Abstract
Implicational sets have showed to be an efficient tool for knowledge representation. An active area is the definition of some canonical sets (basis) to efficiently specify and manage the information specified with implications. Unlike in classical formal concept analysis, in the fuzzy framework it is an open issue to design methods to efficiently compute the corresponding basis from a given set of fuzzy implications and, later, manage it in an automatic way. In this work we use Simplification Logic to tackle this issue. More specifically, we cover the following stages related to this problem: the generalization of the Simplification logic to an arbitrary complete residuated lattice changing its semantic, the introduction of the syntactic closure and an algorithm to compute it, the definition of a fuzzy direct basis with minimum size, providing the so-called directness property as well, and, finally the design of an algorithm to compute this basis.
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Notes
- 1.
Where
and |A| denotes the cardinality of A.
and |A| denotes the cardinality of A.References
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Supported by Grants TIN2014-59471-P and TIN2017-89023-P of the Science and Innovation Ministry of Spain.
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Cordero, P., Enciso, M., Mora, A. (2018). Directness in Fuzzy Formal Concept Analysis. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_50
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