MCDMDecision-makingRankingMath steps
PiF-COPRAS — Picture extension of COPRAS
PIF-COPRAS (PiF-COPRAS — Picture extension of COPRAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Cuong, B. C. 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-copras extends COPRAS to handle Picture uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Picture Fuzzy Set (PiFS: μ, η, ν; μ+η+ν ≤ 1) algebra. The final scores are defuzzified via score function S = μ − ν before ranking.
Strengths & limitations
Strengths
- 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.
Limitations
- 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. (2013). Picture fuzzy sets — first results, parts I and II. Seminar on Neuro-Fuzzy Systems with Applications, Institute of Mathematics, Hanoi (preprint); reprinted as Cuong (2014), J. Comput. Sci. Cybernet. 30, 409–420
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Cite this page
ScholarGate. (2026, June 2). PIF-COPRAS. ScholarGate. https://scholargate.app/decision-making/pif-copras