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Abstrakty
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation spaces to approximate'. The eventual algebraic semantics is developed via many deep results in convexity in ordered structures. A new variation of rough set theory, namely 'ill-posed rough set theory' in which it may suffice to know some of the approximations of sets, is eventually introduced.
Wydawca
Czasopismo
Rocznik
Tom
Strony
249--261
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
autor
- Member, Calcutta Mathematical Society 9B Jatin Bagchi Road Kolkata (Calcutta)-700029, India, a.mani_sc.gs@vsnl.net
Bibliografia
- [1] Adaricheva, K., Gorbunov, V. and Tumanova, V.: Join-semi-distributive lattices and convex geometries, Advances in Math. 173, 2003, 1–49.
- [2] Banerjee,M. and Chakraborty,M.K.: Rough sets through algebraic Logic, Fund. Inform. 28 1996, 211–221.
- [3] Banerjee, M. and Chakraborty,M.K.: Algebras from rough sets – an overview, Preprint, 2003.
- [4] Birkhoff, G. and Bennet, M.K.: Convexity lattice of a poset, Order 2 1985, 223–242.
- [5] Burmeister, P.: A Model-Theoretic Oriented approach to Partial Algebras Akademie Verlag, 1986 (revised e-version, 2002, http://www. mathematik.tu-darmstadt.de/burmeister/ ).
- [6] Bonikowski, Z.: A Certain Concept of the Calculus of rough sets, Notre Dame J of Formal Logic 33 1992, 412–421.
- [7] Chajda, I.: Algebraic Theory of Tolerance Relations, Olomouc Univ.Press, Czechoslovakia, 1991.
- [8] Czedli, G.: Factor Lattices by Tolerances, Acta Sci. Math. (Szeged) 44 1982, 35–42.
- [9] Duntsch, I.: Rough sets and algebras of relations, in Incomplete Information and rough Set Analysis E. Orlowska, et. al. (eds.) pp. 109–190, Physica, Heidelberg 1998.
- [10] Gratzer, G.: Lattice Theory, 2nd Edition, Springer, 1998.
- [11] Hurrioz, L.: Rough sets and 3-valued structures, in Logic at Work : Essays in the Memory of H.Rasiowa, E. Orlowska, et. al. (eds.) pp. 593–603, Physica, Heidelberg 1999.
- [12] Igosin, V.I.: Lattices of intervals and of convex sublattices of lattices, Uporjadocennyje mnozestva : resotki Saratov, 6 1990, 69–76.
- [13] Iwinski, T.B.: Algebraic approach to rough sets, Bull. Pol. Acad. Sci. (Math) 35(9–10), 1987, 673–683.
- [14] Iwinski, T.B.: Rough orders and rough concepts, Bull. Pol. Acad. Sci. (Math) 36(3–4), 1988, 187–192.
- [15] Komorowski, J., Pawlak, Z., Polkowski, L. and Skowron, A.: Rough sets – a tutorial, in Rough Fuzzy Hybridisation S. K. Pal, et. al. (eds), Springer Verlag, 1999, 3–98.
- [16] Lihova, J.: On convexly isomorphic posets, Czech. J. Math.44 (124), 1999, 135–147.
- [17] Lihova, J.: On posets with isomorphic interval posets, Czech. J. Math 44(124), 1999, 67–80.
- [18] Ljapin, E.S.: Partial algebras and their applications, Academic, Kluwer 1997.
- [19] Malcev, A.I.: The Metamathematics of Algebraic Systems – collected papers, North Holland, 1971.
- [20] Mani, A.: V-Perspectives, differences, pseudo-natural number systems and partial orders, Glasnik Math, 2, 37(57), 2002, 245–257.
- [21] Mani, A.: Rough equalities from posets and rough difference orders, Fundamenta Informatica, 53 2002, 321–333.
- Mani / Rough Semantics 261
- [22] Mani, A.: States and degrees of rough approximation, submitted, Fundamenta Informatica.
- [23] Novotny,M. and Pawlak, Z.: On rough equalities, Bull.Pol.Acad.Sci.(Math) 33(1–2), 1985, 99–104.
- [24] Novotny,M. and Pawlak, Z.: On rough top and bottom equalities, Bull.Pol.Acad.Sci.(Math) 33(3–4), 1985, 90–97.
- [25] Pagliani, P.: Rough set theory and logico-algebraic structures, in Incomplete Information and Rough Set Analysis, E. Orlowska, et.al. (eds.) pp. 109–190, Physica, Heidelberg 1998.
- [26] Pawlak, Z. and Skowron, A.: Rough membership functions, in Advances in Dempster-Shaefer Theory of Evidence, R.Yager, et.al. (eds.)Wiley,N.Y. 1994.
- [27] Pomykala, J.A.: Approximation, similarity and rough constructions, Preprint No.93-07 ILLC, Amsterdam 1993.
- [28] Lin, T.Y., Yao, Y.Y., Wong, S.K.: A review of rough set models, in Analysis of Information databases, Rough Sets and Data Mining, Y. Y. Lin, et.al (eds.) Kluwer, 1997.
- [29] Semenova, M and Wehrung, F.: Sublattices of lattices of order-convex sets-1, J of Algebra 277(2), 2004 825–860.
- [30] Semenova, M and Wehrung, F.: Sublattices of lattices of order-convex sets-2, Internat.J of Alg. Computing -to appear.
- [31] Semenova, M and Wehrung, F.: Sublattices of lattices of order-convex sets-3, Internat.J of Alg. Computing 14(3), 2004 357–387.
- [32] Yao, G.T.: Constructions and algebraic methods of the theory of rough sets, Informat. Sci 109 1998 21–47
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0007-0011
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