We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for so far known approaches: a classical crisp Ganter & Wille's [7] case, a fuzzy Pollandt [12] and Bělohlávek' [2] one and one-sided fuzzy concept lattice [5]. We define appropriate (symmetric) mappings and show that they form a Galois connection. In the end we show that these mappings generate a complete lattice.

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