A comparative study of fuzzy rough sets.(English)Zbl 1004.03043

A new approach to the fuzzification of well-known Pawlak’s rough sets is discussed. New sets, called $$({\mathcal I},{\mathcal T})$$-fuzzy sets, are introduced, where $${\mathcal I}$$ is an implicator, i.e., a function $${\mathcal I}:[0,1]^2 \to[0,1]$$ satisfying the conditions: $${\mathcal I}(1,0)=0$$, $${\mathcal I}(0,0)={\mathcal I}(0,1)={\mathcal I}(1,1)=1$$, and $${\mathcal T}$$ is a triangular norm, i.e., an increasing, associative and commutative mapping $${\mathcal T}:[0,1]^2\to [0,1]$$ that satisfies the boundary condition for all $$x\in[0,1]:{\mathcal T}(x,1)=x$$. The basic properties of the new sets are given.

MSC:

 3e+72 Theory of fuzzy sets, etc.
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References:

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