Abstract
Recently, the concept of a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> - neighborhood operator with reflexivity was established and a fuzzy rough set covering based on a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> - neighborhood operator was defined by Zhang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> As a generalization of Zhang <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> models, this article aims to introduce the notion of a complementary fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -neighborhood operator with reflexivity. Also, three new kinds of a fuzzy rough set covering based on a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> - neighborhood operator are constructed and some of their properties are discussed. Further, the relationships between these models are studied. Several new kinds of a fuzzy rough set covering based variable precision are put forward and the relevant properties are constructed. Finally, an application to MADM to solve realistic problems is illustrated.
Highlights
P AWLAK [1], [2] defined the rough set theory to address the vagueness and granularity of information systems and data analysis
We introduce three kinds of a fuzzy rough set covering based on a fuzzy α-neighborhood operator with reflexivity
As a generalization for the methods by Zhang et al [12], firstly we presented the definition of complementary fuzzy αneighborhood operator
Summary
The definitions of neighborhood and granularity further explored these approximation operators [15]. Bonikowski et al [17] proposed a model of CRS based on the concept of minimal description. Ma [25] developed some neighborhood-related forms covering rough sets using the neighborhood and complementary neighborhood concepts. In 2017, the concept of the fuzzy complementary β-neighborhood was constructed by Yang and Hu [27] to define some types of fuzzy covering-based rough sets. In covering-based rough sets studies, the notion of minimal description plays a key role. Yang and Hu [28], [29] firstly defined fuzzy β-minimal description and fuzzy β-maximal description in fuzzy β-covering approximation space and gave some new characterizations of fuzzy covering-based rough sets in terms of fuzzy βminimal description and fuzzy β-maximal description. D’eer et al [30] discussed fuzzy neighborhoods according to fuzzy coverings
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
