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 ψ -soft rough fuzzy coverings (briefly, 1- ψ -SRFC, 2- ψ -SRFC, and 3- ψ -SRFC) and three kinds of D -soft rough fuzzy coverings (briefly, 1- D -SRFC, 2- D -SRFC, and 3- D -SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented.
Highlights
Pawlak [1, 2] developed the rough set theory for addressing the vagueness and granularity of information systems and data analysis
Bonikowski et al [25] proposed a model of covering-based rough sets (CRSs) that depends on the concept of minimal description. ere are other CRS models and relationships between them in [26,27,28,29]
Some CRS models were proposed by Tsang et al [30] and Xu and Zhang [31]
Summary
Pawlak [1, 2] developed the rough set theory for addressing the vagueness and granularity of information systems and data analysis. In 2016, Ma [35] introduced the concept of a fuzzy β-neighborhood to generate two types of fuzzy rough coverings. In 2017, Yang and Hu [36] defined the fuzzy β-complementary neighborhood to establish some types of the fuzzy covering-based rough sets. Yang and Hu [37] in 2019 introduced the concept of fuzzy β-minimal description and fuzzy β-maximal description to propose four types of fuzzy neighborhood operators and studied their properties. E aim of the paper is to increase the lower approximation and decrease the upper approximation of Zhan’s model; this paper’s contribution is to introduce three new kinds of soft rough fuzzy covering based on soft neighborhoods and complementary soft neighborhoods.
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