{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T22:57:51Z","timestamp":1762210671383,"version":"3.40.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"S1","license":[{"start":{"date-parts":[[2012,1,21]],"date-time":"2012-01-21T00:00:00Z","timestamp":1327104000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s00521-011-0801-5","type":"journal-article","created":{"date-parts":[[2012,1,20]],"date-time":"2012-01-20T05:31:16Z","timestamp":1327037476000},"page":"245-253","source":"Crossref","is-referenced-by-count":8,"title":["Rough ideals in lattices"],"prefix":"10.1007","volume":"21","author":[{"given":"Qimei","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingguo","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangnan","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,1,21]]},"reference":[{"key":"801_CR1","first-page":"251","volume":"42","author":"R Biswas","year":"1994","unstructured":"Biswas R, Nanda S (1994) Rough groups and rough subgroups. Bull Pol Acad Sci Math 42:251\u2013254","journal-title":"Bull Pol Acad Sci Math"},{"key":"801_CR2","first-page":"242","volume-title":"Rough sets, fuzzy sets and knowledge discovery","author":"Z Bonikowaski","year":"1995","unstructured":"Bonikowaski Z (1995) Algebraic structures of rough sets. In: Ziarko WP (ed) Rough sets, fuzzy sets and knowledge discovery, Springer, Berlin, pp 242\u2013247"},{"key":"801_CR3","first-page":"208","volume":"3135","author":"G Cattaneo","year":"2004","unstructured":"Cattaneo G, Ciucci D (2004) Algebraic structures for rough sets. LNCS 3135:208\u2013252","journal-title":"LNCS"},{"key":"801_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809088","volume-title":"Introduction to lattices and order","author":"BA Davey","year":"2002","unstructured":"Davey BA, Priestley HA (2002) Introduction to lattices and order. Cambridge University Press, Cambridge"},{"key":"801_CR5","doi-asserted-by":"crossref","first-page":"3658","DOI":"10.1016\/j.ins.2006.02.014","volume":"176","author":"B Davvaz","year":"2006","unstructured":"Davvaz B, Mahdavipour M (2006) Roughness in modules. Inf Sci 176:3658\u20133674","journal-title":"Inf Sci"},{"issue":"11","key":"801_CR6","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1007\/s00500-005-0031-9","volume":"10","author":"B Davvaz","year":"2006","unstructured":"Davvaz B (2006) A new view of approximations in Hv-groups. Soft Comput 10(11):1043\u20131046","journal-title":"Soft Comput"},{"key":"801_CR7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.ins.2003.10.001","volume":"164","author":"B Davvaz","year":"2004","unstructured":"Davvaz B (2004) Roughness in rings. Inf Sci 164:147\u2013163","journal-title":"Inf Sci"},{"key":"801_CR8","doi-asserted-by":"crossref","first-page":"2417","DOI":"10.1016\/j.ins.2005.10.001","volume":"176","author":"B Davvaz","year":"2006","unstructured":"Davvaz B (2006) Roughness based on fuzzy ideals. Inf Sci 176:2417\u20132437","journal-title":"Inf Sci"},{"key":"801_CR9","first-page":"471","volume":"15","author":"B Davvaz","year":"2009","unstructured":"Davvaz B (2009) Approximations in hyperrings. J Multiple-Valued Logic Soft Comput 15:471\u2013488","journal-title":"J Multiple-Valued Logic Soft Comput"},{"key":"801_CR10","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00500-007-0174-y","volume":"12","author":"B Davvaz","year":"2008","unstructured":"Davvaz B (2008) Approximations in n-ary algebraic systems. Soft Comput 12:409\u2013418","journal-title":"Soft Comput"},{"key":"801_CR11","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1016\/j.ins.2005.05.009","volume":"176","author":"C Degang","year":"2006","unstructured":"Degang C, Wenxiu Z, Yeung D, Tsang ECC (2006) Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf Sci 176:1829\u20131848","journal-title":"Inf Sci"},{"key":"801_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59830-2","volume-title":"Formal concept analysis","author":"B Ganter","year":"1999","unstructured":"Ganter B, Wille R (1999) Formal concept analysis. Springer, Berlin"},{"key":"801_CR13","first-page":"673","volume":"35","author":"T Iwinski","year":"1987","unstructured":"Iwinski T (1987) Algebraic approach to rough sets. Bull Pol Acad Sci Math 35:673\u2013683","journal-title":"Bull Pol Acad Sci Math"},{"key":"801_CR14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.3233\/FUN-2002-53203","volume":"53","author":"J J\u00e4rvinen","year":"2002","unstructured":"J\u00e4rvinen J (2002) On the structure of rough approximations. Fundamenta Informaticae 53:135\u2013153","journal-title":"Fundamenta Informaticae"},{"key":"801_CR15","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1016\/j.ins.2007.10.005","volume":"178","author":"O Kazanc\u0131","year":"2008","unstructured":"Kazanc\u0131 O, Davvaz B (2008) On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings. Inf Sci 178:1343\u20131354","journal-title":"Inf Sci"},{"key":"801_CR16","doi-asserted-by":"crossref","first-page":"2349","DOI":"10.1016\/j.ins.2008.01.006","volume":"178","author":"O Kazanc\u0131","year":"2008","unstructured":"Kazanc\u0131 O, Yamak S, Davvaz B (2008) The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets. Inf Sci 178:2349\u20132359","journal-title":"Inf Sci"},{"key":"801_CR17","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/0020-0255(95)00282-0","volume":"90","author":"N Kuroki","year":"1996","unstructured":"Kuroki N, Wang PP (1996) The lower and upper approximations in a fuzzy group. Inf Sci 90:203\u2013220","journal-title":"Inf Sci"},{"key":"801_CR18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0020-0255(96)00274-5","volume":"100","author":"N Kuroki","year":"1997","unstructured":"Kuroki N (1997) Rough ideals in semigroups. Inf Sci 100:139\u201363","journal-title":"Inf Sci"},{"key":"801_CR19","doi-asserted-by":"crossref","first-page":"4114","DOI":"10.1016\/j.ins.2008.06.019","volume":"178","author":"V Leoreanu-Fotea","year":"2008","unstructured":"Leoreanu-Fotea V, Davvaz B (2008) Roughness in n-ary hypergroups. Inf Sci 178:4114\u20134124","journal-title":"Inf Sci"},{"key":"801_CR20","doi-asserted-by":"crossref","first-page":"3605","DOI":"10.1016\/j.ins.2008.05.009","volume":"178","author":"V Leoreanu-Fotea","year":"2008","unstructured":"Leoreanu-Fotea V (2008) The lower and upper approximations in a hypergroup. Inf Sci 178:3605\u20133615","journal-title":"Inf Sci"},{"key":"801_CR21","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.1016\/j.ins.2007.11.010","volume":"178","author":"G Liu","year":"2008","unstructured":"Liu G (2008) Generalized rough sets over fuzzy lattices. Inf Sci 178:1651\u20131662","journal-title":"Inf Sci"},{"key":"801_CR22","doi-asserted-by":"crossref","first-page":"4105","DOI":"10.1016\/j.ins.2008.06.021","volume":"178","author":"G Liu","year":"2008","unstructured":"Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inf Sci 178:4105\u20134113","journal-title":"Inf Sci"},{"key":"801_CR23","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1016\/j.ins.2010.11.016","volume":"181","author":"A Mani","year":"2011","unstructured":"Mani A (2011) Choice inclusive general rough semantics. Inf Sci 181:1097\u20131115","journal-title":"Inf Sci"},{"key":"801_CR24","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/S0165-0114(00)00023-3","volume":"121","author":"N Mordeson","year":"2001","unstructured":"Mordeson N (2001) Rough set theory applied to (fuzzy) ideal theory. Fuzzy Sets Syst 121:315\u2013324","journal-title":"Fuzzy Sets Syst"},{"key":"801_CR25","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341\u2013356","journal-title":"Int J Comput Inf Sci"},{"key":"801_CR26","first-page":"495","volume":"36","author":"J Pomykala","year":"1998","unstructured":"Pomykala J, Pomykala JA (1998) The stone algebra of rough sets. Bull Pol Acad Sci Math 36:495\u2013508","journal-title":"Bull Pol Acad Sci Math"},{"key":"801_CR27","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0888-613X(96)00072-2","volume":"15","author":"L Polkowski","year":"1996","unstructured":"Polkowski L, Skowron A (1996) Rough mereology: a new paradigm for approximate reasoning. Int J Approx Reason 15:333\u2013365","journal-title":"Int J Approx Reason"},{"key":"801_CR28","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.ins.2004.12.010","volume":"176","author":"X Qimei","year":"2006","unstructured":"Qimei X, Zhenliang Z (2006) Rough prime ideals and rough fuzzy prime ideals in semigroups. Inf Sci 176:725\u2013733","journal-title":"Inf Sci"},{"key":"801_CR29","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1016\/j.ins.2009.11.008","volume":"180","author":"S Rasouli","year":"2010","unstructured":"Rasouli S, Davvaz B (2010) Roughness in MV-algebra. Inf Sci 180:737\u2013747","journal-title":"Inf Sci"},{"key":"801_CR30","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/S0020-0255(97)00078-9","volume":"104","author":"A Skowron","year":"1998","unstructured":"Skowron A, Polkowski L (1998) Rough mereological foundations for design, analysis, synthesis, and control in distributed systems. Inf Sci 104:129\u201356","journal-title":"Inf Sci"},{"key":"801_CR31","volume-title":"Theory and method of roughness","author":"Z Wenxiu","year":"2001","unstructured":"Wenxiu Z, Weizhi W (2001) Theory and method of roughness. Science Press, Beijing"},{"key":"801_CR32","doi-asserted-by":"crossref","first-page":"2641","DOI":"10.1016\/j.fss.2007.05.016","volume":"158","author":"C Xueyou","year":"2007","unstructured":"Xueyou C, Li Q (2007) Construction of rough approximations in fuzzy setting. Fuzzy Sets Syst 158:2641\u20132653","journal-title":"Fuzzy Sets Syst"},{"key":"801_CR33","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1016\/j.ins.2009.12.026","volume":"180","author":"S Yamak","year":"2010","unstructured":"Yamak S, Kazanc\u0131 O, Davvaz B (2010) Generalized lower and upper approximations in a ring. Inf Sci 180:1759\u20131768","journal-title":"Inf Sci"},{"key":"801_CR34","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10114-011-9465-4","volume":"27","author":"Y Yunqiang","year":"2011","unstructured":"Yunqiang Y, Jianming Z, Corsini P (2011) L-fuzzy roughness of n-ary polygroups. Acta Mathematica Sinica English Series 27:97\u2013118","journal-title":"Acta Mathematica Sinica English Series"},{"key":"801_CR35","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s00521-010-0465-6","volume":"20","author":"Y Yunqiang","year":"2011","unstructured":"Yunqiang Y, Jianming Z, Corsini P (2011) Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice. Neural Comput Appl 20:41\u201357","journal-title":"Neural Comput Appl"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-011-0801-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-011-0801-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-011-0801-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T00:19:19Z","timestamp":1742343559000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-011-0801-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,21]]},"references-count":35,"journal-issue":{"issue":"S1","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["801"],"URL":"https:\/\/doi.org\/10.1007\/s00521-011-0801-5","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"type":"print","value":"0941-0643"},{"type":"electronic","value":"1433-3058"}],"subject":[],"published":{"date-parts":[[2012,1,21]]}}}