On multi-adjoint concept lattices based on heterogeneous conjunctors

Sets of attributes and objects in fuzzy formal concept analysis are usually different and, hence, it might not make sense to evaluate them on the same carrier. In this context, the operators used to obtain the concept lattice could be defined by associating different lattices to attributes and objects; several reasons exist for which we need to evaluate the sets of attributes and objects in the same carrier. Following this direction, we introduce a new definition of a concept lattice, where objects and attributes are evaluated on the same lattice L, although operators evaluating objects and attributes in different carriers are used. Moreover, we study the relationship between this new concept lattice and the alternative one which can be obtained directly by using different carriers for the sets of attributes and objects.