Rough Sets : Some Foundational Issues

• Autorzy: Chakraborty M.K. , Banerjee M.
• Języki publikacji: EN

Abstrakty

EN

The article analyses prevalent definitions of rough sets from the foundational and mathematical perspectives. In particular, the issue of language dependency in the definitions, and implications of the definitions on the issue of vagueness are discussed in detail.

Słowa kluczowe

EN

rough sets; vagueness

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 127, nr 1-4
• Strony: 1--15
• Opis fizyczny: Bibliogr. 51 poz.

Twórcy

autor

Chakraborty M.K.

• Center for Soft Computing Research, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India, and School of Cognitive Science, Jadavpur University, Raja S.C. Mullick Road, Kolkata 700032, India

autor

Banerjee M.

• Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India

Bibliografia

• [1]. Banerjee, M., Chakraborty, M. K.: Rough algebra, Bull.Polish Acad. Sc.(Math.), 41 (4), 1993, 293-297.
• [2]. Banerjee, M., Chakraborty, M. K.: Rough sets through algebraic logic, Fundamenta Informaticae, 28 (3-4), 1996, 211-221.
• [3]. Banerjee, M., Chakraborty, M. K.: Algebras from rough sets, in: Rough-neuro Computing: Techniques for Computing with Words (S. K. Pal, L. Polkowski, A. Skowron, Eds.), Springer-Verlag, 2004, 157-184.
• [4]. Banerjee, M., Dubois, D.: A simple modal logic for reasoning about revealed beliefs, in: Proc. 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU (C. Sossai, G. Chemello, Eds.), LNCS 5590, Springer-Verlag, 2009, 805-816.
• [5]. Banerjee, M., Yao, Y. Y.: A categorial basis for granular computing, in: Proc. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (A. An et al. Eds.), LNAI4482, Springer-Verlag, 2007, 427-434.
• [6]. Bonikowski, Z.: A certain conception of the calculus of rough sets, Notre Dame J. of Formal Logic, 33, 1992, 412-421.
• [7]. Chakraborty, M. K., Banerjee, M.: Dialogue in rough context, in: Proc. Rough Sets and Current Trends in Computing (S. Tsumoto et al. Eds.), LNAI 3066, Springer-Verlag, 2004, 295-299.
• [8]. Chakraborty, M. K., Banerjee, M.: Rough dialogue and implication lattices, Fundamenta Informaticae, 75 (1-4), 2007, 123-139.
• [9]. Comer, S.: Perfect extensions of regular double Stone algebras, Algebra Universalis, 34, 1995, 96-109.
• [10]. Davidson, D.: Thought and talk, chapter in: Inquiries into Truth and Interpretation, Oxford University Press, 1975.
• [11]. Dubois, D.: Degrees of truth, ill-known sets and contradiction, in: Foundations of Reasoning under Uncertainty (B. Bouchon-Meunier et al. Eds.), Springer-Verlag, 2010, 65-83.
• [12]. Dummett, M.: The Seas of Language, Oxford University Press, 1993.
• [13]. Edgington, D.: Vagueness by degrees, in: Vagueness: A Reader (R. Keefe, P. Smith, Eds.), MIT Press, 1997, 294-316.
• [14]. Evans, G.: Can there be vague objects? Analysis, 38 (4), 1978, 208.
• [15]. Fine, K.: Vagueness, truth and logic, Synthese, 30 (3-4), 1975, 265-300.
• [16]. Gehrke, M., Walker, E.: The structure of rough sets, Bull. Polish Acad. Sc. (Math.) 40, 1992, 235-245.
• [17]. Goguen, J. A.: The logic of inexact concepts, Synthese, 19, 1968-69, 325-373.
• [18]. Inuiguchi, M.: Generalizations of rough sets and rule extraction, Transactions on Rough Sets I, LNCS 3100, Springer-Verlag, 2004, 96-119.
• [19]. Iturrioz, L.: Rough sets and three-valued structures, in: Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa (E. Orłowska, Ed.), volume 24 of Studies in Fuzziness and Soft Computing, Springer Physica-Verlag, 1999, 596-603.
• [20]. Iwinski, T. B.: Algebraic approach to rough sets, Bull.Polish Acad. Sc.(Math.), 35 (9-10), 1987, 673-683.
• [21]. Jankowski, A., Skowron, A.: Logic for artificial intelligence: a Rasiowa-Pawlak school perspective, in: Seventy Years of Foundational Studies (A. Ehrenfeucht et al. Eds.), IOS Press, Amsterdam, 2007, 106-143.
• [22]. Jarvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasi-orders, Algebra Universalis, 66, 2011, 163-179.
• [23]. Keefe, R.: Theories of Vagueness, Cambridge Studies in Philosophy, Cambridge University Press, 2000.
• [24]. Khan, M. A., Banerjee, M.: Formal reasoning with rough sets in multiple-source approximation systems, Int. J. Approximate Reasoning, 49 (2), 2008, 466-477.
• [25]. Khan, M. A., Banerjee, M.: Rough set theory: a temporal logic view, in: Studies in Logic, Vol. 15, Proc. Logic, Navya-Nyaya and Applications: Homage to Bimal Krishna Matilal (M. K. Chakraborty et al. Eds.), College Publications, London, 2008, 1-20.
• [26]. Khan, M. A., Banerjee, M.: Logics for information systems and their dynamic extensions, ACM Transactions on Computational Logic, 4 (12), 2011, 29.
• [27]. Kumar, A., Banerjee, M.: Definable and rough sets in covering-based approximation spaces, in: Proc. Rough Sets and Knowledge Technology (T. Li, et al. Eds.), LNCS 7414, Springer-Verlag, 2012, 488-495.
• [28]. Marek, V. W., Truszczynski, M.: Contributions to the theory of rough sets, Fundamenta Informaticae, 39 (4), 1999, 389-409.
• [29]. Orłowska, E., Pawlak, Z.: Measurement and indiscernibility, Bull. Polish Acad. Sci. (Th. Comp. Sc.), 32 (9-10), 1984, 617-624.
• [30]. Orłowska, E., Radzikowska, A. M.: Knowledge algebras and their discrete duality, in: Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam (A. Skowron, Z. Suraj, Eds.), Intelligent Systems Reference Library, Volume 43, 2013, 7-20.
• [31]. Pagliani, P.: Rough set theory and logic-algebraic structures, in: Incomplete Information: Rough Set Analysis (E. Orłowska, Ed.), volume 13 of Studies in Fuzziness and Soft Computing, Springer Physica-Verlag, 1998, 109-190.
• [32]. Pagliani, P., Chakraborty, M. K.: A Geometry of Approximation; Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns, Springer, 2008.
• [33]. Parikh, R.: The problem of vague predicates, in: Language, Logic and Method (R. S. Cohen et al. Eds.), D. Reidel Pub. Co., 1983, 241-261.
• [34]. Pawlak, Z.: Rough sets, Int. J. Comp. Inf. Sci. 11, 1982, 341-356.
• [35]. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, 1991.
• [36]. Pawlak, Z.: Vagueness and uncertainty: a rough set perspective, Computational Intelligence, 11, 1995, 227232.
• [37]. Pawlak, Z.: Some issues on rough sets, Transactions on Rough Sets I, LNCS 3100, Springer-Verlag, 2004, 1-58.
• [38]. Peters, J. F., Skowron, A., Stepaniuk, J.: Rough sets: foundations and perspectives, in: Encyclopedia of Complexity and Systems Science (R. A. Meyers, Ed.), Springer-Verlag, 2009, 7787-7797.
• [39]. Pomykała, J., Pomykała, J. A.: The Stone algebra of rough sets, Bull. Polish Acad. Sc. (Math.), 36, 1988, 495-508.
• [40]. Ray, S.: Wordygurdyboom! The Nonsense World of Sukumar Ray, Translated from Bengali by Sampurna Chattarji, Puffin Books, Penguin Books India, New Delhi, 2004, 97-98.
• [41]. Samanta, P., Chakraborty, M. K.: Generalized rough sets and implication lattices, Transactions on Rough Sets XIV, LNCS 6600, Springer-Verlag, 2011, 183-201.
• [42]. Shapiro, S.: Vagueness in Context, Clarendon Press, Oxford, 2006.
• [43]. Skala, H. J., Termini, S., Trillas, E.: Aspects of Vagueness, D. Reidel Pub. Co., 1984.
• [44]. Trillas, E., Valverde, L.: An inquiry into indistinguishability operators, in: Aspects of Vagueness (H. J. Skala, S. Termini, E. Trillas, Eds.), D. Reidel Pub. Co., 1984, 231-256.
• [45]. Tye, M.: Vague objects, Mind, XCIX (396), 1990, 535-557.
• [46]. Tye, M.: Sorites paradoxes and the semantics of vagueness, Philosophical Perspectives, 8, Logic and Language, 1994, 189-206.
• [47]. Wasilewski, P., Slezak, D.: Foundations of rough sets from vagueness perspective, in: Rough Computing: Theories, Technologies and Applications, IGI Global, 2008, 1-37.
• [48]. Wright, C.: On the coherence of vague predicates, Synthese, 30, 1975, 325-365.
• [49]. Yao, Y. Y.: Two views of the theory of rough sets in finite universes, Int. J. Approx. Reasoning, 15 (4), 1996, 291-317.
• [50]. Yao, Y. Y.: Constructive and algebraic methods of the theory of rough sets, Information Sciences 109, 1998, 21-47.
• [51]. Zadeh, L. A.: Fuzzy sets, Inf. Control 8, 1965, 338-353.