Granular fuzzy rough sets based on fuzzy implicators and coimplicators. (English) Zbl 1423.03209
Summary: This paper introduces granular fuzzy rough sets in the view of fuzzy implicators and fuzzy coimplicators, and discusses the constructive and axiomatic approach to fuzzy granules based on fuzzy implicators and coimplicators. Moreover, we study the connection between fuzzy granules and fuzzy relations and discuss the relationship between existing granular fuzzy rough set models and that proposed in this paper. Considering the absolute error limit, we introduce the concept of the granular variable precision fuzzy rough sets based on fuzzy implicators and coimplicators. Then, we present four propositions to ensure that the approximation operators can be efficiently calculated.
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
granular fuzzy rough set; fuzzy implicators; fuzzy coimplicators; granular variable precision fuzzy rough setReferences:
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