Frank T-norm — Frank family of associative t-norms and t-conorms
TNORM-FRANK (Frank T-norm — Frank family of associative t-norms and t-conorms) is a t-norm multi-criteria decision-making (MCDM) method introduced by Frank, M.J. in 1979. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
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When to use it
Choose s based on desired compensation: s≈1 (product) → moderate; s→∞ (Łukasiewicz) → bounded; s→0 (min) → non-compensatory. In IFN MCDM: report results for s=1,2,5 to assess sensitivity.
Strengths & limitations
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
- Results depend on the chosen normalisation, weights, and parameter settings.
Sources
- Frank, M.J. (1979). On the simultaneous associativity of F(x,y) and x+y-F(x,y). Aequationes Mathematicae link ↗
How to cite this page
ScholarGate. (2026, June 2). Frank T-norm — Frank family of associative t-norms and t-conorms. ScholarGate. https://scholargate.app/en/decision-making/tnorm-frank
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