PHF-TOPSIS - Probabilistic Hesitant extension of TOPSIS

Overview

phf-topsis extends TOPSIS to handle Probabilistic Hesitant uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Probabilistic Hesitant Fuzzy Element (PHFE: {γ|p} pairs) algebra. The final scores are defuzzified via E[PHFE] = Σ γ_k p_k before ranking.

Output

utility, higher is better

Data

Hesitant, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Probabilistic Hesitant MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid Probabilistic Hesitant 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 PHFE: {γ_k|p_k} where γ_k ∈ [0,1], Σ p_k ≤ 1 before computation.

• Defuzzification method affects ranking: E[PHFE] = Σ γ_k p_k is the canonical choice but alternatives exist.

Works with

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