{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:17:49Z","timestamp":1759033069794},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2015,3,6]],"date-time":"2015-03-06T00:00:00Z","timestamp":1425600000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2015,8]]},"DOI":"10.1007\/s00500-015-1620-x","type":"journal-article","created":{"date-parts":[[2015,3,5]],"date-time":"2015-03-05T07:47:13Z","timestamp":1425541633000},"page":"2083-2094","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["On state residuated lattices"],"prefix":"10.1007","volume":"19","author":[{"given":"Pengfei","family":"He","sequence":"first","affiliation":[]},{"given":"Xiaolong","family":"Xin","sequence":"additional","affiliation":[]},{"given":"Yongwei","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,3,6]]},"reference":[{"key":"1620_CR1","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","volume":"88","author":"CC Chang","year":"1958","unstructured":"Chang CC (1958) Algebraic analysis of many-valued logic. Trans Am Math Soc 88:467\u2013490","journal-title":"Trans Am Math Soc"},{"key":"1620_CR2","unstructured":"Ciungu LC (2008) Bosbach and Rie\u010dan states on residuated lattices. J Appl Funct Anal 2:175\u2013188"},{"key":"1620_CR3","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s00500-010-0571-5","volume":"15","author":"LC Ciungu","year":"2011","unstructured":"Ciungu LC, Dvure\u010denskij A, Hy\u010dko M (2011) State $$BL$$ B L -algebras. Soft Comput 15:619\u2013634","journal-title":"Soft Comput"},{"key":"1620_CR4","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1023\/A:1012490620450","volume":"68","author":"A Dvure\u010denskij","year":"2001","unstructured":"Dvure\u010denskij A (2001) States on pseudo $$MV$$ M V -algebras. Stud Logica 68:301\u2013327","journal-title":"Stud Logica"},{"key":"1620_CR5","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.fss.2011.05.023","volume":"187","author":"A Dvure\u010denskij","year":"2012","unstructured":"Dvure\u010denskij A, Rachunek J, \u0160alounova D (2012) State operators on generalizations of fuzzy structures. Fuzzy Sets Syst 187:58\u201376","journal-title":"Fuzzy Sets Syst"},{"key":"1620_CR6","unstructured":"Flaminio T, Montagna F (2007) An algebraic approach to states on $$MV$$ M V -algebras. In: Nov\u00e1k V (ed) Fuzzy Logic 2, Proceedings of the 5th EUSFLAT conference, Sept 11\u201314, Ostrava, vol II, pp 201\u2013206"},{"key":"1620_CR7","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.ijar.2008.07.006","volume":"50","author":"T Flaminio","year":"2009","unstructured":"Flaminio T, Montagna F (2009) $$MV$$ M V -algebras with internal states and probabilistic fuzzy logic. Int J Approx Reason 50:138\u2013152","journal-title":"Int J Approx Reason"},{"key":"1620_CR8","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00500-003-0266-2","volume":"8","author":"G Georgescu","year":"2004","unstructured":"Georgescu G (2004) Bosbach states on fuzzy structures. Soft Comput 8:217\u2013230","journal-title":"Soft Comput"},{"key":"1620_CR9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511542725","volume-title":"Continuous lattices and domains","author":"G Gierz","year":"2003","unstructured":"Gierz G, Hofmann KH, Keimel K, Lawson JD, Mislove M, Scott DS (2003) Continuous lattices and domains. Cambridge University Press, Cambridge"},{"key":"1620_CR10","volume-title":"Lattice theory","author":"G Gr\u00e4tzer","year":"1979","unstructured":"Gr\u00e4tzer G (1979) Lattice theory. W H Freeman and Company, San Francisco"},{"key":"1620_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-5300-3","volume-title":"Metamathematics of fuzzy Logic. Trends in Logic-Studia Logica Library 4","author":"P H\u00e1jek","year":"1998","unstructured":"H\u00e1jek P (1998) Metamathematics of fuzzy Logic. Trends in Logic-Studia Logica Library 4. Kluwer Academic Publishers, Dordrecht"},{"key":"1620_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-0215-5","volume-title":"Non-classical logics and their applications to Fuzzy subsets","author":"U H\u00f6hle","year":"1995","unstructured":"H\u00f6hle U (1995) Commutative residuated l-monoids. In: H\u00f6hle U, Klement E (eds) Non-classical logics and their applications to Fuzzy subsets. Kluwer, Dordrecht"},{"key":"1620_CR13","unstructured":"Kowalski T, Ono H (2001) Residuated lattices: an algebraic glimpse at logic without contraction"},{"key":"1620_CR14","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1016\/j.fss.2006.06.015","volume":"157","author":"T Kroupa","year":"2006","unstructured":"Kroupa T (2006) Every state on semisimple $$MV$$ M V -algebra is integral. Fuzzy Sets Syst 157:2771\u20132782","journal-title":"Fuzzy Sets Syst"},{"key":"1620_CR15","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.ins.2012.07.046","volume":"220","author":"LZ Liu","year":"2013","unstructured":"Liu LZ (2013) On the existence of states on $$MTL$$ M T L -algebras. Inf Sci 220:559\u2013567","journal-title":"Inf Sci"},{"key":"1620_CR16","doi-asserted-by":"crossref","first-page":"5725","DOI":"10.1016\/j.ins.2007.07.014","volume":"177","author":"LZ Liu","year":"2007","unstructured":"Liu LZ, Li KT (2007) Boolean filters and positive implicative filters of residuated lattices. Inf Sci 177:5725\u20135738","journal-title":"Inf Sci"},{"key":"1620_CR17","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1007\/s00500-011-0701-8","volume":"15","author":"LZ Liu","year":"2011","unstructured":"Liu LZ, Zhang XY (2011) States on finite linearly ordered $$IMTL$$ I M T L -algebras. Soft Comput 15:2021\u20132028","journal-title":"Soft Comput"},{"key":"1620_CR18","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1007\/s00500-008-0276-1","volume":"12","author":"LZ Liu","year":"2008","unstructured":"Liu LZ, Zhang XY (2008) States on $$R_{0}$$ R 0 -algebras. Soft Comput 12:1099\u20131104","journal-title":"Soft Comput"},{"key":"1620_CR19","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.fss.2013.11.009","volume":"247","author":"ZM Ma","year":"2014","unstructured":"Ma ZM, Hu BQ (2014) Characterizations and new subclasses of $$I$$ I -filters in residuated lattices. Fuzzy Sets Syst 247:92\u2013107","journal-title":"Fuzzy Sets Syst"},{"key":"1620_CR20","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF01053035","volume":"55","author":"D Mundici","year":"1995","unstructured":"Mundici D (1995) Averaging the truth-value in \u0141ukasiewicz sentential logic. Stud Logica 55:113\u2013127","journal-title":"Stud Logica"},{"key":"1620_CR21","first-page":"11","volume":"53","author":"C Mure\u015fan","year":"2010","unstructured":"Mure\u015fan C (2010) Dense elements and classes of residuated lattices. Bull Math Soc Sci Math Roumanie 53:11\u201324","journal-title":"Bull Math Soc Sci Math Roumanie"},{"key":"1620_CR22","unstructured":"Piciu D (2007) Algebras of fuzzy logic. Ed. Universitaria, Craiova"},{"key":"1620_CR23","first-page":"3","volume":"4","author":"B Rie\u010dan","year":"2000","unstructured":"Rie\u010dan B (2000) On the probability on $$BL$$ B L -algebras. Acta Math Nitra 4:3\u201313","journal-title":"Acta Math Nitra"},{"key":"1620_CR24","first-page":"49","volume":"6","author":"E Turunen","year":"1999","unstructured":"Turunen E (1999) $$BL$$ B L -algebras of basic fuzzy logic. Mathw Soft Comput 6:49\u201361","journal-title":"Mathw Soft Comput"},{"key":"1620_CR25","unstructured":"Turunen E (1999) Mathematics behind fuzzy logic. Physica-Verlag, Heidelberg"},{"key":"1620_CR26","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s00500-007-0182-y","volume":"12","author":"E Turunen","year":"2008","unstructured":"Turunen E, Mertanen J (2008) States on semi-divisible residuated lattices. Soft Comput 12:353\u2013357","journal-title":"Soft Comput"},{"key":"1620_CR27","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","volume":"45","author":"M Ward","year":"1939","unstructured":"Ward M, Dilworth PR (1939) Residuated lattice. Trans Am Math Soc 45:335\u2013354","journal-title":"Trans Am Math Soc"},{"key":"1620_CR28","doi-asserted-by":"crossref","first-page":"589","DOI":"10.3233\/IFS-120752","volume":"26","author":"XH Zhang","year":"2014","unstructured":"Zhang XH, Zhou HJ, Mao XY (2014) $$IMTL(MV)$$ I M T L ( M V ) -filters and fuzzy $$IMTL(MV)$$ I M T L ( M V ) -filters of residuated lattices. J Intell Fuzzy Syst 26:589\u2013596","journal-title":"J Intell Fuzzy Syst"},{"key":"1620_CR29","volume-title":"Frames and continuous lattices","author":"CY Zheng","year":"2000","unstructured":"Zheng CY, Fan L, Cui HB (2000) Frames and continuous lattices. Capital Normal University Press, Beijing"},{"key":"1620_CR30","doi-asserted-by":"crossref","first-page":"3614","DOI":"10.1016\/j.ins.2010.05.034","volume":"180","author":"YQ Zhu","year":"2010","unstructured":"Zhu YQ, Xu Y (2010) On filter theory of residuated lattices. Inf Sci 180:3614\u20133632","journal-title":"Inf Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1620-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-015-1620-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1620-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,30]],"date-time":"2020-08-30T14:49:49Z","timestamp":1598798989000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-015-1620-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,6]]},"references-count":30,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2015,8]]}},"alternative-id":["1620"],"URL":"https:\/\/doi.org\/10.1007\/s00500-015-1620-x","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,6]]}}}