Abstract
In different theories involving indiscernibility, it is assumed that at some level the objects involved are actually assignable distinct names. This can prove difficult in different application contexts if the main semantic level is distinct from the semantic-naming level. Set-theoretically too this aspect is of much significance. In the present research paper we develop a framework for a generalized form of rough set theory involving partial equivalences on different types of approximation spaces. The theory is also used to develop an algebraic semantics for variable precision rough set and variable precision fuzzy rough set theory. A quasi-inductive concept of relativised rough approximation is also introduced in the last section. Its relation to esoteric rough sets is considered.
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Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets – a tutorial. In: Pal, S.K. (ed.) Rough Fuzzy Hybridization, pp. 3–98. Springer, Heidelberg (1999)
Cattaneo, G., Ciucci, D.: Algebras for rough sets and fuzzy logics. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets 2. LNCS, vol. 3100, pp. 208–252. Springer, Heidelberg (2004)
Inuiguchi, M.: Generalisation of rough sets and rule extraction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 96–116. Springer, Heidelberg (2004)
Mani, A.: Rough equalities from posets and rough difference orders. Fundamenta Informaticae 53, 321–333 (2002)
Mani, A.: Relativised generalized rough sets and bayesian belief networks (to be Submitted, 2007)
Lin, T.Y., Yao, Y.Y., Wong, S.K.: A review of rough set models. In: Lin, Y.Y., et al. (eds.) Analysis of Information databases,Rough Sets and Data Mining, Kluwer Academic Publishers, Dordrecht (1997)
Ziarko, W.: Variable precision rough set model. J. of Computer and System Sciences 46, 39–59 (1993)
Rolka, A.M., Rolka, L.: Variable precision fuzzy rough sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 144–160. Springer, Heidelberg (2004)
Banerjee, M., Chakraborty, M.K.: Algebras from rough sets – an overview. In: Pal, S.K., et al. (eds.) Rough-Neural Computing, pp. 157–184. Springer, Heidelberg (2004)
Yao, G.T.: Constructions and algebraic methods of the theory of rough sets. Information Science 109, 21–47 (1998)
Düntsch, I.: Rough sets and algebras of relations. In: Orlowska, E. (ed.) Incomplete Information and Rough Set Analysis, pp. 109–119. Physica, Heidelberg (1998)
Katrinak, T.: Construction of regular double p-algebras. Bull. Roy. Soc. Sci. Liege 43, 294–301 (1974)
Burmeister, P.: A Model-Theoretic Oriented approach to Partial Algebras. Akademie-Verlag (1986) (2002)
Vojvodic, G.: A note on weak partial congruence algebras. Rev. of Res. Fac. Sci. Univ of Novisad 22, 89–94 (1992)
Seselja, B., Vojvodic, G.: On the lattice of weak congruence relations. Algebra Universalis 25, 121–130 (1988)
Mani, A.: Esoteric rough algebras, p. 24 (submitted, 2006)
Mani, A.: Super rough semantics. Fundamenta Informaticae 65, 249–261 (2005)
Ljapin, E.S.: Partial algebras and their applications. Academic, Kluwer (1996)
Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informaticae 28, 211–221 (1996)
Bleyberg, M., Elumalai, A.: Using rough sets to construct sense type decision trees for text categorisation. Transactions of IEEE, 19–24 (2001)
Katzberg, T., Ziarko, W.: Variable precision extension of rough sets. Fundamenta Informaticae 27, 1–12 (1996)
Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R., et al. (eds.) Advances in Dempster-Schafer Theory of Evidence, Wiley, Chichester (1994)
Kryszkiewicz, M., Cichon, K.: Towards scalable algorithms for discovering rough set reducts. In: Peters, J.F., Skowron, A. (eds.) Transactions of Rough Sets-1, vol. LNCS-3100, pp. 120–143. Springer, Heidelberg (2004)
Bazan, J., Nguyen, S., Nguyen, H., Synak, P., Wroblewski, J.: Rough set algorithms in classification problem. In: Polkowski, L., et al. (eds.) Rough Set Methods and Applications, pp. 49–88. Physica Verlag, Heidelberg (2000)
Bazan, J., Nguyen, S.H., Skowron, A., Szczuka, M.: A view on rough set concept approximations. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 181–188. Springer, Heidelberg (2003)
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Mani, A. (2008). Esoteric Rough Set Theory: Algebraic Semantics of a Generalized VPRS and VPFRS. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets VIII. Lecture Notes in Computer Science, vol 5084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85064-9_9
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DOI: https://doi.org/10.1007/978-3-540-85064-9_9
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