The bijective soft set with its operations

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by scholars in theory and practice. This paper proposes the concept of bijective soft set and some of its operations such as the restricted AND and the relaxed AND operations on a bijective soft set, dependency between two bijective soft sets, bijective soft decision system, significance of bijective soft set with respect to bijective soft decision system, reduction of bijective soft set with respect to bijective soft decision system, and decision rules in bijective soft decision system. With these notions and operations, an application of bijective soft set in decision-making problems is also discussed. (C) 2010 Elsevier Ltd. All rights reserved.