T-norm
Frank T-norm: Frank family of associative t-norms and t-conorms
Frank, M.J. · 1979
Strengths
- •Continuously parametric from min to Łukasiewicz
- •Includes product and min as special cases
- •Algebraically elegant (generator: log-based)
Limitations
- •s=1 requires special handling (L'Hôpital)
- •Less computationally transparent than Hamacher
Method assistant
Grounded explanations: it explains the method, it does not compute.
Assumptions to verify
- •s > 0, s ≠ 1 (or use limiting formulas)
- •IFN constraint μ+ν ≤ 1 preserved
When not to use
- •Non-fuzzy crisp MCDM: unnecessary complexity
How to cite
Frank, M.J. (1979). On the simultaneous associativity of F(x,y) and x+y-F(x,y). Aequationes Mathematicae. https://doi.org/10.1007/BF02189866