Article
Full entry |
PDF
(0.6 MB)
Feedback
PDF
(0.6 MB)
Feedback
Keywords:
fuzzy concept lattice; Chu space; category theory
fuzzy concept lattice; Chu space; category theory
Summary:
We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang’s ones.
References:
[1] Bělohlávek R.: Fuzzy concepts and conceptual structures: induced similarities. In: Proc. Joint Conference Inform. Sci. ’98, Durham (U.S.A.) 1998, Vol. I, pp. 179–182
[2] Bělohlávek R.: Concept lattices and order in fuzzy logic. Ann. Pure Appl. Logic 128 (2004), 277–298 MR 2060556 | Zbl 1060.03040
[3] Bělohlávek R., Sklenář, V., Zacpal J.: Crisply generated fuzzy concepts. In: ICFCA 2005 (B. Ganter and R. Godin, eds., Lecture Notes in Computer Science 3403), Springer–Verlag, Berlin – Heidelberg 2005, pp. 268–283 Zbl 1078.68142
[4] Bělohlávek R., Vychodil V.: Reducing the size of fuzzy concept lattices by hedges. In: Proc. FUZZ–IEEE 2005, The IEEE Internat. Conference Fuzzy Systems, Reno 2005, pp. 663–668
[5] Yahia S. Ben, Jaoua A.: Discovering knowledge from fuzzy concept lattice. In: Data Mining and Computational Intelligence (A. Kandel, M. Last, and H. Bunke, eds.), Physica–Verlag, Heidelberg 2001, pp. 169–190
[6] Ganter B., Wille R.: Formal Concept Analysis, Mathematical Foundation. Springer–Verlag, Berlin 1999 MR 1707295
[7] Krajči S.: A generalized concept lattice. Logic J. of the IGPL 13 (2005), 5, 543–550 MR 2187880 | Zbl 1088.06005
[8] Krajči S.: The basic theorem on generalized concept lattice. In: Proc. 2nd Internat. Workshop CLA 2004 (V. Snášel and R. Bělohlávek, eds.), Ostrava 2004, pp. 25–33
[9] Krajči S.: Every concept lattice with hedges is isomorphic to some generalized concept lattice. In: Proc. 3nd Internat. Workshop CLA 2004 (R. Bělohlávek and V. Snášel, eds.), Olomouc 2005, pp. 1–9
[10] Krajči S.: Cluster based efficient generation of fuzzy concepts. Neural Network World 13 (2003), 5, 521–530
[11] Pollandt S.: Fuzzy Begriffe. Springer–Verlag, Berlin 1997 MR 1710383 | Zbl 0870.06008
[12] Pollandt S.: Datenanalyse mit Fuzzy–Begriffen. In: Begriffliche Wissensverarbeitung, Methoden und Anwendungen (G. Stumme and R. Wille, eds.), Springer–Verlag, Heidelberg 2000, pp. 72–98 Zbl 0958.68162
[13] Shostak A.: Fuzzy categories versus categories of fuzzily structured sets: Elements of the theory of fuzzy categories. In: Mathematik–Arbeitspapiere N 48: Categorical Methods in Algebra and Topology (A collection of papers in honor of Horst Herrlich, Hans-E. Porst, ed.), Bremen 1977, pp. 407–438
[14] Zhang G. Q.: Chu spaces, concept lattices, and domains. In: Proc. Nineteenth Conference on the Mathematical Foundations of Programming Semantics, Montreal 2003, Electronic Notes in Theoretical Computer Science 83, 2004
Search
Partner of
