PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

A Logic-Algebraic Approach to Graded Inclusion

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we continue searching for functions which might be used as measures of inclusion of information granules in information granules. Starting with a 3-valued logic having an adequate logical matrix, we show how to derive a corresponding graded inclusion function. We report on the results of examination of several best known 3-valued logics in this respect. We also give some basic properties of the inclusion functions obtained.
Wydawca
Rocznik
Strony
265--279
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
Bibliografia
  • [1] Artiemjew, P.: Rough mereological classifiers obtained from weak variants of rough inclusions, Lecture Notes in AI, 5009, 2008, 229-236.
  • [2] Avron, A., Konikowska, B.: Rough sets and 3-valued logics, Studia Logica, 90(1), 2008, 69-92.
  • [3] Bolc, L., Borowik, P.: Many-valued Logics, vol. 1, Springer-V., Berlin, 1992.
  • [4] Bolc, L., Dziewicki, K., Rychlik, P., Szałas, A.: Reasoning in Non-classical Logics: Theoretical Foundations (in Polish), Akademicka OficynaWydawnicza PLJ, Warszawa, 1995.
  • [5] Borkowski, L., Ed.: Jan Łukasiewicz - Selected Works, North Holland/Polish Scientific Publ., Amsterdam/Warszawa, 1970.
  • [6] Drwal, G., Mr´ozek, A.: System RClass - software implementation of a rough classifier, Proc. 7th Int. Symp. Intelligent Information Systems (IIS'1998), Malbork, Poland, June 1998 (M. A. Kłopotek, M. Michalewicz, Z. W. Raś, Eds.), PAS Institute of Computer Science,Warszawa, 1998, 392-395.
  • [7] Gomolińska, A.: On certain rough inclusion functions, Transactions on Rough Sets IX: journal subline of LNCS, 5390, 2008, 35-55.
  • [8] Gomolińska, A.: Rough approximation based on weak q-RIFs, Transactions on Rough Sets X: journal subline of LNCS, 5656, 2009, 117-135.
  • [9] Gomolińska, A.: A logic-algebraic approach to graded inclusion, Proc. 19th Workshop on Concurrency, Specification, and Programming (CS&P'2010), Helenenau, Germany, September 2010 (L. Popova-Zeugmann et al., Ed.), 237, Humboldt-Universit¨at zu Berlin, Berlin, 2010, 154-165.
  • [10] Kleene, S. C.: On a notation for ordinal numbers, The Journal of Symbolic Logic, 3, 1938, 150-155.
  • [11] Kleene, S. C.: Introduction to Metamathematics, North-Holland, Amsterdam, 1952.
  • [12] Leśniewski, S.: Foundations of the General Set Theory 1 (in Polish), vol. 2 of Works of the Polish Scientific Circle, Moscow, 1916, also in [28], pages 128-173.
  • [13] Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Krak´ow, 1913, English transl. in [5], pages 16-63.
  • [14] Łukasiewicz, J.: On three-valued logic (in Polish), Ruch Filozoficzny, 5, 1920, 170-171, English transl. in [5], pages 87-88.
  • [15] Malinowski, G.: Many-valued Logics (in Polish), Państwowe Wydawnictwo Naukowe,Warszawa, 1990.
  • [16] Pawlak, Z.: Rough sets, Int. J. Computer and Information Sciences, 11, 1982, 341-356.
  • [17] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data, Kluwer, Dordrecht, 1991.
  • [18] Polkowski, L.: Rough mereology in analysis of vagueness, Lecture Notes in AI, 5009, 2008, 197-204.
  • [19] Polkowski, L.: Reasoning by Parts: An Outline of Rough Mereology, Warszawa, 2011.
  • [20] Polkowski, L., Semeniuk-Polkowska, M.: Reasoning about concepts by rough mereological logics, Lecture Notes in AI, 5009, 2008, 205-212.
  • [21] Polkowski, L., Skowron, A.: Rough mereology, Lecture Notes in Artificial Intelligence, 869, 1994, 85-94.
  • [22] 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.
  • [23] Polkowski, L., Skowron, A.: Rough mereology in information systems. A case study: Qualitative spatial reasoning, in: [24], 2001, 89-135.
  • [24] Polkowski, L., Tsumoto, S., Lin, T. Y., Eds.: Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems, Physica, Heidelberg New York, 2001.
  • [25] Post, E. L.: Introduction to a general theory of elementary propositions, American Journal of Mathematics, 43, 1921, 163-185.
  • [26] Słupecki, J.: A complete three-valued propositional calculus (in Polish), AnnalesUniversitatisMariae Curie-Skłodowska, Lublin, Sectio F, 1(3), 1946, 193-209.
  • [27] Stepaniuk, J.: Knowledge discovery by application of rough set models, in: [24], 2001, 137-233.
  • [28] Surma, S. J., Srzednicki, J. T., Barnett, J. D., Eds.: Stanisław Leśniewski Collected Works, Kluwer/Polish Scientific Publ., Dordrecht/Warszawa, 1992.
  • [29] Xu, Z. B., Liang, J. Y., Dang, C. Y., Chin, K. S.: Inclusion degree: A perspective on measures for rough set data analysis, Information Sciences, 141, 2002, 227-236.
  • [30] Zadeh, L. A.: Fuzzy sets, Information and Control, 8, 1965, 338-353.
  • [31] Zadeh, L. A.: Outline of a new approach to the analysis of complex system and decision processes, IEEE Trans. on Systems, Man, and Cybernetics, 3, 1973, 28-44.
  • [32] Zhang, W. X., Leung, Y.: Theory of including degrees and its applications to uncertainty inference, Proc. Of 1996 Asian Fuzzy System Symposium, 1996, 496-501.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0018-0047
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.