PiF-TOPSIS — Picture extension of TOPSIS
PIF-TOPSIS (PiF-TOPSIS — Picture extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Cuong, B. C., Kreinovich, V. in 2013. 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
PIF-TOPSIS follows Sindhu 2019: build the PF decision matrix R, extract PFPIS/PFNIS per-criterion using extrema rules (Eq.7-8), compute weighted absolute-difference similarity with a max-term (Eq.6), and rank by relative closeness CR_i = S⁺/(S⁺+S⁻). Weights may be DM-supplied (default) or derived from an LP model (Sindhu Eq.11 — optional F4/F5). Highest CR_i is the best alternative.
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.
- May exhibit rank reversal when alternatives are added to or removed from the set.
- Assumes full compensation — a strong score on one criterion can offset a weak score on another.
Common pitfalls
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Sources
- 1.Cuong, B. C., Kreinovich, V. (2013). Picture fuzzy sets — A new concept for computational intelligence problems. 2013 Third World Congress on Information and Communication Technologies (WICT 2013)
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ScholarGate. (2026, June 2). PIF-TOPSIS. ScholarGate. https://scholargate.app/decision-making/pif-topsis