m-Polar Hesitant Fuzzy TOPSIS (Akram, Adeel & Alcantud 2019, Symmetry 11(6):795) — multi-criteria group decision-making by extending TOPSIS to the m-polar hesitant fuzzy (mHF) set framework; pole-wise mHPIS/mHNIS extraction, mHF Euclidean distance and closeness coefficient ranking
MPF-HF-TOPSIS (m-Polar Hesitant Fuzzy TOPSIS (Akram, Adeel & Alcantud 2019, Symmetry 11(6):795) — multi-criteria group decision-making by extending TOPSIS to the m-polar hesitant fuzzy (mHF) set framework; pole-wise mHPIS/mHNIS extraction, mHF Euclidean distance and closeness coefficient ranking) is a ranking multi-criteria decision-making (MCDM) method introduced by Akram, M., Adeel, A., Alcantud, J. C. R. in 2019. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
Key highlights
- 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.
Intuition
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How it works
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When to use it
Read the result as a complete descending ranking of alternatives a_j by the closeness coefficient E_j' ∈ [0,1] (Eq. 5). E_j' near 1 means the alternative is close to the m-polar hesitant fuzzy positive ideal (mHPIS) and far from the negative ideal (mHNIS); E_j' near 0 means the opposite. The §3.1 case study yields Bn_1 ≻ Bn_3 ≻ Bn_4 ≻ Bn_5 ≻ Bn_2 — Bn_1 is the perfect brand name. To interpret WHY one alternative dominates, inspect the pole-wise membership polygons (viz H4) and the mHPIS/mHNIS per criterion (viz H1).
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.
- Assumes full compensation — a strong score on one criterion can offset a weak score on another.
Common pitfalls
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Sources
- 1.Akram, M., Adeel, A., Alcantud, J. C. R. (2019). Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach. Symmetry (MDPI)
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ScholarGate. (2026, June 2). MPF-HF-TOPSIS. ScholarGate. https://scholargate.app/decision-making/mpf-hf-topsis