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On the measure of M-rough approximation of L-fuzzy sets
Sang-Eon Han 1 - Personal Name
Alexander Šostak 2,3 - Personal Name
We develop an approach allowing to measure the “quality” of rough approximation of fuzzy sets. It is based on what we call “an approximative quadruple” Q =
(L , M, φ, ψ) where L and M are complete lattice commu-tative monoids and φ : L → M, ψ : M → L are mappings satisfying certain conditions. By realization of this scheme, we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with an M-preoder R : X × X → M. In case R is symmetric, these mea-sures coincide. Basic properties of such measures are studied. Besides, we present an interpretation of measures of rough
approximation in terms of L M-fuzzy topologies.
(L , M, φ, ψ) where L and M are complete lattice commu-tative monoids and φ : L → M, ψ : M → L are mappings satisfying certain conditions. By realization of this scheme, we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with an M-preoder R : X × X → M. In case R is symmetric, these mea-sures coincide. Basic properties of such measures are studied. Besides, we present an interpretation of measures of rough
approximation in terms of L M-fuzzy topologies.
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| EB00000002922K | Available |
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Subject(s)
Upper M-rough approximation operator
Lower M-rough approximation operator
Measure of inclusion
Measure of M-rough approximation of an L-fuzzy set
L M-ditopology
L-fuzzy set
Ditopology
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