期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 18, 期 3, 页码 546-557出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2010.2041006
关键词
Algorithm; fixpoint; fuzzy closure operator; fuzzy logic
资金
- Ghent University [011S01106]
- Academy of Sciences of the Czech Republic [1ET101370417]
- Czech Science Foundation [201/05/0079, P103/10/1056]
- [MSM 6198959214]
We present a fast bottom-up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees, along with the partial order on the set of all fixpoints. Fuzzy closure operators appear in several areas of fuzzy logic and its applications, including formal concept analysis (FCA) that we use as a reference area of application in this paper. Several problems in FCA, such as computing all formal concepts from data with graded attributes or computing non-redundant bases of all attribute dependencies, can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data. The development of a general algorithm that is applicable, in particular, to these problems is the ultimate purpose of this paper. We present the algorithm, its theoretical foundations, and experimental evaluation.
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