What do you mean by comparing? Isomorphy?

It's propably much easier to compare the corresponding reduced contexts.

We can compare two lattices by using lattice homomorphisms

Dear Tobias Schlemmer

I mean if I have two concept lattices, how do we know these lattices are similar or different from each other?

Dear Husein Hadi Abbass

Thank you very much for your answer.

There is any clue about how to calculate lattice homomorphisms?

Dear Bryar A. Hassan ,

Since the reduced context encodes the infimum irreducible and the supremum irreducuble concepts, two finite reduced formal contexts are isomorphic if and only if the corresponding concept lattices are isomorphic. See eg. Ganter/Wille: “Formal Concept Analysis: Mathematical Foundations” (http://doi.org/10.1007%2F978-3-642-59830-2).

As the resulting relation is usually much smaller than the concept lattice, comparing the contexts is much more efficient than comparing the lattices which contain a lot of redundant information. One easy algorithm is to encode the context as a bipartite graph where the objects and attributes are the nodes and the crosses are edges (directed/undirected does not matter as all edges go from objects to attributes). Then you could use any graph isomorphism algorithm to compare them. E.g. Nauty.

Note that the cross table of the order relation of the lattice already is an – usually non-reduced – formal context.

Note that the above mentioned book has a chapter about context comparisons.

Thank you very much dear Tobias Schlemmer

Dear Tobias Schlemmer

Is there any calculator, app, code to do this comparison?

Regards

For the calculation of reduced contexts you can use any standard software on Formal Concept Analysis see https://conceptanalysis.wordpress.com/fca-software/ for a list of tools algorithms are available at https://conceptanalysis.wordpress.com/fca-algorithms/.

There is a GAP package featuring concept lattice automorphisms and orbifolds, written by Daniel Borchmann.