PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Attribute Exploration of Properties of Functions on Sets

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Exam- ple functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration is run on contexts where objects are functions and attributes are 16 function properties. Minimal implication bases are presented. The list of proved implications is presented and discussed.
Wydawca
Rocznik
Strony
377--394
Opis fizyczny
Bibliogr. 19 poz., tab.
Twórcy
autor
  • School of Applied Mathematics and Information Science Higher School of Economics Moscow, Russia, artreven@gmail.com
Bibliografia
  • [1] Aizerman, M., Aleskerov, F.: Theory of Choice, North-Holland/Elsevier, Amsterdam, 1995.
  • [2] Aizerman, M., Malishevskiy, A.: General theory of best variants choice, IEEE Trans. Automatic Control, AC-26(5), 1981, 1030-1040.
  • [3] Babin, M., Kuznetsov, S. O.: Recognizing Pseudo-Intent is coNP-complete, Proc. 7th International Conference on Concept Lattices and Their Applications, University of Sevilla, 2010, 294-301.
  • [4] Birkhoff, G.: Lattice Theory, 3rd edition, Am. Math. Soc., Providence, RI, 1967.
  • [5] Danilov, V., Koshevoy, G.: A new characterization of the path independent choice functions, Mathematical Social Sciences, 51, 2006, 238-245.
  • [6] Dau, F.: Implications of properties concerning complementation in finite lattices, In: Contributions to General Algebra 12 (D. Dorninger et al., eds.), Proceedings of the 58th workshop on general algebra "58. Arbeitstagung Allgemeine Algebra", Vienna, Austria, June 3-6, 1999, Verlag Johannes Heyn, Klagenfurt, 2000, 145-154.
  • [7] Felix Distel, B. S.: On the complexity of enumerating pseudo-intents, Discrete Applied Mathematics, 159, 2011, 450-466.
  • [8] Ganter, B.: Two Basic Algorithms in Concept Analysis, Preprint-Nr. 831, 1984.
  • [9] Ganter, B., Wille, R.: Formal Concept Analysis : Mathematical Foundations, Springer, 1999.
  • [10] Guigues, J.-L., Duquenne, V.: Familles minimales d'implications informatives r_esultant d'un tableau de donn_ees binaires, Math. Sci. Hum, 24(95), 1986, 5-18.
  • [11] Koshevoy, G.: Choice functions and abstract convex geometries, Mathematical Social Sciences, 38(5), 1999, 35-44.
  • [12] Kuznetsov, S. O.: On Complexity of Computing the Duquenne-Guigues Basis, Journal of Universal Computer Science, 10(8), 2004, 927-933.
  • [13] Kwuida, L., Pech, C., Reppe, H.: Generalizations of Boolean algebras. An attribute exploration, Mathematica Slovaca, 56(2), 2006, 145-165.
  • [14] Monjardet, B., Raderanirina, V.: The duality between the anti-exchange closure operators and the path independent choice operators on a finite set, Mathematical Social Sciences, 41, 2000, 131-150.
  • [15] Moulin, H.: Choice functions over finite sets: a summary, Soc. Choice Welf., 2, 1985, 147-160.
  • [16] Obiedkov, S., Duquenne, V.: Incremental Construction of the Canonical Implication Basis, Proc. of JIM 2003, Metz, France, 2003.
  • [17] Plott, C.: Path independence, rationality and social choice, Econometrica, 41, 1973, 1075-1091.
  • [18] S. O. Kuznetsov, S. O.: Some Decision and Counting Problems of the Duquenne-Guigues Basis of Implications, Discrete Applied Mathematics, 156(11), 2008, 1994-2003.
  • [19] Sen, A.: Choice functions and revealed preference, Review of Economics Studies, 38, 1971, 307-313.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0024-0031
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.