000044","volume":"4","author":"R. Cignoli","year":"2000","unstructured":"Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Computing\u00a04, 106\u2013112 (2000)","journal-title":"Soft Computing"},{"issue":"1","key":"4_CR6","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.apal.2009.01.012","volume":"160","author":"P. Cintula","year":"2009","unstructured":"Cintula, P., Esteva, F., Gispert, J., Godo, L., Montagna, F., Noguera, C.: Distinguished algebraic semantics for t-norm based fuzzy logics: methods and algebraic equivalencies. Annals of Pure and Applied Logic\u00a0160(1), 53\u201381 (2009)","journal-title":"Annals of Pure and Applied Logic"},{"key":"4_CR7","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.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning\u00a035, 55\u201395 (2004)","journal-title":"International Journal of Approximate Reasoning"},{"issue":"5","key":"4_CR8","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1016\/j.fss.2005.10.007","volume":"157","author":"C. Cornelis","year":"2006","unstructured":"Cornelis, C., Deschrijver, G., Kerre, E.: Advances and challenges in interval-valued fuzzy logic. Fuzzy Sets and Systems\u00a0157(5), 622\u2013627 (2006)","journal-title":"Fuzzy Sets and Systems"},{"key":"4_CR9","unstructured":"Deschrijver, G.: The \u0141ukasiewicz t-norm in interval-valued fuzzy and intuitionistic fuzzy set theory. In: Atanassov, K.T., Kacprzyk, J., Krawczak, M., Szmidt, E. (eds.) Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics, Akademicka Oficyna Wydawnicza EXIT, pp. 83\u2013101 (2005)"},{"key":"4_CR10","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1109\/TFUZZ.2003.822678","volume":"12","author":"G. Deschrijver","year":"2004","unstructured":"Deschrijver, G., Cornelis, C., Kerre, E.: On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Transactions on Fuzzy Systems\u00a012, 45\u201361 (2004)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"4_CR11","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1142\/S021848850300248X","volume":"11","author":"G. Deschrijver","year":"2003","unstructured":"Deschrijver, G., Kerre, E.: Classes of intuitionistic fuzzy t-norms satisfying the residuation principle. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems\u00a011, 691\u2013709 (2003)","journal-title":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"},{"key":"4_CR12","unstructured":"Dubois, D.: On ignorance and contradiction considered as truth values. Personal communication (2006)"},{"key":"4_CR13","unstructured":"Dubois, D., Prade, H.: Can we enforce full compositionality in uncertainty calculi? In: Proceedings of the 11th National Conference on Artificial Intelligence (AAAI 1994), Seattle, Washington, pp. 149\u2013154 (1994)"},{"issue":"2","key":"4_CR14","doi-asserted-by":"publisher","first-page":"97","DOI":"10.2307\/2964753","volume":"24","author":"M. Dummett","year":"1959","unstructured":"Dummett, M.: A propositional calculus with denumerable matrix. The Journal of Symbolic Logic\u00a024(2), 97\u2013106 (1959)","journal-title":"The Journal of Symbolic Logic"},{"issue":"1","key":"4_CR15","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1142\/S0218488594000055","volume":"2","author":"F. Esteva","year":"1994","unstructured":"Esteva, F., Garcia-Calv\u00e9s, P., Godo, L.: Enriched interval bilattices and partial many-valued logics: an approach to deal with graded truth and imprecision. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems\u00a02(1), 37\u201354 (1994)","journal-title":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/S0165-0114(01)00098-7","volume":"124","author":"F. Esteva","year":"2001","unstructured":"Esteva, F., Godo, L.: Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems\u00a0124, 271\u2013288 (2001)","journal-title":"Fuzzy Sets and Systems"},{"key":"4_CR17","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/978-3-7908-1769-0_11","volume-title":"Beyond Two: Theory and Applications of Multiple Valued Logic","author":"F. Esteva","year":"2003","unstructured":"Esteva, F., Godo, L., Garcia-Cerda\u00f1a, A.: On the hierarchy of t-norm based residuated fuzzy logics. In: Fitting, M., Orlowska, E. (eds.) Beyond Two: Theory and Applications of Multiple Valued Logic, pp. 251\u2013272. Physica-Verlag, Heidelberg (2003)"},{"issue":"2","key":"4_CR18","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/s11225-006-7196-9","volume":"82","author":"J. Font","year":"2006","unstructured":"Font, J.: Beyond rasiowa\u2019s algebraic approach to non-classical logics. Studia Logica.\u00a082(2), 172\u2013209 (2006)","journal-title":"Studia Logica."},{"key":"4_CR19","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1023\/A:1024621922509","volume":"74","author":"J. Font","year":"2003","unstructured":"Font, J., Jansana, R., Pigozzi, D.: A survey of abstract algebraic logic. Studia Logica.\u00a074, 13\u201379 (2003)","journal-title":"Studia Logica."},{"key":"4_CR20","first-page":"5","volume":"8","author":"J. Font","year":"1984","unstructured":"Font, J., Rodriguez, A., Torrens, A.: Wajsberg algebras. Stochastica\u00a08, 5\u201331 (1984)","journal-title":"Stochastica"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1002\/(SICI)1098-111X(199610)11:10<751::AID-INT3>3.3.CO;2-N","volume":"11","author":"M. Gehrke","year":"1996","unstructured":"Gehrke, M., Walker, C., Walker, E.: Some comments on interval-valued fuzzy sets. International Journal of Intelligent Systems\u00a011, 751\u2013759 (1996)","journal-title":"International Journal of Intelligent Systems"},{"key":"4_CR22","unstructured":"G\u00f6del, K.: Zum intuitionistischen aussagenkalk\u00fcl. In: Anzeiger der Akademie der Wissenschaften in Wien, pp. 65\u201366 (1932)"},{"key":"4_CR23","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.ins.2005.02.004","volume":"172","author":"S. Gottwald","year":"2005","unstructured":"Gottwald, S.: Mathematical fuzzy logic as a tool for the treatment of vague information. Information Sciences\u00a0172, 41\u201371 (2005)","journal-title":"Information Sciences"},{"key":"4_CR24","volume-title":"Trends in Logic\u2014Studia Logica Library","author":"P. H\u00e1jek","year":"1998","unstructured":"H\u00e1jek, P.: Metamathematics of Fuzzy Logic. In: Trends in Logic\u2014Studia Logica Library. Kluwer Academic Publishers, Dordrecht (1998)"},{"key":"4_CR25","unstructured":"Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der preuszischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 42\u201356, 57\u201371, 158\u2013169 (1930)"},{"key":"4_CR26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/978-94-011-0215-5_5","volume-title":"Non-classical Logics and their Applications to Fuzzy Subsets: a Handbook of the Mathematical Foundations of Fuzzy Set Theory","author":"U. H\u00f6hle","year":"1995","unstructured":"H\u00f6hle, U.: Commutative, residuated l-monoids. In: H\u00f6hle, U., Klement, E. (eds.) Non-classical Logics and their Applications to Fuzzy Subsets: a Handbook of the Mathematical Foundations of Fuzzy Set Theory, pp. 53\u2013106. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"4_CR27","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1090\/S0002-9947-1904-1500675-4","volume":"5","author":"E. Huntington","year":"1904","unstructured":"Huntington, E.: Sets of independent postulates for the algebra of logic. Transactions of the American Mathematical Society\u00a05, 288\u2013309 (1904)","journal-title":"Transactions of the American Mathematical Society"},{"key":"4_CR28","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":"4_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1015122331293","volume":"70","author":"S. Jenei","year":"2002","unstructured":"Jenei, S., Montagna, F.: A proof of standard completeness for Esteva and Godo\u2019s logic MTL. Studia Logica.\u00a070, 1\u201310 (2002)","journal-title":"Studia Logica."},{"key":"4_CR30","unstructured":"\u0141ukasiewicz, J., Tarski, A.: Untersuchungen \u00fcber den Aussagenkalk\u00fcl. Comptes Rendus de la Soci\u00e9t\u00e9 des Sciences et des Lettres de Varsovie, 1\u201321 (1930)"},{"key":"4_CR31","first-page":"113","volume":"9","author":"M. Ohnishi","year":"1957","unstructured":"Ohnishi, M., Matsumoto, K.: Gentzen method in modal calculi, part I. Osaka Mathematical Journal\u00a09, 113\u2013130 (1957)","journal-title":"Osaka Mathematical Journal"},{"key":"4_CR32","first-page":"115","volume":"11","author":"M. Ohnishi","year":"1959","unstructured":"Ohnishi, M., Matsumoto, K.: Gentzen method in modal calculi, part II. Osaka Mathematical Journal\u00a011, 115\u2013120 (1959)","journal-title":"Osaka Mathematical Journal"},{"key":"4_CR33","unstructured":"Rasiowa, H.: An algebraic approach to non-classical logics. Studies in Logic and the Foundations of Mathematics\u00a078 (1974)"},{"key":"4_CR34","volume-title":"Mathematical Logic","author":"J. Shoenfield","year":"1967","unstructured":"Shoenfield, J.: Mathematical Logic. Addison-Wesley, Reading (1967)"},{"key":"4_CR35","volume-title":"Mathematics behind Fuzzy Logic","author":"E. Turunen","year":"1999","unstructured":"Turunen, E.: Mathematics behind Fuzzy Logic. Physica-Verlag, Heidelberg (1999)"},{"key":"4_CR36","doi-asserted-by":"crossref","unstructured":"Van Gasse, B.: Interval-valued algebras and fuzzy logics. Ph. D. Thesis, Ghent University, Belgium (2010)","DOI":"10.1007\/978-3-642-16629-7_4"},{"issue":"16","key":"4_CR37","doi-asserted-by":"publisher","first-page":"3006","DOI":"10.1016\/j.ins.2010.04.010","volume":"180","author":"B. Gasse Van","year":"2010","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: Filters of residuated lattices and triangle algebras. Information Sciences\u00a0180(16), 3006\u20133020 (2010)","journal-title":"Information Sciences"},{"key":"4_CR38","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: The standard completeness of interval-valued monoidal t-norm based logic (submitted)"},{"key":"4_CR39","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/11908029_14","volume-title":"Rough Sets and Current Trends in Computing","author":"B. Van Gasse","year":"2006","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: Triangle algebras: towards an axiomatization of interval-valued residuated lattices. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., S\u0142owi\u0144ski, R. (eds.) RSCTC 2006. LNCS (LNAI), vol.\u00a04259, pp. 117\u2013126. Springer, Heidelberg (2006)"},{"key":"4_CR40","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/j.ijar.2008.04.006","volume":"49","author":"B. Van Gasse","year":"2008","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: A characterization of interval-valued residuated lattices. International Journal of Approximate Reasoning\u00a049, 478\u2013487 (2008)","journal-title":"International Journal of Approximate Reasoning"},{"key":"4_CR41","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1016\/j.fss.2007.09.003","volume":"159","author":"B. Van Gasse","year":"2008","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: Triangle algebras: A formal logic approach to interval-valued residuated lattices. Fuzzy Sets and Systems\u00a0159, 1042\u20131060 (2008)","journal-title":"Fuzzy Sets and Systems"},{"key":"4_CR42","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1016\/j.ins.2008.11.005","volume":"179","author":"B. Van Gasse","year":"2009","unstructured":"Van Gasse, B., Cornelis, C., Deschrijver, G., Kerre, E.: The pseudo-linear semantics of interval-valued fuzzy logics. Information Sciences\u00a0179, 717\u2013728 (2009)","journal-title":"Information Sciences"},{"key":"4_CR43","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"8","author":"L. Zadeh","year":"1975","unstructured":"Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning - i. Information Sciences\u00a08, 199\u2013249 (1975)","journal-title":"Information Sciences"},{"key":"4_CR44","unstructured":"Zalta, E.: Basic concepts in modal logic (1995), http:\/\/mally.stanford.edu\/notes.pdf"}],"container-title":["Studies in Fuzziness and Soft Computing","35 Years of Fuzzy Set Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-16629-7_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T12:21:35Z","timestamp":1559737295000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-16629-7_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642166280","9783642166297"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-16629-7_4","relation":{},"ISSN":["1434-9922","1860-0808"],"issn-type":[{"type":"print","value":"1434-9922"},{"type":"electronic","value":"1860-0808"}],"subject":[],"published":{"date-parts":[[2010]]}}}