VIKOR
A method for ranking and selecting the best compromise solution among multiple alternatives with conflicting criteria, by finding the closest option to the ideal solution while balancing group utility and individual regret.
Understanding VIKOR
What is VIKOR?
VIKOR is a multi-criteria decision-making method that ranks alternatives by finding a compromise solution closest to the ideal — balancing overall group utility with minimum individual regret.
When to Use VIKOR
When criteria conflict and no single option dominates on all of them, and you need a practical compromise ranking rather than a theoretical optimum.
Why Choose VIKOR
- Balances group benefit with worst-case regret, unlike distance-only methods
- Simple, transparent computation
- Works well with conflicting, non-commensurable criteria
- Provides both a ranking and a stability check on the result
Where VIKOR Is Applied
Supplier selection, engineering/material design, energy and environmental project evaluation, investment decisions, healthcare management, infrastructure planning.
How to Calculate VIKOR — Step by Step
Step 1: Build the Decision Matrix
List alternatives and criteria, and assign a performance value to each alternative for each criterion.
Step 2: Determine Criteria Weights
Assign a weight to each criterion reflecting its relative importance (weights sum to 1).
Step 3: Determine Best and Worst Values
For each criterion, find the best value f_j* (max for benefit criteria, min for cost criteria) and the worst value f_j⁻ (min for benefit, max for cost).
Step 4: Compute the Utility Measure (S)
For each alternative, calculate S_i — the weighted sum of normalized distances from the best value across all criteria (represents overall group utility).
Step 5: Compute the Regret Measure (R)
For each alternative, calculate R_i — the maximum weighted normalized distance from the best value among all criteria (represents the worst individual regret).
Step 6: Compute the VIKOR Index (Q)
Combine S and R into a single index Q_i using a weighting parameter v (typically v = 0.5) that balances group utility against individual regret.
Step 7: Rank the Alternatives
Rank alternatives by S, R, and Q separately (ascending order — lower is better).
Step 8: Propose the Compromise Solution
Check the acceptable advantage and acceptable stability conditions on the alternative with the lowest Q. If both conditions hold, it's the compromise solution; otherwise, a set of compromise alternatives is proposed.
See It in Action
Want to see VIKOR applied to a real decision problem? Explore worked examples showing the method in action, from setting up the decision matrix to identifying the final compromise solution
No installation required
Advantages and Limitations of VIKOR
| Advantages | Limitations |
| ✓ Provides a compromise solution even when no alternative dominates on all criteria | ! Choice of the parameter v can influence the final ranking |
| ✓ Balances group utility and individual regret in one index | ! Requires normalization, which can be sensitive to data scale |
| ✓ Simple, transparent computation compared to more complex MCDM methods | ! Ranking stability depends on the closeness of alternatives' scores |
| ✓ Includes a built-in stability check on the proposed compromise solution | ! Less effective with a very large number of alternatives or criteria |
How VIKOR Compares to Other Methods
VIKOR vs. Fuzzy VIKOR
Classical VIKOR uses precise numerical judgments, while Fuzzy VIKOR incorporates fuzzy numbers to handle uncertainty and imprecision in decision-makers' evaluations.
VIKOR vs. TOPSIS
Both rank alternatives by closeness to an ideal solution, but VIKOR explicitly balances group utility (S) and individual regret (R) via a compromise index, while TOPSIS ranks by relative closeness to the ideal alone — making VIKOR better suited to compromise-seeking decisions.
VIKOR vs. AHP
AHP focuses on structuring a decision hierarchy and deriving criteria weights through pairwise comparisons, while VIKOR focuses on ranking alternatives once weights are known — the two are often used together, with AHP supplying weights for VIKOR.
VIKOR Books
Explore key books that cover VIKOR in depth — from its theoretical foundations to applied case studies across engineering, business, and management decisions.
Fuzzy Multi-Criteria Decision Making
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Fuzzy TOPSIS Logic, Approaches, and Case Studies
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VIKOR Articles
Academic and industry articles on VIKOR's methodology and use cases.
VIKOR Blog Posts
Read practical guides, tutorials, and case studies about applying VIKOR
Fuzzy Multi-Criteria Decision Making
Overview Editors: Cengiz KahramanClassifies...
Fuzzy TOPSIS Logic, Approaches, and Case Studies
Fuzzy TOPSISLogic, Approaches, and Case Studies...
Swara FAQ
Discover the most common questions and answers...
VIKOR FAQ
Answers to the most common questions about VIKOR
What does VIKOR stand for?
VIKOR comes from the Serbian phrase "VIseKriterijumska Optimizacija I Kompromisno Resenje," meaning "Multicriteria Optimization and Compromise Solution."
How is VIKOR different from TOPSIS?
VIKOR ranks alternatives using a compromise index that balances group utility and individual regret, while TOPSIS ranks based on relative closeness to an ideal solution alone.
What does the parameter v represent in VIKOR?
It's a weight (usually 0.5) that balances the strategy of maximum group utility against minimum individual regret when combining S and R into the final index Q.
Can VIKOR be used with fuzzy data?
Yes — Fuzzy VIKOR extends the method to handle uncertain or imprecise judgments using fuzzy numbers.
Yes — Fuzzy VIKOR extends the method to handle uncertain or imprecise judgments using fuzzy numbers.
It works best with a moderate number of alternatives and criteria; very large decision problems can make interpretation and stability checks harder.
Can I perform DEMATEL analysis online?
Yes, you can use the DEMATEL online software at OnlineOutput.com.
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