Scales behind computational intelligence: exploring properties of finite lattices

Finite lattices are fundamental structures which can be found in many fields of information science and computational intelligence: data analysis, data mining, multiple-valued logics, fuzzy logics, hierarchical modelling, graph theory, combinatorics, etc. Surprisingly, not much attention has been paid to structural properties of finite lattices. In this paper we study properties of finite lattices up to eleven elements. We present algorithms for generating non-isomorphic finite lattices up to a given size. We propose heuristic tests of non-isomorphism of finite lattices and examine their performance. We present a summary of selected properties of finite lattices