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As a generalization of Zhan’s method (i.e., to increase the lower approximation and decrease the upper approximation), the present paper aims to define the family of complementary fuzzy - neighborhoods and thus three kinds of covering-based multigranulation ( )- fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation ( )- fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations and illustrates with a numerical example to describe its performance.

complexity

Certain Types of Covering-Based Multigranulation (<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi mathvariant="normal">ℐ</mi> <mo>,</mo> <mi mathvariant="script">T</mi> </math>)-Fuzzy Rough Sets with Application to Decision-Making

Certain Types of Covering-Based Multigranulation ( ℐ , T )-Fuzzy Rough Sets with Application to Decision-Making

Certain Types of Covering-Based Multigranulation ( $ℐ, T$ )-Fuzzy Rough Sets with Application to Decision-Making