A comparative study of multigranulation rough sets and concept lattices via rule acquisition

• Transforming decision systems into formal decision contexts is studied.
• Relationship between “AND” decision rules and granular rules is discussed.
• Relationship between “OR” decision rules and disjunctive rules is investigated.
• Support and certainty factors of different rules are compared.
• Algorithm complexity of rule acquisition is analyzed.

Recently, by combining rough set theory with granular computing, pessimistic and optimistic multigranulation rough sets have been proposed to derive “AND” and “OR” decision rules from decision systems. At the same time, by integrating granular computing and formal concept analysis, Wille’s concept lattice and object-oriented concept lattice were used to obtain granular rules and disjunctive rules from formal decision contexts. So, the problem of rule acquisition can bring rough set theory, granular computing and formal concept analysis together. In this study, to shed some light on the comparison and combination of rough set theory, granular computing and formal concept analysis, we investigate the relationship between multigranulation rough sets and concept lattices via rule acquisition. Some interesting results are obtained in this paper: (1) “AND” decision rules in pessimistic multigranulation rough sets are proved to be granular rules in concept lattices, but the inverse may not be true; (2) the combination of the truth parts of an “OR” decision rule in optimistic multigranulation rough sets is an item of the decomposition of a disjunctive rule in concept lattices; (3) a non-redundant disjunctive rule in concept lattices is shown to be the multi-combination of the truth parts of “OR” decision rules in optimistic multigranulation rough sets; and (4) the same rule is defined with a same certainty factor but a different support factor in multigranulation rough sets and concept lattices. Moreover, algorithm complexity analysis is made for the acquisition of “AND” decision rules, “OR” decision rules, granular rules and disjunctive rules.