We present a new approach for handling fuzzy triadic data in the setting of Formal Concept Analysis. The starting point is a fuzzy-valued triadic context (K₁, K₂,K₃,Y), where K₁, K₂ and K₃ are sets and Y is a ternary fuzzy relation between these sets. First, we generalise the methods of Triadic Concept Analysis to our setting and show how they fit other approaches to Fuzzy Triadic Concept Analysis. Afterwards, we develop the fuzzy-valued triadic implications as counterparts of the various triadic implications studied in the literature. These are of major importance for the integrity of Fuzzy and Fuzzy-Valued Triadic Concept Analysis.