{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T12:28:57Z","timestamp":1748348937415,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":87,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662627976"},{"type":"electronic","value":"9783662627983"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-662-62798-3_4","type":"book-chapter","created":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T20:09:07Z","timestamp":1608149347000},"page":"123-251","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces"],"prefix":"10.1007","author":[{"given":"Arun","family":"Kumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,12,17]]},"reference":[{"key":"4_CR1","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s11225-008-9144-3","volume":"90","author":"A Avron","year":"2008","unstructured":"Avron, A., Konikowska, B.: Rough sets and 3-valued logics. Studia Logica 90, 69\u201392 (2008)","journal-title":"Studia Logica"},{"key":"4_CR2","volume-title":"Distributive Lattices","author":"R Balbes","year":"1974","unstructured":"Balbes, R., Dwinger, P.: Distributive Lattices. University of Missouri Press, Columbia (1974)"},{"key":"4_CR3","doi-asserted-by":"publisher","first-page":"213","DOI":"10.3233\/FI-1997-313401","volume":"31","author":"M Banerjee","year":"1997","unstructured":"Banerjee, M.: Rough sets and 3-valued \u0141ukasiewicz logic. Fundamenta Informaticae 31, 213\u2013220 (1997)","journal-title":"Fundamenta Informaticae"},{"issue":"3\u20134","key":"4_CR4","doi-asserted-by":"publisher","first-page":"211","DOI":"10.3233\/FI-1996-283401","volume":"28","author":"M Banerjee","year":"1996","unstructured":"Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informaticae 28(3\u20134), 211\u2013221 (1996)","journal-title":"Fundamenta Informaticae"},{"key":"4_CR5","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/978-3-642-18859-6_7","volume-title":"Rough-neuro Computing: Techniques for Computing with Words","author":"M Banerjee","year":"2004","unstructured":"Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-neuro Computing: Techniques for Computing with Words, pp. 157\u2013184. Springer, Berlin (2004). https:\/\/doi.org\/10.1007\/978-3-642-18859-6_7"},{"key":"4_CR6","doi-asserted-by":"publisher","unstructured":"Banerjee, M., Khan, M.: Propositional logics from rough set theory. In: Peters, J.F., Skowron, A., Duntsch, I., Grzyma\u0142a-Busse, J., Or\u0142owska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 1\u201325. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-71200-8_1","DOI":"10.1007\/978-3-540-71200-8_1"},{"key":"4_CR7","doi-asserted-by":"crossref","unstructured":"Bezhanishvili, G.: Varieties of monadic Heyting algebras. part I. Studia Logica 61(3), 367\u2013402 (1998)","DOI":"10.1023\/A:1005073905902"},{"key":"4_CR8","unstructured":"Bezhanishvili, N., de Jongh D.: Intuitionistic logic. Institute for Logic, Language and Computation (ILLC), University of Amsterdam PP-2006-25 (2006)"},{"key":"4_CR9","unstructured":"Birkhoff, G.: Lattice Theory. Colloquium Publications, vol. XXV, 3rd edn., American Mathematical Society, Providence (1995)"},{"key":"4_CR10","unstructured":"Blackburn, P., de\u00a0Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (1991)"},{"key":"4_CR11","volume-title":"\u0141ukasiewicz-Moisil Algebras","author":"V Boicescu","year":"1991","unstructured":"Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S.: \u0141ukasiewicz-Moisil Algebras. North-Holland, Amsterdam (1991)"},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S1571-0661(04)80705-9","volume":"82","author":"Z Bonikowski","year":"2003","unstructured":"Bonikowski, Z.: Algebraic structures of rough sets in representative approximation spaces. Electronic Notes Theoret. Comput. Sci. 82, 1\u201312 (2003)","journal-title":"Electronic Notes Theoret. Comput. Sci."},{"key":"4_CR13","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/S0020-0255(97)10046-9","volume":"107","author":"Z Bonikowski","year":"1998","unstructured":"Bonikowski, Z., Bryniariski, E., Skardowska, V.W.: Extension and intension in the rough set theory. Inf. Sci. 107, 149\u2013167 (1998)","journal-title":"Inf. Sci."},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3233\/FI-2013-892","volume":"127","author":"MK Chakraborty","year":"2013","unstructured":"Chakraborty, M.K., Banerjee, M.: Rough sets: some foundational issues. Fundamenta Informaticae 127, 1\u201315 (2013)","journal-title":"Fundamenta Informaticae"},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"670","DOI":"10.3792\/pja\/1195522292","volume":"41","author":"R Cignoli","year":"1965","unstructured":"Cignoli, R.: Boolean elements in \u0141ukasiewicz algebras. I. Proc. Japan Acad. 41, 670\u2013675 (1965)","journal-title":"I. Proc. Japan Acad."},{"issue":"3","key":"4_CR16","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1007\/BF01230621","volume":"23","author":"R Cignoli","year":"1986","unstructured":"Cignoli, R.: The class of Kleene algebras satisfying an interpolation property and Nelson algebras. Algebra Universalis 23(3), 262\u2013292 (1986)","journal-title":"Algebra Universalis"},{"key":"4_CR17","series-title":"LNAI","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-3-540-75939-3_5","volume-title":"Algebraic and Proof-theoretic Aspects of Non-classical Logics","author":"R Cignoli","year":"2007","unstructured":"Cignoli, R.: The algebras of \u0141ukasiewicz many-valued logic: a historical overview. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds.) Algebraic and Proof-theoretic Aspects of Non-classical Logics. LNAI, vol. 4460, pp. 69\u201383. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-75939-3_5"},{"key":"4_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-54756-0_1","volume-title":"Transactions on Rough Sets XVII","author":"D Ciucci","year":"2014","unstructured":"Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough sets. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XVII. LNCS, vol. 8375, pp. 1\u201332. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-54756-0_1"},{"issue":"1","key":"4_CR19","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1007\/BF01200492","volume":"34","author":"S Comer","year":"1995","unstructured":"Comer, S.: Perfect extensions of regular double Stone algebras. Algebra Universalis 34(1), 96\u2013109 (1995)","journal-title":"Algebra Universalis"},{"key":"4_CR20","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/11548669_15","volume-title":"Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing","author":"J-H Dai","year":"2005","unstructured":"Dai, J.-H.: Logic for rough sets with rough double stone algebraic semantics. In: Slezak, D., Wang, G., Szczuka, M., D\u00fcntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 141\u2013148. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11548669_15"},{"key":"4_CR21","doi-asserted-by":"crossref","unstructured":"Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press (2002)","DOI":"10.1017\/CBO9780511809088"},{"key":"4_CR22","doi-asserted-by":"publisher","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, E.: Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Inf. Sci. 176, 1829\u20131848 (2006)","journal-title":"Inf. Sci."},{"key":"4_CR23","unstructured":"Dunn, J.: The algebra of intensional logic. Doctoral dissertation, University of Pittsburgh (1966)"},{"key":"4_CR24","first-page":"331","volume-title":"Philosophical Perspectives","author":"J Dunn","year":"1994","unstructured":"Dunn, J.: Star and perp: two treatments of negation. In: Tomberlin, J. (ed.) Philosophical Perspectives, vol. 7, pp. 331\u2013357. Ridgeview Publishing Company, Atascadero, California (1994)"},{"key":"4_CR25","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF01061239","volume":"55","author":"J Dunn","year":"1995","unstructured":"Dunn, J.: Positive modal logic. Studia Logica 55, 301\u2013317 (1995)","journal-title":"Studia Logica"},{"key":"4_CR26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1515\/9783110876802.3","volume-title":"Negation: A Notion in Focus","author":"J Dunn","year":"1996","unstructured":"Dunn, J.: Generalised ortho negation. In: Wansing, H. (ed.) Negation: A Notion in Focus, pp. 3\u201326. Walter de Gruyter, Berlin (1996)"},{"key":"4_CR27","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-94-015-9309-0_2","volume-title":"What is Negation?","author":"J Dunn","year":"1999","unstructured":"Dunn, J.: A comparative study of various model-theoretic treatments of negation: a history of formal negations. In: Gabbay, D., Wansing, H. (eds.) What is Negation?, pp. 23\u201351. Kluwer Academic Publishers, Netherlands (1999)"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1026740726955","volume":"66","author":"J Dunn","year":"2000","unstructured":"Dunn, J.: Partiality and its dual. Studia Logica 66, 5\u201340 (2000)","journal-title":"Studia Logica"},{"key":"4_CR29","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s11225-005-8470-y","volume":"80","author":"J Dunn","year":"2005","unstructured":"Dunn, J.: Negation in the context of gaggle theory. Studia Logica 80, 235\u2013264 (2005)","journal-title":"Studia Logica"},{"key":"4_CR30","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/S0304-3975(96)00334-9","volume":"179","author":"I D\u00fcntsch","year":"1997","unstructured":"D\u00fcntsch, I.: A logic for rough sets. Theoret. Comput. Sci. 179, 427\u2013436 (1997)","journal-title":"Theoret. Comput. Sci."},{"issue":"1","key":"4_CR31","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s11225-011-9349-8","volume":"99","author":"I D\u00fcntsch","year":"2011","unstructured":"D\u00fcntsch, I., Or\u0142owska, E.: Discrete dualities for double Stone algebras. Studia Logica 99(1), 127\u2013142 (2011)","journal-title":"Studia Logica"},{"key":"4_CR32","unstructured":"Fidel, M.: An algebraic study of a propositional system of Nelson. In: Arruda, A.I., da Costa, N.C.A., Chuaqui, R. (eds.) Mathematical Logic: Proceedings of First Brazilian Conference, pp. 99\u2013117. Lecture Notes in Pure and Applied Mathematics, vol. 39, M.Dekker Inc., New York (1978)"},{"issue":"3","key":"4_CR33","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s11083-013-9311-7","volume":"31","author":"M Gehrke","year":"2014","unstructured":"Gehrke, M., van Gool, S.J.: Distributive envelopes and topological duality for lattices via canonical extensions. Order 31(3), 435\u2013461 (2014)","journal-title":"Order"},{"key":"4_CR34","unstructured":"Gehrke, M., Walker, E.: On the structure of rough sets. Bull. Polish Acad. Sci. Math. 40(3), 235\u2013255 (1992)"},{"key":"4_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-2217(00)00167-3","volume":"129","author":"S Greco","year":"2001","unstructured":"Greco, S., Matarazzo, B., S\u0142owinski, R.: Rough sets theory for multi-criteria decision analysis. Eur. J. Oper. Res. 129, 1\u201347 (2001)","journal-title":"Eur. J. Oper. Res."},{"key":"4_CR36","volume-title":"Handbook of Data Mining and Knowledge discovery","author":"S Greco","year":"2002","unstructured":"Greco, S., Matarazzo, B., Slowinski, R.: Multicriteria classification by dominance based rough set approach. In: Kloesgen, W., Zytkow, J. (eds.) Handbook of Data Mining and Knowledge discovery. Oxford University Press, New York (2002)"},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-642-05183-8_3","volume-title":"Advances in Intelligent Information Systems","author":"S Greco","year":"2010","unstructured":"Greco, S., Matarazzo, B., S\u0142owinski, R.: Algebra and topology for dominance-based rough set approach. In: Ras, Z., Tsay, L.S. (eds.) Advances in Intelligent Information Systems, pp. 43\u201378. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-05183-8_3"},{"key":"4_CR38","unstructured":"Iturrioz, L.: Rough sets and three-valued structures. In: Or\u0142owska, E. (ed.) Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa. Studies in Fuzziness and Soft Computing, vol. 24, pp. 596\u2013603. Springer, Heidelberg (1999)"},{"issue":"5","key":"4_CR39","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1007\/s11225-012-9421-z","volume":"101","author":"J J\u00e4rvinen","year":"2013","unstructured":"J\u00e4rvinen, J., Pagliani, P., Radeleczki, S.: Information completeness in Nelson algebras of rough sets induced by quasiorders. Studia Logica 101(5), 1073\u20131092 (2013)","journal-title":"Studia Logica"},{"key":"4_CR40","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1007\/s00012-011-0149-9","volume":"66","author":"J J\u00e4rvinen","year":"2011","unstructured":"J\u00e4rvinen, J., Radeleczki, S.: Representation of Nelson algebra by rough sets determined by quasiorder. Algebra Universalis 66, 163\u2013179 (2011)","journal-title":"Algebra Universalis"},{"issue":"6","key":"4_CR41","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1016\/j.ijar.2013.12.005","volume":"55","author":"J J\u00e4rvinen","year":"2014","unstructured":"J\u00e4rvinen, J., Radeleczki, S.: Rough sets determined by tolerances. Int. J. Approximate Reason. 55(6), 1419\u20131438 (2014)","journal-title":"Int. J. Approximate Reason."},{"key":"4_CR42","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s11083-009-9130-z","volume":"26","author":"J J\u00e4rvinen","year":"2009","unstructured":"J\u00e4rvinen, J., Radeleczki, S., Veres, L.: Rough sets determined by quasiorders. Order 26, 337\u2013355 (2009)","journal-title":"Order"},{"key":"4_CR43","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1090\/S0002-9947-1958-0095135-X","volume":"87","author":"J Kalman","year":"1958","unstructured":"Kalman, J.: Lattices with involution. Trans. Am. Math. Soc. 87, 485\u2013491 (1958)","journal-title":"Trans. Am. Math. Soc."},{"key":"4_CR44","first-page":"238","volume":"43","author":"T Katri\u0148\u00e1k","year":"1974","unstructured":"Katri\u0148\u00e1k, T.: Construction of regular double p-algebras. Bull. Soc. Roy. Sci. Liege 43, 238\u2013246 (1974)","journal-title":"Bull. Soc. Roy. Sci. Liege"},{"key":"4_CR45","doi-asserted-by":"crossref","unstructured":"Khan, M.A., Banerjee, M.: Logics for information systems and their dynamic extensions. ACM Trans. Comput. Logic 12(4), art. no. 29 (2011)","DOI":"10.1145\/1970398.1970405"},{"issue":"1","key":"4_CR46","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1016\/j.ijar.2013.07.007","volume":"55","author":"MA Khan","year":"2014","unstructured":"Khan, M.A., Banerjee, M., Rieke, R.: An update logic for information systems. Int. J. Approximate Reasoning 55(1), 436\u2013456 (2014)","journal-title":"Int. J. Approximate Reasoning"},{"key":"4_CR47","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1007\/BFb0029594","volume-title":"Mathematical Foundations of Computer Science 1990","author":"D Kozen","year":"1990","unstructured":"Kozen, D.: On kleene algebras and closed semirings. In: Rovan, B. (ed.) MFCS 1990. LNCS, vol. 452, pp. 26\u201347. Springer, Heidelberg (1990). https:\/\/doi.org\/10.1007\/BFb0029594"},{"key":"4_CR48","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1007\/978-3-642-31900-6_60","volume-title":"Rough Sets and Knowledge Technology","author":"A Kumar","year":"2012","unstructured":"Kumar, A., Banerjee, M.: Definable and rough sets in covering-based approximation spaces. In: Li, T., Nguyen, H., Wang, G., Grzyma\u0142a-Busse, J., Janicki, R., Hassanien, A., Yu, H. (eds.) Rough Sets and Knowledge Technology, pp. 488\u2013495. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-31900-6_60"},{"key":"4_CR49","doi-asserted-by":"publisher","first-page":"37","DOI":"10.3233\/FI-2015-1262","volume":"141","author":"A Kumar","year":"2015","unstructured":"Kumar, A., Banerjee, M.: Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae 141, 37\u201355 (2015)","journal-title":"Fundamenta Informaticae"},{"key":"4_CR50","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1007\/s11225-016-9696-6","volume":"105","author":"A Kumar","year":"2017","unstructured":"Kumar, A., Banerjee, M.: Kleene algebras and logic: boolean and rough set representations, 3-valued, rough set and perp semantics. Studia Logica 105, 439\u2013469 (2017)","journal-title":"Studia Logica"},{"key":"4_CR51","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/978-3-662-54069-5_11","volume-title":"ICLA 2017","author":"A Kumar","year":"2017","unstructured":"Kumar, A., Banerjee, M.: A semantic analysis of Stone and dual Stone negations with regularity. In: Ghosh, S., Prasad, S. (eds.) ICLA 2017, pp. 139\u2013153. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54069-5_11"},{"key":"4_CR52","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/11908029_20","volume-title":"RSCTC 2006","author":"TJ Li","year":"2006","unstructured":"Li, T.J.: Rough approximation operators in covering approximation spaces. In: Greco, S., et al. (eds.) RSCTC 2006, pp. 174\u2013182. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11908029_20"},{"key":"4_CR53","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s11083-011-9245-x","volume":"30","author":"EKR Nagarajan","year":"2013","unstructured":"Nagarajan, E.K.R., Umadevi, D.: A method of representing rough sets system determined by quasi orders. Order 30, 313\u2013337 (2013)","journal-title":"Order"},{"key":"4_CR54","doi-asserted-by":"publisher","first-page":"687","DOI":"10.2977\/prims\/1195189604","volume":"13","author":"H Ono","year":"1977","unstructured":"Ono, H.: On some intuitionistic modal logic. Publ. Inst. Math. Sci. Kyoto Univ. 13, 687\u2013722 (1977)","journal-title":"Publ. Inst. Math. Sci. Kyoto Univ."},{"issue":"4","key":"4_CR55","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1093\/jigpal\/jzi035","volume":"13","author":"E Or\u0142owska","year":"2005","unstructured":"Or\u0142owska, E., Rewitzky, I.: Duality via truth: semantic frameworks for lattice-based logics. Logic J. IGPL 13(4), 467\u2013490 (2005)","journal-title":"Logic J. IGPL"},{"issue":"1\u20133","key":"4_CR56","first-page":"275","volume":"81","author":"E Or\u0142owska","year":"2007","unstructured":"Or\u0142owska, E., Rewitzky, I.: Discrete duality for Heyting algebras with operators. Fundamenta Informaticae 81(1\u20133), 275\u2013295 (2007)","journal-title":"Fundamenta Informaticae"},{"key":"4_CR57","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/11734673_2","volume-title":"Relational Methods in Computer Science","author":"E Or\u0142owska","year":"2006","unstructured":"Or\u0142owska, E., Rewitzky, I., D\u00fcntsch, I.: Relational semantics through duality. In: MacCaull, W., Winter, M., D\u00fcntsch, I. (eds.) Relational Methods in Computer Science, pp. 17\u201332. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11734673_2"},{"issue":"2\u20133","key":"4_CR58","doi-asserted-by":"publisher","first-page":"205","DOI":"10.3233\/FI-1996-272308","volume":"27","author":"P Pagliani","year":"1996","unstructured":"Pagliani, P.: Rough sets and Nelson algebras. Fundamenta Informaticae 27(2\u20133), 205\u2013219 (1996)","journal-title":"Fundamenta Informaticae"},{"key":"4_CR59","doi-asserted-by":"publisher","unstructured":"Pagliani, P.: Rough set theory and logic-algebraic structures. In: Or\u0142owska, E. (ed.) Incomplete Information: Rough Set Analysis. Studies in Fuzziness and Soft Computing, vol. 13, pp. 109\u2013190. Springer, Heidelberg (1998). https:\/\/doi.org\/10.1007\/978-3-7908-1888-8_6","DOI":"10.1007\/978-3-7908-1888-8_6"},{"key":"4_CR60","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341\u2013356 (1982)","journal-title":"Int. J. Comput. Inf. Sci."},{"key":"4_CR61","doi-asserted-by":"crossref","unstructured":"Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers (1991)","DOI":"10.1007\/978-94-011-3534-4"},{"key":"4_CR62","unstructured":"Pomyka\u0142a, J., Pomyka\u0142a, J.A.: The Stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36, 495\u2013508 (1988)"},{"key":"4_CR63","unstructured":"Pomyka\u0142a, J.A.: Approximation, similarity and rough construction. ILLC prepublication series CT-93-07, University of Amsterdam (1993)"},{"key":"4_CR64","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/978-3-540-72458-2_4","volume-title":"Rough Sets and Knowledge Technology","author":"K Qin","year":"2007","unstructured":"Qin, K., Gao, Y., Pei, Z.: On covering rough sets. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M., Cercone, N.J., \u015aezak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 34\u201341. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-72458-2_4"},{"key":"4_CR65","unstructured":"Rasiowa, H.: An Algebraic Approach to Non-classical Logics. North-Holland (1974)"},{"issue":"6","key":"4_CR66","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1093\/jigpal\/8.6.853","volume":"8","author":"G Restall","year":"2000","unstructured":"Restall, G.: Defining double negation elimination. L. J. IGPL 8(6), 853\u2013860 (2000)","journal-title":"L. J. IGPL"},{"key":"4_CR67","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.ins.2014.06.004","volume":"282","author":"A Saha","year":"2014","unstructured":"Saha, A., Sen, J., Chakraborty, M.K.: Algebraic structures in the vicinity of pre-rough algebra and their logics. Inf. Sci. 282, 296\u2013320 (2014)","journal-title":"Inf. Sci."},{"key":"4_CR68","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.ins.2015.11.018","volume":"333","author":"A Saha","year":"2016","unstructured":"Saha, A., Sen, J., Chakraborty, M.K.: Algebraic structures in the vicinity of pre-rough algebra and their logics II. Inf. Sci. 333, 44\u201360 (2016)","journal-title":"Inf. Sci."},{"key":"4_CR69","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-3-642-21563-6_10","volume-title":"Transactions on Rough Sets XIV","author":"P Samanta","year":"2011","unstructured":"Samanta, P., Chakraborty, M.K.: Generalized rough sets and implication lattices. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets XIV. LNCS, vol. 6600, pp. 183\u2013201. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-21563-6_10"},{"key":"4_CR70","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/978-3-662-47815-8_8","volume-title":"Transactions on Rough Sets XIX","author":"P Samanta","year":"2015","unstructured":"Samanta, P., Chakraborty, M.K.: Interface of rough set systems and modal logics: a survey. In: Peters, J.F., Skowron, A., \u015al\u0229zak, D., Nguyen, H.S., Bazan, J.G. (eds.) Transactions on Rough Sets XIX. LNCS, vol. 8988, pp. 114\u2013137. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-47815-8_8"},{"key":"4_CR71","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1016\/j.dam.2007.08.050","volume":"156","author":"E Sanjuan","year":"2008","unstructured":"Sanjuan, E.: Heyting algebras with Boolean operators of rough sets and information retrieval applications. Discrete Appl. Math. 156, 967\u2013983 (2008)","journal-title":"Discrete Appl. Math."},{"issue":"2","key":"4_CR72","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/BF02770508","volume":"48","author":"N Suzuki","year":"1989","unstructured":"Suzuki, N.: An algebraic approach to intuitionistic modal logics in connection with intermediate predicate logics. Studia Logica 48(2), 141\u2013155 (1989)","journal-title":"Studia Logica"},{"key":"4_CR73","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/978-94-017-0452-6_4","volume-title":"Handbook of Philosophical Logic","author":"A Urquhart","year":"2001","unstructured":"Urquhart, A.: Basic many-valued logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 2, pp. 249\u2013295. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/978-94-017-0452-6_4"},{"key":"4_CR74","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/BF02121118","volume":"36","author":"D Vakarelov","year":"1977","unstructured":"Vakarelov, D.: Notes on N-lattices and constructive logic with strong negation. Studia Logica 36, 109\u2013125 (1977)","journal-title":"Studia Logica"},{"key":"4_CR75","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1007\/BF02945029","volume":"2","author":"J Varlet","year":"1972","unstructured":"Varlet, J.: A regular variety of type (2,2,1,1,0,0). Algebra Universalis 2, 218\u2013223 (1972)","journal-title":"Algebra Universalis"},{"key":"4_CR76","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/11847465_14","volume-title":"Transactions on Rough Sets V. LNCS","author":"Y Yao","year":"2006","unstructured":"Yao, Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 285\u2013305. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11847465_14"},{"key":"4_CR77","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/S0020-0255(98)10006-3","volume":"111","author":"Y Yao","year":"1998","unstructured":"Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 111, 239\u2013259 (1998)","journal-title":"Inf. Sci."},{"key":"4_CR78","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1007\/978-1-4471-0819-1_40","volume-title":"Advances in Soft Computing: Engineering Design and Manufacturing","author":"Y Yao","year":"1999","unstructured":"Yao, Y.: Granular computing using neighborhood system. In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing: Engineering Design and Manufacturing, pp. 539\u2013553. Springer, New York (1999). https:\/\/doi.org\/10.1007\/978-1-4471-0819-1_40"},{"key":"4_CR79","doi-asserted-by":"crossref","unstructured":"Yao, Y.: Rough sets, neighborhood system and granular computing. In: Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, pp. 1553\u20131558. IEEE Press (1999)","DOI":"10.1109\/CCECE.1999.804943"},{"issue":"1","key":"4_CR80","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1002\/1098-111X(200101)16:1<87::AID-INT7>3.0.CO;2-S","volume":"16","author":"Y Yao","year":"2001","unstructured":"Yao, Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16(1), 87\u2013104 (2001)","journal-title":"Int. J. Intell. Syst."},{"key":"4_CR81","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.: Covering based rough set approximations. Inf. Sci. 200, 91\u2013107 (2012)","journal-title":"Inf. Sci."},{"issue":"2","key":"4_CR82","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1080\/10798587.1996.10750660","volume":"2","author":"Y Yao","year":"1996","unstructured":"Yao, Y., Lin, T.: Generalization of rough sets using modal logic. Intell. Autom. Soft Comput. Int. J. 2(2), 103\u2013120 (1996)","journal-title":"Intell. Autom. Soft Comput. Int. J."},{"key":"4_CR83","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.ins.2012.10.018","volume":"225","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Luo, M.: Relationships between covering-based rough sets and relation based rough sets. Inf. Sci. 225, 55\u201371 (2013)","journal-title":"Inf. Sci."},{"key":"4_CR84","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1016\/j.ins.2013.12.035","volume":"269","author":"N Zhoua","year":"2014","unstructured":"Zhoua, N., Hua, B.: Rough sets based on complete completely distributive lattice. Inf. Sci. 269, 378\u2013387 (2014)","journal-title":"Inf. Sci."},{"key":"4_CR85","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, 1499\u20131508 (2007)","journal-title":"Inf. Sci."},{"key":"4_CR86","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/S0020-0255(03)00056-2","volume":"152","author":"W Zhu","year":"2003","unstructured":"Zhu, W., Wang, F.Y.: Reduction and axiomatization of covering generalized rough sets. Inf. Sci. 152, 217\u2013230 (2003)","journal-title":"Inf. Sci."},{"key":"4_CR87","doi-asserted-by":"crossref","unstructured":"Zhu, W., Wang, F.Y.: Relationship among three types of covering rough sets. In: Proceedings of IEEE International Conference on Granular Computing, pp. 43\u201348 (2006)","DOI":"10.1109\/GRC.2006.1635755"}],"container-title":["Lecture Notes in Computer Science","Transactions on Rough Sets XXII"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-62798-3_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T08:32:16Z","timestamp":1724056336000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-62798-3_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783662627976","9783662627983"],"references-count":87,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-62798-3_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"17 December 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}