n-Dimensional Intervals and Fuzzy S-implications

As a relevant extension of fuzzy sets, n-dimensional fuzzy sets consider membership degrees as ordered n-tuples on U = [0, 1], providing n-dimensional intervals on Ln(U). As our main contribution, n-dimensional fuzzy implications are studied considering duality and conjugation operators. Additionally, the conditions over that main properties are preserved based on their representability from Un to Ln(U) are also presented. Some results in the class of S-implications obtained from t-representable conorms and involutive n-dimensional fuzzy negations on Ln(U) are discussed.

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