{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:23:12Z","timestamp":1742912592197,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":41,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642391644"},{"type":"electronic","value":"9783642391651"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-39165-1_40","type":"book-chapter","created":{"date-parts":[[2013,6,20]],"date-time":"2013-06-20T07:25:29Z","timestamp":1371713129000},"page":"417-428","source":"Crossref","is-referenced-by-count":1,"title":["Implications Satisfying the Law of Importation with a Given T-norm"],"prefix":"10.1007","author":[{"given":"S.","family":"Massanet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Torrens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"20","key":"40_CR1","doi-asserted-by":"publisher","first-page":"3992","DOI":"10.1016\/j.ins.2010.06.023","volume":"180","author":"I. Aguil\u00f3","year":"2010","unstructured":"Aguil\u00f3, I., Su\u00f1er, J., Torrens, J.: A characterization of residual implications derived from left-continuous uninorms. Information Sciences\u00a0180(20), 3992\u20134005 (2010)","journal-title":"Information Sciences"},{"issue":"10","key":"40_CR2","doi-asserted-by":"publisher","first-page":"1406","DOI":"10.1016\/j.fss.2009.12.001","volume":"161","author":"M. Baczy\u0144ski","year":"2010","unstructured":"Baczy\u0144ski, M.: On the distributivity of fuzzy implications over continuous and archimedean triangular conorms. Fuzzy Sets and Systems\u00a0161(10), 1406\u20131419 (2010)","journal-title":"Fuzzy Sets and Systems"},{"issue":"17","key":"40_CR3","doi-asserted-by":"publisher","first-page":"2256","DOI":"10.1016\/j.fss.2010.03.005","volume":"161","author":"M. Baczy\u0144ski","year":"2010","unstructured":"Baczy\u0144ski, M.: On the distributivity of fuzzy implications over representable uninorms. Fuzzy Sets and Systems\u00a0161(17), 2256\u20132275 (2010)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR4","first-page":"157","volume":"43","author":"M. Baczy\u0144ski","year":"2007","unstructured":"Baczy\u0144ski, M., Jayaram, B.: Yager\u2019s classes of fuzzy implications: some properties and intersections. Kybernetika\u00a043, 157\u2013182 (2007)","journal-title":"Kybernetika"},{"key":"40_CR5","volume-title":"Fuzzy Implications","author":"M. Baczy\u0144ski","year":"2008","unstructured":"Baczy\u0144ski, M., Jayaram, B.: Fuzzy Implications. Springer, Heidelberg (2008)"},{"key":"40_CR6","doi-asserted-by":"publisher","first-page":"1836","DOI":"10.1016\/j.fss.2007.11.015","volume":"159","author":"M. Baczy\u0144ski","year":"2008","unstructured":"Baczy\u0144ski, M., Jayaram, B.: (S,N)- and R-implications: A state-of-the-art survey. Fuzzy Sets and Systems\u00a0159, 1836\u20131859 (2008)","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"40_CR7","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1109\/TFUZZ.2008.924201","volume":"17","author":"M. Baczy\u0144ski","year":"2009","unstructured":"Baczy\u0144ski, M., Jayaram, B.: On the distributivity of fuzzy implications over nilpotent or strict triangular conorms. Transactions on Fuzzy Systems\u00a017(3), 590\u2013603 (2009)","journal-title":"Transactions on Fuzzy Systems"},{"key":"40_CR8","doi-asserted-by":"publisher","first-page":"2049","DOI":"10.1016\/j.fss.2008.11.001","volume":"160","author":"M. Baczy\u0144ski","year":"2009","unstructured":"Baczy\u0144ski, M., Jayaram, B.: (U,N)-implications and their characterizations. Fuzzy Sets and Systems\u00a0160, 2049\u20132062 (2009)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR9","doi-asserted-by":"crossref","unstructured":"Baczy\u0144ski, M., Jayaram, B.: Intersections between some families of (U,N)- and RU-implications. Fuzzy Sets and Systems\u00a0167(1), 30\u201344 (2011); Special Issue: Aggregation techniques and applications Selected papers from AGOP 2009 dedicated to Jaume Casasnovas","DOI":"10.1016\/j.fss.2010.07.011"},{"key":"40_CR10","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1109\/TFUZZ.2004.825075","volume":"12","author":"J. Balasubramaniam","year":"2004","unstructured":"Balasubramaniam, J., Rao, C.: On the distributivity of implication operators over T and S norms. IEEE Transactions on Fuzzy Systems\u00a012, 194\u2013198 (2004)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"40_CR11","doi-asserted-by":"publisher","first-page":"3190","DOI":"10.1016\/j.ins.2005.06.006","volume":"176","author":"H. Bustince","year":"2006","unstructured":"Bustince, H., Mohedano, V., Barrenechea, E., Pagola, M.: Definition and construction of fuzzy DI-subsethood measures. Information Sciences\u00a0176, 3190\u20133231 (2006)","journal-title":"Information Sciences"},{"key":"40_CR12","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1016\/j.ins.2006.07.021","volume":"177","author":"H. Bustince","year":"2007","unstructured":"Bustince, H., Pagola, M., Barrenechea, E.: Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. Information Sciences\u00a0177, 906\u2013929 (2007)","journal-title":"Information Sciences"},{"issue":"1","key":"40_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/91.660804","volume":"6","author":"W. Combs","year":"1998","unstructured":"Combs, W., Andrews, J.: Combinatorial rule explosion eliminated by a fuzzy rule configuration. IEEE Transactions on Fuzzy Systems\u00a06(1), 1\u201311 (1998)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"40_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1648-2","volume-title":"Fuzzy Preference Modelling and Multicriteria Decision Support","author":"J.C. Fodor","year":"1994","unstructured":"Fodor, J.C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)"},{"key":"40_CR15","volume-title":"Treatise on Many-Valued Logic","author":"S. Gottwald","year":"2001","unstructured":"Gottwald, S.: Treatise on Many-Valued Logic. Research Studies Press, Baldock (2001)"},{"key":"40_CR16","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1109\/TFUZZ.2007.895969","volume":"16","author":"B. Jayaram","year":"2008","unstructured":"Jayaram, B.: On the law of importation (x\u2009\u2227\u2009y)\u2009\u2192\u2009z\u2009\u2261\u2009(x\u2009\u2192\u2009(y\u2009\u2192\u2009z)) in fuzzy logic. IEEE Transactions on Fuzzy Systems\u00a016, 130\u2013144 (2008)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"1","key":"40_CR17","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/j.ijar.2007.07.009","volume":"48","author":"B. Jayaram","year":"2008","unstructured":"Jayaram, B.: Rule reduction for efficient inferencing in similarity based reasoning. International Journal of Approximate Reasoning\u00a048(1), 156\u2013173 (2008)","journal-title":"International Journal of Approximate Reasoning"},{"key":"40_CR18","volume-title":"Fuzzy Set Theory and Approximate Reasoning","author":"E. Kerre","year":"2004","unstructured":"Kerre, E., Huang, C., Ruan, D.: Fuzzy Set Theory and Approximate Reasoning. Wu Han University Press, Wu Chang (2004)"},{"key":"40_CR19","series-title":"STUDFUZZ","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1847-5","volume-title":"Fuzzy techniques in image processing","author":"E. Kerre","year":"2000","unstructured":"Kerre, E., Nachtegael, M.: Fuzzy techniques in image processing. STUDFUZZ, vol.\u00a052. Springer, New York (2000)"},{"key":"40_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7","volume-title":"Triangular norms","author":"E. Klement","year":"2000","unstructured":"Klement, E., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)"},{"issue":"2","key":"40_CR21","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1016\/j.ijar.2008.04.002","volume":"49","author":"M. Mas","year":"2008","unstructured":"Mas, M., Monserrat, M., Torrens, J.: Modus ponens and modus tollens in discrete implications. Int. J. Approx. Reasoning\u00a049(2), 422\u2013435 (2008)","journal-title":"Int. J. Approx. Reasoning"},{"key":"40_CR22","doi-asserted-by":"publisher","first-page":"4208","DOI":"10.1016\/j.ins.2009.08.028","volume":"179","author":"M. Mas","year":"2009","unstructured":"Mas, M., Monserrat, M., Torrens, J.: The law of importation for discrete implications. Information Sciences\u00a0179, 4208\u20134218 (2009)","journal-title":"Information Sciences"},{"key":"40_CR23","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1016\/j.fss.2009.10.022","volume":"161","author":"M. Mas","year":"2010","unstructured":"Mas, M., Monserrat, M., Torrens, J.: A characterization of (U,N), RU, QL and D-implications derived from uninorms satisfying the law of importation. Fuzzy Sets and Systems\u00a0161, 1369\u20131387 (2010)","journal-title":"Fuzzy Sets and Systems"},{"issue":"6","key":"40_CR24","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1109\/TFUZZ.2007.896304","volume":"15","author":"M. Mas","year":"2007","unstructured":"Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Transactions on Fuzzy Systems\u00a015(6), 1107\u20131121 (2007)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"1","key":"40_CR25","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.fss.2010.12.012","volume":"168","author":"S. Massanet","year":"2011","unstructured":"Massanet, S., Torrens, J.: The law of importation versus the exchange principle on fuzzy implications. Fuzzy Sets and Systems\u00a0168(1), 47\u201369 (2011)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR26","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/j.ijar.2011.11.001","volume":"53","author":"S. Massanet","year":"2012","unstructured":"Massanet, S., Torrens, J.: Intersection of Yager\u2019s implications with QL and D-implications. International Journal of Approximate Reasoning\u00a053, 467\u2013479 (2012)","journal-title":"International Journal of Approximate Reasoning"},{"key":"40_CR27","series-title":"CCIS","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/978-3-642-31715-6_34","volume-title":"Advances in Computational Intelligence","author":"S. Massanet","year":"2012","unstructured":"Massanet, S., Torrens, J.: On a generalization of yager\u2019s implications. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part II. CCIS, vol.\u00a0298, pp. 315\u2013324. Springer, Heidelberg (2012)"},{"key":"40_CR28","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.fss.2012.01.018","volume":"205","author":"S. Massanet","year":"2012","unstructured":"Massanet, S., Torrens, J.: On some properties of threshold generated implications. Fuzzy Sets and Systems\u00a0205, 30\u201349 (2012)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2012.03.008","volume":"201","author":"S. Massanet","year":"2012","unstructured":"Massanet, S., Torrens, J.: On the characterization of Yager\u2019s implications. Information Sciences\u00a0201, 1\u201318 (2012)","journal-title":"Information Sciences"},{"key":"40_CR30","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.fss.2012.01.013","volume":"205","author":"S. Massanet","year":"2012","unstructured":"Massanet, S., Torrens, J.: Threshold generation method of construction of a new implication from two given ones. Fuzzy Sets and Systems\u00a0205, 50\u201375 (2012)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR31","doi-asserted-by":"crossref","unstructured":"Massanet, S., Torrens, J.: On the vertical threshold generation method of fuzzy implication and its properties. Fuzzy Sets and Systems (2013), doi:10.1016\/j.fss.2013.03.003","DOI":"10.1016\/j.fss.2013.03.003"},{"issue":"2","key":"40_CR32","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/S0165-0114(01)00032-X","volume":"126","author":"A.M. Radzikowska","year":"2002","unstructured":"Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems\u00a0126(2), 137\u2013155 (2002)","journal-title":"Fuzzy Sets and Systems"},{"volume-title":"Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications","year":"2000","key":"40_CR33","unstructured":"Ruan, D., Kerre, E.E. (eds.): Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications. Kluwer Academic Publishers, Norwell (2000)"},{"issue":"2","key":"40_CR34","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1109\/TFUZZ.2005.864087","volume":"14","author":"D. Ruiz-Aguilera","year":"2006","unstructured":"Ruiz-Aguilera, D., Torrens, J.: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm. IEEE Transactions on Fuzzy Systems\u00a014(2), 180\u2013190 (2006)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"40_CR35","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.fss.2006.08.008","volume":"158","author":"D. Ruiz-Aguilera","year":"2007","unstructured":"Ruiz-Aguilera, D., Torrens, J.: Distributivity of residual implications over conjunctive and disjunctive uninorms. Fuzzy Sets and Systems\u00a0158, 23\u201337 (2007)","journal-title":"Fuzzy Sets and Systems"},{"key":"40_CR36","series-title":"CCIS","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1007\/978-3-642-14055-6_55","volume-title":"Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods","author":"Y. Shi","year":"2010","unstructured":"Shi, Y., Van Gasse, B., Ruan, D., Kerre, E.: On a new class of implications in fuzzy logic. In: H\u00fcllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. CCIS, vol.\u00a080, pp. 525\u2013534. Springer, Heidelberg (2010)"},{"issue":"1","key":"40_CR37","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1109\/91.983281","volume":"10","author":"E. Trillas","year":"2002","unstructured":"Trillas, E., Alsina, C.: On the law [(p\u2009\u2227\u2009q)\u2009\u2192\u2009r]\u2009=\u2009[(p\u2009\u2192\u2009r)\u2009\u2228\u2009(q\u2009\u2192\u2009r)] in fuzzy logic. IEEE Transactions on Fuzzy Systems\u00a010(1), 84\u201388 (2002)","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"40_CR38","first-page":"259","volume":"98","author":"E. Trillas","year":"2004","unstructured":"Trillas, E., Alsina, C., Pradera, A.: On MPT-implication functions for fuzzy logic. Rev. R. Acad. Cien. Serie A. Mat.\u00a098, 259\u2013271 (2004)","journal-title":"Rev. R. Acad. Cien. Serie A. Mat."},{"key":"40_CR39","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1002\/int.20068","volume":"20","author":"E. Trillas","year":"2005","unstructured":"Trillas, E., Alsina, C., Renedo, E., Pradera, A.: On contra-symmetry and MPT condicionality in fuzzy logic. International Journal of Intelligent Systems\u00a020, 313\u2013326 (2005)","journal-title":"International Journal of Intelligent Systems"},{"key":"40_CR40","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1002\/(SICI)1098-111X(200007)15:7<647::AID-INT5>3.0.CO;2-T","volume":"15","author":"E. Trillas","year":"2000","unstructured":"Trillas, E., del Campo, C., Cubillo, S.: When QM-operators are implication functions and conditional fuzzy relations. International Journal of Intelligent Systems\u00a015, 647\u2013655 (2000)","journal-title":"International Journal of Intelligent Systems"},{"key":"40_CR41","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.ins.2005.03.003","volume":"173","author":"P. Yan","year":"2005","unstructured":"Yan, P., Chen, G.: Discovering a cover set of ARsi with hierarchy from quantitative databases. Information Sciences\u00a0173, 319\u2013336 (2005)","journal-title":"Information Sciences"}],"container-title":["Advances in Intelligent Systems and Computing","Aggregation Functions in Theory and in Practise"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-39165-1_40","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T14:40:13Z","timestamp":1676817613000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-39165-1_40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642391644","9783642391651"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-39165-1_40","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2013]]}}}