{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:47:46Z","timestamp":1777427266517,"version":"3.51.4"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319257532","type":"print"},{"value":"9783319257549","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-25754-9_31","type":"book-chapter","created":{"date-parts":[[2015,11,21]],"date-time":"2015-11-21T09:12:37Z","timestamp":1448097157000},"page":"347-356","source":"Crossref","is-referenced-by-count":8,"title":["Formalizing Lattice-Theoretical Aspects of Rough and Fuzzy Sets"],"prefix":"10.1007","author":[{"given":"Adam","family":"Grabowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takashi","family":"Mitsuishi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"2\/3","key":"31_CR1","doi-asserted-by":"publisher","first-page":"109","DOI":"10.3233\/FI-1996-272302","volume":"27","author":"E Bryniarski","year":"1996","unstructured":"Bryniarski, E.: Formal conception of rough sets. Fundamenta Informaticae 27(2\/3), 109\u2013136 (1996)","journal-title":"Fundamenta Informaticae"},{"issue":"6","key":"31_CR2","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1080\/00207727808941724","volume":"9","author":"D Dubois","year":"1978","unstructured":"Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613\u2013626 (1978)","journal-title":"Int. J. Syst. Sci."},{"issue":"2\u20133","key":"31_CR3","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1080\/03081079008935107","volume":"17","author":"D Dubois","year":"1990","unstructured":"Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17(2\u20133), 191\u2013209 (1990)","journal-title":"Int. J. Gen. Syst."},{"key":"31_CR4","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.ins.2012.02.060","volume":"200","author":"AA Estaji","year":"2012","unstructured":"Estaji, A.A., Hooshmandasl, M.R., Davvaz, B.: Rough set theory applied to lattice theory. Inf. Sci. 200, 108\u2013122 (2012)","journal-title":"Inf. Sci."},{"issue":"1","key":"31_CR5","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/0022-247X(67)90189-8","volume":"18","author":"JA Goguen","year":"1967","unstructured":"Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 18(1), 145\u2013174 (1967)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"31_CR6","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s10817-015-9333-5","volume":"55","author":"A Grabowski","year":"2015","unstructured":"Grabowski, A.: Mechanizing complemented lattices within Mizar type system. J. Autom. Reasoning 55(3), 211\u2013221 (2015). doi:10.1007\/s10817-015-9333-5","journal-title":"J. Autom. Reasoning"},{"issue":"4","key":"31_CR7","doi-asserted-by":"publisher","first-page":"321","DOI":"10.2478\/forma-2014-0032","volume":"22","author":"A Grabowski","year":"2014","unstructured":"Grabowski, A.: The formal construction of fuzzy numbers. Formalized Math. 22(4), 321\u2013327 (2014)","journal-title":"Formalized Math."},{"key":"31_CR8","unstructured":"Grabowski, A.: On the computer certification of fuzzy numbers. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of Federated Conference on Computer Science and Information Systems, FedCSIS 2013, pp. 51\u201354 (2013)"},{"issue":"1\u20132","key":"31_CR9","doi-asserted-by":"publisher","first-page":"65","DOI":"10.3233\/FI-2013-933","volume":"128","author":"A Grabowski","year":"2013","unstructured":"Grabowski, A.: Automated discovery of properties of rough sets. Fundamenta Informaticae 128(1\u20132), 65\u201379 (2013)","journal-title":"Fundamenta Informaticae"},{"key":"31_CR10","series-title":"Advances in Soft Computing","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/3-540-32370-8_15","volume-title":"Monitoring, Security and Rescue Techniques in Multiagent Systems","author":"A Grabowski","year":"2005","unstructured":"Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-K\u0229plicz, B., Jankowski, A., Szczuka, M. (eds.) Monitoring, Security and Rescue Techniques in Multiagent Systems. Advances in Soft Computing, vol. 28, pp. 215\u2013226. Springer, Heidelberg (2005)"},{"key":"31_CR11","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-540-73451-2_17","volume-title":"Rough Sets and Intelligent Systems Paradigms","author":"A Grabowski","year":"2007","unstructured":"Grabowski, A., Jastrz\u0229bska, M.: Rough set theory from a math-assistant perspective. In: Kryszkiewicz, M., Peters, J.F., Rybi\u0144ski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 152\u2013161. Springer, Heidelberg (2007)"},{"issue":"2","key":"31_CR12","first-page":"153","volume":"3","author":"A Grabowski","year":"2010","unstructured":"Grabowski, A., Korni\u0142owicz, A., Naumowicz, A.: Mizar in a nutshell. J. Formalized Reasoning 3(2), 153\u2013245 (2010)","journal-title":"J. Formalized Reasoning"},{"key":"31_CR13","volume-title":"General Lattice Theory","author":"G Gr\u00e4tzer","year":"1998","unstructured":"Gr\u00e4tzer, G.: General Lattice Theory. Birkh\u00e4user, Boston (1998)"},{"key":"31_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1007\/978-3-540-71200-8_22","volume-title":"Transactions on Rough Sets VI","author":"J J\u00e4rvinen","year":"2007","unstructured":"J\u00e4rvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., D\u00fcntsch, I., Grzyma\u0142a-Busse, J.W., Or\u0142owska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400\u2013498. Springer, Heidelberg (2007)"},{"key":"31_CR15","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/S0165-0114(97)00061-4","volume":"101","author":"Y Kawahara","year":"1999","unstructured":"Kawahara, Y., Furusawa, H.: An algebraic formalization of fuzzy relations. Fuzzy Sets Syst. 101, 125\u2013135 (1999)","journal-title":"Fuzzy Sets Syst."},{"key":"31_CR16","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/S0165-0114(97)00138-3","volume":"91","author":"GJ Klir","year":"1997","unstructured":"Klir, G.J.: Fuzzy arithmetic with requisite constraints. Fuzzy Sets Syst. 91, 165\u2013175 (1997)","journal-title":"Fuzzy Sets Syst."},{"issue":"2","key":"31_CR17","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10817-012-9261-6","volume":"50","author":"A Korni\u0142owicz","year":"2013","unstructured":"Korni\u0142owicz, A.: On rewriting rules in Mizar. J. Autom. Reasoning 50(2), 203\u2013210 (2013)","journal-title":"J. Autom. Reasoning"},{"issue":"2","key":"31_CR18","first-page":"351","volume":"9","author":"T Mitsuishi","year":"2001","unstructured":"Mitsuishi, T., Endou, N., Shidama, Y.: The concept of fuzzy set and membership function and basic properties of fuzzy set operation. Formalized Math. 9(2), 351\u2013356 (2001)","journal-title":"Formalized Math."},{"issue":"1","key":"31_CR19","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/S0165-0114(02)00246-4","volume":"135","author":"R Moore","year":"2003","unstructured":"Moore, R., Lodwick, W.: Interval analysis and fuzzy set theory. Fuzzy Sets Syst. 135(1), 5\u20139 (2003)","journal-title":"Fuzzy Sets Syst."},{"key":"31_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-642-03359-9_5","volume-title":"Theorem Proving in Higher Order Logics","author":"A Naumowicz","year":"2009","unstructured":"Naumowicz, A., Korni\u0142owicz, A.: A brief overview of Mizar. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 67\u201372. Springer, Heidelberg (2009)"},{"key":"31_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3534-4","volume-title":"Rough Sets: Theoretical Aspects of Reasoning about Data","author":"Z Pawlak","year":"1991","unstructured":"Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)"},{"issue":"2","key":"31_CR22","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s10817-012-9267-0","volume":"50","author":"K Pak","year":"2013","unstructured":"Pak, K.: Methods of lemma extraction in natural deduction proofs. J. Autom. Reasoning 50(2), 217\u2013228 (2013)","journal-title":"J. Autom. Reasoning"},{"key":"31_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-642-14128-7_12","volume-title":"Intelligent Computer Mathematics","author":"J Urban","year":"2010","unstructured":"Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in mizar. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC 2010. LNCS, vol. 6167, pp. 132\u2013146. Springer, Heidelberg (2010)"},{"issue":"11","key":"31_CR24","first-page":"1408","volume":"55","author":"F Wiedijk","year":"2008","unstructured":"Wiedijk, F.: Formal proof - getting started. Not. AMS 55(11), 1408\u20131414 (2008)","journal-title":"Not. AMS"},{"issue":"4","key":"31_CR25","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/S0888-613X(96)00071-0","volume":"15","author":"YY Yao","year":"1996","unstructured":"Yao, Y.Y.: Two views of the rough set theory in finite universes. Int. J. Approximate Reasoning 15(4), 291\u2013317 (1996)","journal-title":"Int. J. Approximate Reasoning"},{"key":"31_CR26","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.ins.2012.02.065","volume":"200","author":"Y Yao","year":"2012","unstructured":"Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91\u2013107 (2012)","journal-title":"Inf. Sci."},{"issue":"3","key":"31_CR27","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"L Zadeh","year":"1965","unstructured":"Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338\u2013353 (1965)","journal-title":"Inf. Control"},{"issue":"22","key":"31_CR28","doi-asserted-by":"publisher","first-page":"4997","DOI":"10.1016\/j.ins.2007.05.037","volume":"177","author":"W Zhu","year":"2007","unstructured":"Zhu, W.: Generalized rough sets based on relations. Inf. Sci. 177(22), 4997\u20135011 (2007)","journal-title":"Inf. Sci."},{"issue":"6","key":"31_CR29","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1016\/j.ins.2006.06.009","volume":"177","author":"W Zhu","year":"2007","unstructured":"Zhu, W.: Topological approaches to covering rough sets. Inf. Sci. 177(6), 1499\u20131508 (2007)","journal-title":"Inf. Sci."}],"container-title":["Lecture Notes in Computer Science","Rough Sets and Knowledge Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-25754-9_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T16:07:07Z","timestamp":1729094827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-25754-9_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319257532","9783319257549"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-25754-9_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}