Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
On factorization of concept lattices by incompatible tolerances
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
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Reducing the size of concept lattices is a well-known problem in Formal Concept Analysis. A particular instance of this problem is the size reduction of concept lattices using factorization by complete tolerances. We show that all complete tolerances on a complete lattice (i.e., all possible ways of factorizing the lattice) with a naturally-defined operation of multiplication form a residuated lattice. This allows looking at the set of all complete tolerances as a scale of truth degrees using which we can evaluate formulas of predicate logic specifying the desired parameters of the factorization. We present illustrative example to clarify our approach.