Ranking method · Chen, 2000

Fuzzy TOPSIS

TOPSIS under fuzzy environment (triangular fuzzy numbers)

TOPSIS when your numbers are estimates, not measurements every value carries an uncertainty band.

How it works

1. Turn every crisp value x into the triangular fuzzy number (x·(1−δ), x, x·(1+δ)) δ is your imprecision estimate.
2. Normalize linearly: benefit values ÷ the largest upper bound, cost criteria via the smallest lower bound.
3. Weight the fuzzy values, then measure each alternative's vertex-method distance to the fuzzy positive ideal (1,1,1) and negative ideal (0,0,0).
4. Score by closeness CC = d⁻ / (d⁺ + d⁻); rank by descending CC.

Use it when

• Your data are expert estimates, forecasts, or ratings with honest imprecision.
• You want to check whether the crisp TOPSIS winner survives once measurement fuzziness is admitted.

Watch out for

• This studio fuzzifies crisp data symmetrically with one δ native (l, m, u) input per cell is not supported yet.
• Requires strictly positive data; Chen's normalization breaks on zeros and negatives.
• With δ = 0 it does not reduce to classic TOPSIS: the normalization (linear vs vector) and ideals differ.

Parameters

δ the symmetric fuzzification spread (0 to 0.5, default 0.10).

Cite the method

Chen, C.-T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 114(1), 1-9.

@article{chen2000extensions,
  author  = {Chen, Chen-Tung},
  title   = {Extensions of the {TOPSIS} for group decision-making under fuzzy environment},
  journal = {Fuzzy Sets and Systems},
  volume  = {114},
  number  = {1},
  pages   = {19},
  year    = {2000},
  doi     = {10.1016/S0165-0114(97)00377-1}
}