A general reduction method for fuzzy objective relation systems

Fuzzy objective relation systems are an important class of datasets that are generalizations of many types of decision tables. This paper proposes an approach, based on relation systems and fuzzy sets, to reduce data redundancy in fuzzy objective relation systems. We study lower and upper approximation reductions of a relation system for a given fuzzy set. As a generalization of such reductions, we consider lower and upper approximation reductions of fuzzy objective relation systems and give their corresponding reduction algorithms using methods based on the discernibility matrix. We note that the usual positive region reduction for a decision table can be considered a special case of our lower approximation reduction. Finally, we provide two examples from the UCI datasets to verify our theoretical results. These results can help in the decision making analysis of fuzzy objective relation systems. (C) 2018 Elsevier Inc. All rights reserved.