Twofold fuzzy sets and rough sets—Some issues in knowledge representation
Fuzzy Sets and Systems
Rough sets and fuzzy sets—some remarks on interrelations
Fuzzy Sets and Systems
Measures of similarity between vague sets
Fuzzy Sets and Systems
Vague sets are intuitionistic fuzzy sets
Fuzzy Sets and Systems
Information Sciences: an International Journal
Remark on the intuitionistic fuzzy logics
Fuzzy Sets and Systems
On the composition of intuitionistic fuzzy relations
Fuzzy Sets and Systems - Theme: Basic concepts
Information Sciences: an International Journal
Generalized fuzzy rough approximation operators based on fuzzy coverings
International Journal of Approximate Reasoning
Axiomatic systems for rough sets and fuzzy rough sets
International Journal of Approximate Reasoning
Fuzzy rough approximations of process data
International Journal of Approximate Reasoning
On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse
International Journal of Approximate Reasoning
A fuzzy extension of Saaty's priority theory
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A comparative study of fuzzy sets and rough sets
Information Sciences: an International Journal
A roughness measure for fuzzy sets
Information Sciences: an International Journal
Comparative study of variable precision rough set model and graded rough set model
International Journal of Approximate Reasoning
Nearness approximation space based on axiomatic fuzzy sets
International Journal of Approximate Reasoning
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
Probabilistic rough set over two universes and rough entropy
International Journal of Approximate Reasoning
Generalization of Pawlak's rough approximation spaces by using δβ-open sets
International Journal of Approximate Reasoning
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The combination of the rough set theory, vague set theory and fuzzy set theory is a novel research direction in dealing with incomplete and imprecise information. This paper mainly concerns the problem of how to construct rough approximations of a vague set in fuzzy approximation space. Firstly, the @b-operator and its complement operator are introduced, and some new properties are examined. Secondly, the approximation operators are constructed based on @b-(complement) operator. Meantime, @l-lower (upper) approximation is firstly proposed, and then some properties of two types of approximation operators are studied. Afterwards, for two different kinds of approximation operators, we introduce two roughness measure methods of the same vague set and discuss a property. Finally, an example is given to illustrate how to calculate the rough approximations and roughness measure of a vague set using the @b-(complement) product between two fuzzy matrixes. The results show that the proposed rough approximations and roughness measure of a vague set in fuzzy environment are reasonable.