Abstract
In the rough fuzzy set theory, the rough degree is used to characterize the uncertainty of a fuzzy set, and the rough entropy of a knowledge is used to depict the roughness of a rough classification. Both of them are effective, but they are not accurate enough. In this paper, we propose a new rough entropy of a rough fuzzy set combining the rough degree with the rough entropy of a knowledge. Theoretical studies and examples show that the new rough entropy of a rough fuzzy set is suitable. As an application, we introduce it into a fuzzy-target decision-making table and establish a new method for evaluating the entropy weight of attributes.
Highlights
The rough set theory, introduced by Pawlak [1, 2], is a useful and important tool to deal with uncertain information systems
We propose a new rough entropy of a rough fuzzy set combining the rough degree with the rough entropy of a knowledge
Theoretical studies and examples show that the new rough entropy of a rough fuzzy set is suitable. We introduce it into a fuzzy-target decision-making table and establish a new method for evaluating the entropy weight of attributes
Summary
The rough set theory, introduced by Pawlak [1, 2], is a useful and important tool to deal with uncertain information systems. The kind of roughness is classified into system uncertainty and measured by the rough degree [3, 10] from the view of algebra Another reason is the roughness produced by a knowledge which is a division and divided by the binary relation on universe. In order to overcome these limitations, we propose a new rough entropy about rough fuzzy sets, which considers the rough degree and the rough entropy of a knowledge This is the first aim in this paper (see Section 3). From the view of algebraic theory [13, 14], the rough degree is used to determine weights of attribute This method is effective but sometimes leads to an impractical case in which some weights may be zero. That is the second aim in this paper (see Section 4)
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