CHARACTERIZING TREES IN CONCEPT LATTICES

Author:

BĚLOHLÁVEK RADIM12,DE BAETS BERNARD3,OUTRATA JAN4,VYCHODIL VILEM56

Affiliation:

1. Deparment of Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University–SUNY, PO Box 6000, Binghamton, NY 13902–6000, USA

2. Deparment of Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

3. Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium

4. Dept. Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

5. Deparmentt of Systems Science and Industrial Engineering, T. J. Watson School of Engineering and Applied Science, Binghamton University – SUNY, PO Box 6000, Binghamton, NY 13902–6000, USA

6. Department of Computer Science, Palacky University, Olomouc, Tomkova 40, CZ-779 00 Olomouc, Czech Republic

Abstract

Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.

Publisher

World Scientific Pub Co Pte Lt

Subject

Artificial Intelligence,Information Systems,Control and Systems Engineering,Software

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