Granular knowledge and rational approximation in general rough sets – I

References

• Abo-Tabl, A. (2011). A comparison of two kinds of definitions of rough approximations based on a similarity relation. Information Sciences, 181(12), 2587–2596. https://doi.org/10.1016/j.ins.2011.01.007
   Web of Science ®Google Scholar
• Al-shami, T. M., & Ciucci, D. (2022). Subset neighbourhood rough sets. Knowledge-Based Systems, 237, 107868. https://doi.org/10.1016/j.knosys.2021.107868
   Web of Science ®Google Scholar
• Allam, A., Bakeir, M., & Abo-Tabl, E. (2006). New approach for closure spaces by relations. Acta Mathematica Academiae Paedagogicae Nyiregyháziensis, 22, 285–304.
   Google Scholar
• Allam, A., Bakeir, M. Y., & Abo-Tabl, E. A. (2008). Some methods for generating topologies by relations. The Bulletin of the Malaysian Mathematical Society Series, 31(2), 35–45.
   Google Scholar
• Atef, M., Khalil, A., Li, S., Azzam, A., & Atik, A. E. (2020). Comparison of six types of rough approximations based on J-Neighborhood space and J-Adhesion neighborhood space. Journal of Intelligent Fuzzy Systems, 39(3), 4515–4531. https://doi.org/10.3233/JIFS-200482
   Web of Science ®Google Scholar
• Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
   Web of Science ®Google Scholar
• Banerjee, M., & Chakraborty, M. K. (2004). Algebras from rough sets – An overview. In S. K. Pal, L. Polkowski, & A. Skowron (Eds.), Rough-neural computing (pp. 157–184). Springer Verlag.
   Google Scholar
• Banerjee, M., & Khan, M. A. (2007). Propositional logics for rough set theory. In Transactions on rough sets VI, LNCS 4374 (pp. 1–25). Springer Verlag.
   Google Scholar
• Burkhardt, H., Seibt, J., Imaguire, G., & Gerogiorgakis, S. (2017). Handbook of mereology. Philosophia Verlag.
   Google Scholar
• Burmeister, P. (1986). A model-theoretic oriented approach to partial algebras. Akademie-Verlag.
   Google Scholar
• Cattaneo, G. (1998). Abstract approximation spaces for rough set theory. In L. Polkowski, & A. Skowron (Eds.), Rough sets in knowledge discovery 2 (pp. 59–98). Physica Heidelberg.
   Google Scholar
• Cattaneo, G., & Ciucci, D. (2004). Algebras for rough sets and fuzzy logics. Transactions on Rough Sets, 2(LNCS 3100), 208–252.
   Google Scholar
• Cattaneo, G., & Ciucci, D. (2018). Algebraic methods for orthopairs and induced rough approximation spaces. In A. Mani, I. Düntsch, & G. Cattaneo (Eds.), Algebraic methods in general rough sets (pp. 553–640). Birkhauser Basel.
   Google Scholar
• Chajda, I., Niederle, J., & Zelinka, B. (1976). On existence conditions for compatible tolerances. Czechoslovak Mathematical Journal, 26, 304–311. https://doi.org/10.21136/CMJ
   Web of Science ®Google Scholar
• Chakraborty, M. K. (2016). On some issues in the foundation of rough sets: The problem of definition. Fundamenta Informaticae, 148, 123–132. https://doi.org/10.3233/FI-2016-1426
   Web of Science ®Google Scholar
• Chen, J., van Ditmarsch, H., Greco, G., & Tzimoulis, A. (2021). Neighbourhood semantics for graded modal logic. arXiv 2105.09202.
   Google Scholar
• Ciucci, D., Dubois, D., & Prade, H. (2012). Oppositions in rough set theory. In T. Li, H. S. Nguyen, G. Wang, J. Grzymala-Busse, R. Janicki, A. E. Hassanien, & H. Yu (Eds.), Rough sets and knowledge technology RSKT'2012, LNAI 7414 (pp. 504–513). Springer-Verlag.
   Google Scholar
• Cotnoir, A. J., & Varzi, A. (2021). Mereology. Oxford University Press.
   Google Scholar
• Duda, J., & Chajda, I. (1977). Ideals of binary relational systems. Casopis Pro Pestovani Matematiki, 102(3), 280–291.
   Google Scholar
• Dujmovic, J. (2018). Soft computing evaluation logic. Wiley.
   Google Scholar
• Düntsch, I., & Orłowska, E. (2011). Discrete dualities for double stone algebras. Studia Logica, 99(1), 127–142. https://doi.org/10.1007/s11225-011-9349-8
   Web of Science ®Google Scholar
• Felisiak, P. A., Qin, K., & Li, G. (2020). Generalized multiset theory. Fuzzy Sets and Systems, 380, 104–130. https://doi.org/10.1016/j.fss.2019.05.015
   Web of Science ®Google Scholar
• Freese, R., Mckenzie, R., McNulty, G., & Taylor, W. (2022). Algebra lattices, varieties: Volume 2 (1st ed.). AMS.
   Google Scholar
• Godoy, D., & Tommasel, A. (2021). Is my model biased? Exploring unintended bias in misogyny detection tasks. In Ceur workshop proceedings (Vol. 2942, pp. 97–111). RWTH Aachen University.
   Google Scholar
• Grzegorczyk, A. (1955). The systems of Lesniewski in relation to contemporary logical research. Studia Logica, 3, 77–95. https://doi.org/10.1007/BF02067248
   Google Scholar
• Gumm, H., & Ursini, A. (1984). Ideals in universal algebras. Algebra Universalis, 19, 45–54. https://doi.org/10.1007/BF01191491
   Web of Science ®Google Scholar
• Jacobs, G. M., Renandya, W. A., & Power, A. (2016). Simple, powerful strategies for student centered learning. Springer Nature.
   Google Scholar
• Janicki, R., & Le, D. T. (2007). Towards a pragmatic mereology. Fundamenta Informaticae, 75(1-4), 295–314.
   Web of Science ®Google Scholar
• Järvinen, J., Pagliani, P., & Radeleczki, S. (2012). Information completeness in Nelson algebras of rough sets induced by quasiorders. Studia Logica, 101, 1073–1092. https://doi.org/10.1007/s11225-012-9421-z
   Web of Science ®Google Scholar
• Järvinen, J., & Radeleczki, S. (2017). Representing regular pseudocomplemented Kleene algebras by tolerance-based rough sets. Journal of The Australian Mathematical Society, 105(1), 1–22.
   Web of Science ®Google Scholar
• Kandil, A., Yakout, M., & Zakaria, A. (2016). New approaches of rough sets via ideals. In S. J. John (Ed.), Handbook of research on generalized and hybrid set structures and applications for soft computing (pp. 247–264). IGI Global.
   Google Scholar
• Kolodny, N., & Brunero, J. (2020). Instrumental rationality. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. Stanford University.
   Google Scholar
• Lewis, D. K. (1991). Parts of classes. Basil Blackwell.
   Google Scholar
• Lin, T. Y. (2009). Granular computing-1: The concept of granulation and its formal model. International Journal of Granular Computing, Rough Sets and Int Systems, 1(1), 21–42.
   Google Scholar
• Lin, T., & Liu, Q. (1994). Rough approximate operators: Axiomatic rough set theory. In W. Ziarko (Ed.), Rough sets, fuzzy sets and knowledge discovery (pp. 256–260). Springer.
   Google Scholar
• Liu, G. (2006). The axiomatization of the rough set upper approximation operations. Fundamenta Informaticae, 69(23), 331–342.
   Google Scholar
• Ljapin, E. S. (1996). Partial algebras and their applications. Academic, Kluwer.
   Google Scholar
• Maffezioli, P., & Varzi, A. (2021). Intuitionist mereology. Synthese, 198(S4), 277–302.
   Google Scholar
• Mani, A. (2005). Super rough semantics. Fundamenta Informaticae, 65(3), 249–261.
   Web of Science ®Google Scholar
• Mani, A. (2009). Algebraic semantics of similarity-based Bitten rough set theory. Fundamenta Informaticae, 97(1–2), 177–197. https://doi.org/10.3233/FI-2009-196
   Web of Science ®Google Scholar
• Mani, A. (2011). Choice inclusive general rough semantics. Information Sciences, 181(6), 1097–1115. https://doi.org/10.1016/j.ins.2010.11.016
   Web of Science ®Google Scholar
• Mani, A. (2012). Dialectics of counting and the mathematics of vagueness. Transactions on Rough Sets, 15(LNCS 7255), 122–180. https://doi.org/10.1007/978-3-642-31903-7
   Google Scholar
• Mani, A. (2013). Approximation dialectics of proto-transitive rough sets. In M. K. Chakraborty, A. Skowron, & S. Kar (Eds.), Facets of uncertainties and applications (pp. 99–109). Springer.
   Google Scholar
• Mani, A. (2014). Ontology, rough Y-systems and dependence. International Journal of Computer Science and Applications, 11(2), 114–136. Special Issue of IJCSA on Computational Intelligence.
   Google Scholar
• Mani, A. (2015). Antichain based semantics for rough sets. In D. Ciucci, G. Wang, S. Mitra, & W. Wu (Eds.), 2015 Rough sets and knowledge technology (pp. 319–330). Springer-Verlag.
   Google Scholar
• Mani, A. (2016). Algebraic semantics of proto-transitive rough sets. Transactions on Rough Sets, 20(LNCS 10020), 51–108. https://doi.org/10.1007/978-3-662-53611-7
   Google Scholar
• Mani, A. (2017a). Generalized ideals and co-granular rough sets. In L. Polkowski, Y. Yao, P. Artiemjew, D. Ciucci, D. Liu, D. Slezak, & B. Zielosko (Eds.), Rough sets, Part 2, IJCRS, 2017 (pp. 23–42). Springer International.
   Google Scholar
• Mani, A. (2017b). Knowledge and consequence in AC semantics for general rough sets. In G. Wang, A. Skowron, Y. Yao, D. Slezak, & L. Polkowski (Eds.), Thriving rough sets (Vol. 708, pp. 237–268). Springer International.
   Google Scholar
• Mani, A. (2018a). Algebraic methods for granular rough sets. In A. Mani, I. Düntsch, & G. Cattaneo (Eds.), Algebraic methods in general rough sets (pp. 157–336). Birkhauser Basel.
   Google Scholar
• Mani, A. (2018b). Dialectical rough sets, parthood and figures of opposition-I. Transactions on Rough Sets, 21(LNCS 10810), 96–141.
   Google Scholar
• Mani, A. (2018c). Representation, duality and beyond. In A. Mani, I. Düntsch, & G. Cattaneo (Eds.), Algebraic methods in general rough sets (pp. 459–552). Birkhauser Basel.
   Google Scholar
• Mani, A. (2020a). Comparative approaches to granularity in general rough sets. In R. Bello, D. Miao, R. Falcon, M. Nakata, A. Rosete, & D. Ciucci (Eds.), IJCRS 2020 Rough sets (Vol. 12179, pp. 500–518). Springer.
   Google Scholar
• Mani, A. (2020b). Towards student centric rough concept inventories. In R. Bello, D. Miao, R. Falcon, M. Nakata, A. Rosete, & D. Ciucci (Eds.), Rough sets: International joint conference, IJCRS 2020 (Vol. 12179, pp. 251–266). Springer International.
   Google Scholar
• Mani, A. (2021). General rough modeling of cluster analysis. In S. Ramanna, C. Cornelis, & D. Ciucci (Eds.), Rough sets: IJCRS-EUSFLAT 2021 (pp. 75–82). Springer Nature.
   Google Scholar
• Mani, A. (2022a). Granularity and rational approximation: Rethinking graded rough sets. Transactions on Rough Sets, 23(LNCS 13610), 33–59.
   Google Scholar
• Mani, A. (2022b). Mereology for STEAM and education research. In D. Chari, & A. Gupta (Eds.), EpiSTEMe 9 (Vol. 9, pp. 122–129). TIFR.
   Google Scholar
• Mani, A., Düntsch, I., & Cattaneo, G. (2018). Algebraic methods in general rough sets. Birkhauser Basel.
   Google Scholar
• Mani, A., & Mitra, S. (2022). Granular generalized variable precision rough sets and rational approximations. arxiv 2205.14365. http://arxiv.org/abs/2205.14365.
   Google Scholar
• Mckenzie, R., McNulty, G., & Taylor, W. (1987). Algebra, lattices, varieties: Volume 1. AMS.
   Google Scholar
• Mundici, D. (1984). Generalization of abstract model theory. Fundamenta Mathematicae, 124, 1–25. https://doi.org/10.4064/fm-124-1-1-25
   Web of Science ®Google Scholar
• Orłowska, E., & Pawlak, Z. (1984). Logical foundations of knowledge representation – reports of the computing centre (Vol. 537, Tech. Rep.), Polish Academy of Sciences.
   Google Scholar
• Pagliani, P. (2018). Three lessons on the topological and algebraic hidden core of rough set theory. In A. Mani, I. Düntsch, & G. Cattaneo (Eds.), Algebraic methods in general rough sets (pp. 337–415). Springer International.
   Google Scholar
• Pagliani, P., & Chakraborty, M. (2008). A geometry of approximation: Rough set theory: Logic, algebra and topology of conceptual patterns. Springer.
   Google Scholar
• Pawlak, Z. (1991). Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers.
   Google Scholar
• Pawlak, Z., & Skowron, A. (2007). Rough sets and boolean reasoning. Information Sciences, 77, 41–73. https://doi.org/10.1016/j.ins.2006.06.007
   Google Scholar
• Polkowski, L. (2004). Rough neural computation model based on rough mereology. In S. K. Pal, L. Polkowski, & A. Skowron (Eds.), Rough neural computation: Techniques for computing with words (pp. 85–108). Springer Verlag.
   Google Scholar
• Polkowski, L. (2011). Approximate reasoning by parts. Springer Verlag.
   Google Scholar
• Polkowski, L., & Polkowska, S. M. (2008). Reasoning about concepts by rough mereological logics. In G. Wang, T. Li, J. W. Grzymala-Busse, D. Miao, A. Skowron, & Y. Yao (Eds.), RSKT 2008: Rough sets and knowledge technology, LNAI 5009 (pp. 197–204). Springer.
   Google Scholar
• Pomykala, J. A. (1993). Approximation, similarity and rough constructions (Report No. CT-93-07, Tech. Rep.), ILLC, Univ of Amsterdam.
   Google Scholar
• de Rijke, M. (2000). A note on graded modal logic. Studia Logica, 64(2), 271–283. https://doi.org/10.1023/A:1005245900406
   Google Scholar
• Rudeanu, S. (2015). On ideals and filters in posets. Revue Roumaine de Mathématique Pures et Appliquées, 60(2), 155–175.
   Google Scholar
• Sands, D., Parker, M., Hedgeland, H., Jordan, S., & Galloway, R. (2018). Using concept inventories to measure understanding. Higher Education Pedagogies, 3(1), 173–182. https://doi.org/10.1080/23752696.2018.1433546
   Web of Science ®Google Scholar
• Skowron, A., Jankowski, A., & Dutta, S. (2016). Interactive granular computing. Granular Computing, 1(2), 95–113. https://doi.org/10.1007/s41066-015-0002-1
   Google Scholar
• Skowron, A., & Stepaniuk, O. (1996). Tolerance approximation spaces. Fundamenta Informaticae, 27, 245–253. https://doi.org/10.3233/FI-1996-272311
   Google Scholar
• Ślezak, D., & Wasilewski, P. (2007). Granular sets – Foundations and case study of tolerance spaces. In A. An, J. Stefanowski, S. Ramanna, C. J. Butz, W. Pedrycz, & G. Wang (Eds.), RSFDGrC 2007, LNCS (Vol. 4482, pp. 435–442). Springer.
   Google Scholar
• Turksen, I. B. (2005). An ontological and epistemological perspective of fuzzy set theory. Elsevier.
   Google Scholar
• Venkataranasimhan, P. (1971). Pseudo-complements in posets. Proceedings of the American Mathematical Society, 28, 9–17. https://doi.org/10.1090/proc/1971-028-01
   Web of Science ®Google Scholar
• Vieu, L., & Aurnague, M. (2007). Part-of relations, functionality and dependence Amsterdam. In M. Aurnague, NewEditor1 & L. Vieu (Eds.), The categorization of spatial entities in language and cognition (pp. 307–336). Benjamins Publishing Company.
   Google Scholar
• Wasilewski, P., & Ślezak, D. (2008). Foundations of rough sets from vagueness perspective. In A. Hassanien, Z. Suraj, D. Slezak, & P. Lingras (Eds.), Rough computing: Theories, technologies and applications (pp. 1–37). IGI, Global.
   Google Scholar
• Werner, K. (2020). Enactment and construction of the cognitive niche: Toward an ontology of the mind-world connection. Synthese, 197, 1313–1341. https://doi.org/10.1007/s11229-018-1756-1
   Web of Science ®Google Scholar
• Yao, Y. Y. (1996). Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning, 15(4), 291–317. https://doi.org/10.1016/S0888-613X(96)00071-0
   Web of Science ®Google Scholar
• Yao, Y. Y. (2001). Information granulation and rough set approximation. International Journal of Intelligent Systems, 16, 87–104. https://doi.org/10.1002/1098-111X(200101)16:1¡¿1.0.CO;2-B
   Web of Science ®Google Scholar
• Yao, Y. Y. (2007). The art of granular computing. In M. Kryszkiewicz, J. F. Peters, H. Rybinski, & A. Skowron (Eds.), RSEISP 2007: Rough sets and intelligent systems paradigms, LNAI 4585 (pp. 101–112). Springer Verlag.
   Google Scholar
• Yao, Y. Y. (2015). The two sides of the theory of rough sets. Knowledge-Based Systems, 80, 67–77. https://doi.org/10.1016/j.knosys.2015.01.004
   Web of Science ®Google Scholar
• Yao, Y. Y. (2016). Rough-set concept analysis: Interpreting Rs-definable concepts based on ideas from formal concept analysis. Information Sciences, 347, 442–462. https://doi.org/10.1016/j.ins.2016.01.091
   Google Scholar
• Yao, Y. Y., & Lin, T. Y. (1996). Generalizing rough sets using modal logics. Intelligent Automation and Soft Computing, 2(2), 103–120. https://doi.org/10.1080/10798587.1996.10750660
   Google Scholar
• Zadeh, L. A. (1979). Fuzzy sets and information granularity. In N. Gupta (Ed.), Advances in fuzzy set theory and applications (pp. 3–18). North Holland.
   Google Scholar
• Zadeh, L. A. (1997). Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90(2), 111–127. https://doi.org/10.1016/S0165-0114(97)00077-8
   Web of Science ®Google Scholar
• Zhang, X., Mo, Z., Xiong, F., & Cheng, W. (2012). Comparative study of variable precision rough set model and graded rough set model. International Journal of Approximate Reasoning, 53, 104–116. https://doi.org/10.1016/j.ijar.2011.10.003
   Web of Science ®Google Scholar