Possible Rough Ingredients of Concepts in Approximation Spaces

• Autorzy: Gomolińska A.
• Języki publikacji: EN

Abstrakty

EN

We discuss the problem of rough ingredients and parts of concepts of an indiscernibility-based approximation space. The notion of a (rough) ingredient is extended to the notion of a possible (rough) ingredient, and analogously in the case of parts. The term "possible" means that a concept is perceived as a candidate for a future substitute of some ingredient. Our approach is in line with rough mereology except for allowing the empty concept for the sake of simplicity.

Słowa kluczowe

EN

approximation space; concept; closeness; rough mereology; ingredient/part

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 72, nr 1-3
• Strony: 139--154
• Opis fizyczny: bibliogr. 31 poz.

Twórcy

autor

Gomolińska A.

• Department of Mathematics University of Białystok, Akademicka 2, 15-267 Białystok, Poland,

Bibliografia

• [1] Clarke, B. L.: A calculus of individuals based on connection, Notre Dame J. Formal Logic, 22(2), 1981, 204-218.
• [2] Cohn, A. G., Gotts, N. M.: The "egg-yolk" representation of regions with indeterminate boundaries, in: Proc. GISDATA Specialist Meeting on Geographical Objects with Undetermined Boundaries (P. A. Burrough, A. U. Frank, Eds.), Taylor & Francis, 1996, 171-187.
• [3] Cohn, A. G., Gotts, N. M.: Representing spatial vagueness: A mereological approach, in: Proc. 5th Int. Conf. Principles of Knowledge Representation and Reasoning (KR'96), Morgan Kaufmann, San Francisco, 1996, 230-241.
• [4] Düntsch, I., Orłowska, E., Wang, H.: Algebras of approximating regions, Fundamenta Informaticae, 46, 2001, 71-82.
• [5] Gomolińska, A.: Possible rough ingredients of concepts, in: Proc. Workshop Concurrency, Specification, and Programming CS&P'2005, Ruciane-Nida, Poland, 2005, September 28-30 (L. Czaja, Ed.), Warsaw University,Warsaw, 2005, 144-155.
• [6] Janicki, R.: On a mereological system for relational software specification, in: Proc. 27th Int. Symp. on Mathematical Foundations of Computer Science (MFCS'2002), Warsaw, Poland, 2002, August 26-30 (K. Diks, W. Rytter, Eds.), vol. 2420 of Lecture Notes in Computer Science, Springer, Berlin, 2002, 375-386.
• [7] Janicki, R.: Basic mereology with equivalence relations, in: Proc. 30th Int. Symp. on Mathematical Foundations of Computer Science (MFCS'2005), Gdańsk, Poland, 2005, August 29-September 2 (J. Jedrzejowicz, A. Szepietowski, Eds.), vol. 3618 of Lecture Notes in Computer Science, Springer, Berlin, 2005, 507-519.
• [8] Leonard, H., Goodman, N.: The calculus of individuals and its uses, J. Symbolic Logic, 5, 1940, 45-55.
• [9] Leśniewski, S.: Foundations of the general set theory 1 (in Polish), Works of the Polish Scientific Circle, 2, 1916, see also Stanisław Leśniewski Collected Works (S. J. Surma et al., Eds.), Kluwer, Dordrecht, 1992, 128-173.
• [10] Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, in: Jan Łukasiewicz - Selected Works (L. Borkowski, Ed.), North Holland, Amsterdam London, 1970, 16-63, first published Kraków 1913.
• [11] Nguyen, S. H., Skowron, A., Stepaniuk, J.: Granular computing: A rough set approach, J. Comput. Intelligence, 17(3), 2001, 514-544.
• [12] Novotný, M., Pawlak, Z.: Characterization of rough top equalities and rough bottom equalities, Bull. Polish Acad. Sci. Math., 33(1-2), 1985, 91-97.
• [13] Novotný, M., Pawlak, Z.: On rough equalities, Bull. Polish Acad. Sci. Math., 33(1-2), 1985, 99-104.
• [14] Pawlak, Z.: Information systems - Theoretical foundations, Information Systems, 6(3), 1981, 205-218.
• [15] Pawlak, Z.: Rough sets, Computer and Information Sciences, 11, 1982, 341-356.
• [16] Pawlak, Z.: Information Systems. Theoretical Foundations (in Polish), Wydawnictwo Naukowo-Techniczne, Warsaw, 1983.
• [17] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data, Kluwer, Dordrecht, 1991.
• [18] Polkowski, L.: On connection synthesis via rough mereology, Fundamenta Informaticae, 46, 2001, 83-96.
• [19] Polkowski, L., Skowron, A.: Rough mereology, in: Lecture Notes in Artificial Intelligence, vol. 869, Springer, Berlin, 1994, 85-94.
• [20] Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning, Approximated Reasoning, 15(4), 1996, 333-365.
• [21] Polkowski, L., Skowron, A.: Towards adaptive calculus of granules, in: Computing with Words in Information/ Intelligent Systems (L. A. Zadeh, J. Kacprzyk, Eds.), vol. 1, Physica-Verlag, Heidelberg, 1999, 201-228.
• [22] Polkowski, L., Skowron, A.: Rough mereological calculi of granules: A rough set approach to computation, Comput. Intelligence, 17(3), 2001, 472-492.
• [23] Polkowski, L., Skowron, A.: Rough mereology in information systems. A case study: Qualitative spatial reasoning, in: Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems (L. Polkowski et al., Ed.), Physica-Verlag, Heidelberg, 2001, 89-135.
• [24] Skowron, A.: Toward intelligent systems: Calculi of information granules, in: New Frontiers in Artificial Intelligence, Joint JSAI Workshop Post Proceedings (T. Terano et al., Ed.), vol. 2253 of Lecture Notes in Artificial Intelligence, Springer, Berlin Heidelberg, 2001, 251-260, also in: Bull. Int. Rough Set Soc. 5(1-2), 2001, 9-30.
• [25] Skowron, A., Stepaniuk, J.: Generalized approximation spaces, in: Proc. 3rd Int. Workshop Rough Sets and Soft Computing, San Jose, USA, 1994, November 10-12, 1994, 156-163.
• [26] Skowron, A., Stepaniuk, J.: Tolerance approximation spaces, Fundamenta Informaticae, 27, 1996, 245-253.
• [27] Słupecki, J.: S. Leśniewski's calculus of names, Studia Logica, 3, 1955, 7-76.
• [28] Smith, B.: Agglomerations, in: Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science (C. Freksa, D. M. Mark, Eds.), vol. 1661 of Lecture Notes in Computer Science, Springer, Berlin, 1999, 267-282.
• [29] Surma, S. J., Ed.: On Leśniewski's Systems, Proc. XXII Conf. History of Logic, vol. 36(4) of Studia Logica, 1977.
• [30] Tarski, A.: Les fondements de la géométrie des corps, in: Memorial Book of the 1st Polish Mathematical Congress, a supplement to Annales de la Sociéte Polonaise de Mathématique, Kraków, 1929, 29-33.
• [31] Whitehead, A. N.: Process and Reality. An Essay in Cosmology, Macmillan, New York, 1929, corrected edition from 1978 (D. R. Griffin, D. W. Sherbourne, Eds.).