Exclusive disjunctive soft sets

Soft sets theory, initiated by Molodtsov, is an emerging tool to deal with uncertain problems and has been studied by scholars in both theory and practice. This paper proposes the notion of exclusive disjunctive soft sets and studies some of its operations, such as, restricted/relaxed AND operations, dependency between exclusive disjunctive soft sets and bijective soft sets, exclusive disjunctive soft decision systems, reduction of exclusive disjunctive soft decision systems, core of exclusive disjunctive soft decision systems, decision rules in exclusive disjunctive decision soft sets. Moreover, this study gives an application of exclusive disjunctive soft sets, which shows that it can be applied to attribute reduction of incomplete information system.