Abstract
We introduce three algebraic structures induced by a doubly distance space on a complete co-residuated lattice. We show that (1) the two families of f-stable fuzzy sets and g-stable fuzzy sets induced by a doubly distance space are complete lattices and (2) these two families are isomorphic as lattices. We define the fuzzy concept lattice induced by a doubly distance space and show that this fuzzy concept lattice forms a complete lattice. Moreover, we give two examples related to them for an information system.
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