Abstract
We introduce the notions of various fuzzy connections by using distance functions on complete co-residuated lattices instead of using fuzzy partial orders on complete co-residuated lattices. We show that (1) fuzzy residuated connections induce attribute-oriented fuzzy concept lattices and object-oriented fuzzy concept lattices, (2) fuzzy Galois (resp. dual Galois) connections induce formal (resp. dual formal) fuzzy concept lattices, (3) various fuzzy concept lattices are complete lattices and (4) the relations between various fuzzy concept lattices are isomorphic or anti-isomorphic. It is shown that fuzzy relation equations can be solved using the properties of various fuzzy connections. Moreover, the concepts of closure operators, interior operators and generalized fuzzy rough sets are defined on complete co-residuated lattices.
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