On Three Types of Soft Rough Covering-Based Fuzzy Sets

Abstract

Recently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present work aims to define the complementary soft neighborhood and hence three types of soft rough fuzzy covering models (briefly, 1-SRFC, 2-SRFC, and 3-SRFC) are proposed. We discuss their axiomatic properties. According to these results, we investigate three types of fuzzy soft measure degrees (briefly, 1-SMD, 2-SMD, and 3-SMD). Also, three kinds of $\psi$ -soft rough fuzzy coverings (briefly, 1- $\psi$ -SRFC, 2- $\psi$ -SRFC, and 3- $\psi$ -SRFC) and three kinds of $\mathcal{D}$ -soft rough fuzzy coverings (briefly, 1- $\mathcal{D}$ -SRFC, 2- $\mathcal{D}$ -SRFC, and 3- $\mathcal{D}$ -SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented.