Rule extraction based on granulation order in interval-valued fuzzy information system

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. This paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Two different approximation methods are then defined. Two algorithms based on the two approximation methods, called MRBFA and MRBBA are proposed for rule extraction. The two algorithms are evaluated by a housing database from UCI. The experimental results show that MRBFA and MRBBA achieve better classification performances than the method based on attribute reduction.

► This paper intends to avoid the attribute reduction process and establish the structure of the approximation by introducing granulation order.
► Rule extraction is based on a granulation order, thus the adverse effects of attribute reduction are excluded as much as possible.
► When one interval is nested in the other, rules can still be generated.
► For MRBFA, computational consumption can be reduced effectively as the domain gradually narrows.