0000000000653122
AUTHOR
Sang-eon Han
showing 3 related works from this author
Variable-Range Approximate Systems Induced by Many-Valued L-Relations
2014
The concept of a many-valued L-relation is introduced and studied. Many-valued L-relations are used to induce variable-range quasi-approximate systems defined on the lines of the paper (A. Sostak, Towards the theory of approximate systems: variable-range categories. Proceedings of ICTA2011, Cambridge Univ. Publ. (2012) 265–284.) Such variable-range (quasi-)approximate systems can be realized as special families of L-fuzzy rough sets indexed by elements of a complete lattice.
M-valued Measure of Roughness for Approximation of L-fuzzy Sets and Its Topological Interpretation
2015
We develop a scheme allowing to measure the “quality” of rough approximation of fuzzy sets. This scheme is based on what we call “an approximation quadruple” \((L,M,\varphi ,\psi )\) where L and M are cl-monoids (in particular, \(L=M=[0,1]\)) and \(\psi : L \rightarrow M\) and \(\varphi : M \rightarrow L\) are satisfying certain conditions mappings (in particular, they can be the identity mappings). In the result of realization of this scheme we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive M-fuzzy relation R. In case the relation R is also symmetric, these measures coincide and we call their value by the measure of rou…
On approximate-type systems generated by L-relations
2014
The aim of this work is to study approximate-type systems induced by L-relations in the framework of the general theory of M-approximate systems introduced in [42] and its generalizations. Special attention is payed to the structural properties of lattices of such systems and to the study of connections between categories of such systems and the corresponding categories of sets endowed with L-relations.