CF-TOPSIS - Complex extension of TOPSIS

Overview

cf-topsis extends TOPSIS to handle Complex uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Complex Fuzzy Set (CFS: amplitude r ∈ [0,1], phase ω ∈ [0,2π]) algebra. The final scores are defuzzified via real part: r·cos(ω) before ranking.

Output

utility, higher is better

Data

Complex Intuitionistic Fuzzy, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Complex Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid Complex Fuzzy numbers/tuples
• Underlying crisp method's compensation assumption holds in uncertain space
• All decision-maker(s) and experts use the same linguistic/uncertainty scale

Edge cases and pitfalls

• Value-space violation: ensure all entries satisfy CFS: r(x)·e^{iω(x)} where r ∈ [0,1], ω ∈ [0,2π] before computation.

• Defuzzification method affects ranking: real part: r·cos(ω) is the canonical choice but alternatives exist.

Works with

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