FF-SAW - Fermatean extension of FF-SAW

Overview

ff-saw extends FF-SAW to handle Fermatean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Fermatean Fuzzy Set (FFS: μ, ν; μ³+ν³ ≤ 1) algebra. The final scores are defuzzified via score function S = μ³ − ν³ before ranking.

Output

utility, higher is better

Data

Fermatean Fuzzy, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

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

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid Fermatean 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 FFS: μ³+ν³ ≤ 1 (q=3 special case of q-ROF) before computation.

• Defuzzification method affects ranking: score function S = μ³ − ν³ is the canonical choice but alternatives exist.

Works with

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