# An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets

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##### Citations

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### Cites background or methods from "An Analysis of Generalised Approxim..."

...Like the approach through which we could incorporate human knowledge using rough sets to define four types of rough equalities for crisp sets, four types of rough equalities were defined for fuzzy sets in [15]....

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...Here, we modify the definition given in [15] so that it is compatible with the definition of rough fuzzy sets provided by Dubois and Prade [2]....

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...In [15] some examples were provided in order to illustrate the relative efficiencies of the four types of approximate equalities of fuzzy sets....

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...In this paper we introduced the concept of leveled approximate equality by taking rough intuitionistic fuzzy sets instead of rough fuzzy sets considered in [15] in defining approximate equality....

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...The four types of approximate equalities of sets introduced in [12] were recently extended to the context of fuzzy sets by Tripathy et al [15] by using the hybrid notion of rough fuzzy sets....

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### Cites background or methods or result from "An Analysis of Generalised Approxim..."

...This is the most natural and best among the four types as provided in [1]....

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...In order to illustrate the relative efficiencies of the four types of approximate equalities of fuzzy sets several examples were produced in [1]....

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...In [1] the studies of approximate equalities using rough sets were extended by considering the hybrid notion of rough fuzzy set....

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...In [1] it has been established that the properties for approximate equalities established for sets using rough sets could be extended to the context of fuzzy sets by using rough...

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...In [1], all the four types of approximate equalities of sets introduced in [8] were extended to the context of fuzzy sets....

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##### References

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### "An Analysis of Generalised Approxim..." refers background in this paper

...The properties obtained from these properties by interchanging bottom and top approximate equalities are called replacement properties [3, 10, 11, 12, 13]....

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...It is worth noting that each of the above four types of approximate equalities are defined through three notions called bottom equality, top equality and total equality defined in [3]....

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...It was mentioned in [3] that these replacement properties do not hold in general....

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