A New Type of Soft Multi Rough Sets

Abstract

Soft multi rough sets which are a hybrid model combining rough sets with soft multisets are defined by using soft multi rough approximation operators. Soft multi rough sets can be seen as a generalized rough set model based on soft multisets. In this paper, we contribute to a recent modelization of uncertainty. To be precise, in order to approach the uncertainty issue, we introduce a novel type of soft multi rough set by means of soft multi neighborhoods and then we use it to improve decision making in a multicriteria group environment. The motivation and method of this paper are as follows. Firstly we establish a soft multi covering approximation space. Secondly we define the soft multi neighborhood of the objects. We also introduce a new type of soft multi upper approximation operator by using soft multi neighborhood of the objects. Based on this new type of soft multi upper approximation operator, we propose a new kind of soft multi rough set. We present its basic properties and provide some illustrative examples. Thirdly, we show that our soft multi upper approximation operator is smaller than other multi upper approximation operator. Finally, we present an application of multicriteria group decision making using new type of soft multi covering rough approximation operators.