Soft rough sets based on covering and their applications

Abstract

Abstract Soft rough based on covering $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> in a fusion of soft set theory $\mathcal {S}ST$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>S</mml:mi> <mml:mi>T</mml:mi> </mml:math> and rough set depending on covering $\mathcal {C}RS$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> <mml:mi>R</mml:mi> <mml:mi>S</mml:mi> </mml:math> . We put forth a definition of soft rough covering approximation space $\mathcal {S}CAS$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>C</mml:mi> <mml:mi>A</mml:mi> <mml:mi>S</mml:mi> </mml:math> via neighborhood concept. Some axiomatic systems of our model of $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> are discussed. We study the relationship between our model of $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> and three other $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> -models. An algorithm for reduction of the attributes of the information systems using $\mathcal {S}CAS$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>C</mml:mi> <mml:mi>A</mml:mi> <mml:mi>S</mml:mi> </mml:math> is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via $\mathcal {S}RC$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mi>C</mml:mi> </mml:math> theory.