Fuzzy Vikor
A method for ranking alternatives and finding a compromise solution among conflicting criteria, in situations where judgments or data are not certain and are expressed using fuzzy numbers.
Understanding Fuzzy Vikor
What is Fuzzy VIKOR?
Fuzzy VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) is a multi-criteria decision-making method used to rank and select alternatives based on multiple conflicting criteria. Unlike the classical VIKOR method, which relies on crisp numerical judgments, Fuzzy VIKOR incorporates fuzzy numbers to handle the uncertainty and vagueness that often exist in expert opinions, and identifies a compromise solution that balances overall group utility with individual regret.
When to Use Fuzzy VIKOR
This makes it especially useful when decision-makers cannot express their ratings with exact numbers — for example, when selecting the best supplier under conflicting cost and quality criteria, evaluating investment options with incomplete information, or ranking alternatives where no single option dominates on every criterion. By converting linguistic terms like “good” or “very poor” into triangular fuzzy numbers, the method produces a more realistic and balanced ranking than its classical counterpart.
Why Choose Fuzzy VIKOR
Choose Fuzzy VIKOR over other ranking methods whenever your criteria are conflicting and non-commensurable, and you need a compromise solution rather than one that is simply closest to an ideal point — this is common in situations where full consensus among criteria is unlikely and a balanced trade-off is more realistic than an extreme choice.
Where Fuzzy VIKOR Is Applied
Fuzzy VIKOR is widely applied in supplier selection, project evaluation, healthcare, environmental management and …. , where alternatives must be ranked under uncertain, conflicting, and subjective criteria.
How to Calculate Fuzzy VIKOR — Step by Step
Step 1: Define Alternatives and Criteria
List the set of alternatives you are comparing and the criteria you will evaluate them against.
Step 2: Collect Expert Judgments
Ask experts to rate each alternative on each criterion using linguistic terms (e.g., “very poor,” “poor,” “fair,” “good,” “very good”), and to rate the importance of each criterion the same way.
Step 3: Convert to Fuzzy Numbers
Translate each linguistic rating into a triangular fuzzy number (a lower, middle, and upper value), then aggregate expert responses to build the fuzzy decision matrix and the fuzzy criteria weights.
Step 4: Normalize the Fuzzy Decision Matrix
Scale the fuzzy ratings for benefit and cost criteria onto a consistent range so they can be compared and combined fairly.
Step 5: Determine the Fuzzy Best and Worst Values
For each criterion, identify the fuzzy best value (f*) — the most favorable rating achieved by any alternative — and the fuzzy worst value (f⁻) — the least favorable one.
Step 6: Calculate S and R Values
For each alternative, compute the weighted fuzzy distance from the best value across all criteria (S — overall utility) and the maximum weighted fuzzy distance on any single criterion (R — individual regret).
Step 7: Calculate the Q Value
Combine S and R for each alternative into a single VIKOR index (Q), using a strategy weight (v) that balances group utility against individual regret — then defuzzify Q into a crisp score.
Step 8: Rank Alternatives and Check Conditions
Rank the alternatives by increasing Q value, then verify the “acceptable advantage” and “acceptable stability” conditions to confirm whether the top-ranked alternative is a valid compromise solution.
See It in Action
Curious how Fuzzy VIKOR works? Walk through a solved example — or skip straight to analyzing your own criteria with our free online tool.
No installation required
Advantages and Limitations of Fuzzy VIKOR
| Advantages | Limitations |
| ✓ Handles uncertain or vague expert judgments | ! Requires defining a strategy weight (v), which involves subjective judgment |
| ✓ Finds a compromise solution close to the ideal, even when criteria conflict | ! Defuzzification can introduce subjectivity |
| ✓ Considers both group utility (S) and individual regret (R) simultaneously | ! Results can be sensitive to the number and scale of alternatives |
| ✓ Provides a ranking plus a stability check, not just a raw score | ! Not designed for analyzing cause-and-effect relationships — only for ranking alternatives |
How Fuzzy VIKOR Compares to Other Methods
Fuzzy VIKOR vs. Classical VIKOR
Classical VIKOR uses crisp numerical judgments, while Fuzzy VIKOR captures uncertainty through fuzzy numbers — making it more suitable when expert opinions are vague, linguistic, or inconsistent.
Fuzzy VIKOR vs. Fuzzy TOPSIS
Both methods rank alternatives based on distance from ideal solutions, but Fuzzy VIKOR balances group utility and individual regret through a compromise ranking, while Fuzzy TOPSIS ranks alternatives purely by closeness to the ideal solution — Fuzzy VIKOR is often preferred when a true trade-off compromise is needed rather than a simple closeness score.
Fuzzy VIKOR vs. Fuzzy AHP
Fuzzy AHP is used to derive criteria weights through pairwise comparisons, while Fuzzy VIKOR uses those (or similarly derived) weights to rank alternatives — the two methods are often combined, with Fuzzy AHP supplying weights and Fuzzy VIKOR producing the final ranking.
Fuzzy VIKOR Books
Here are a few of the most commonly referenced books on understanding and applying Fuzzy VIKOR, useful for both academic research and real-world decision-making.
Multi-Criteria Decision Analysis: Case Studies in Disaster Management 1st Edition, Kindle Edition
Author Muhammet Gul (Editor), Melih Yucesan...
New Concepts and Trends of Hybrid Multiple Criteria Decision Making 1st Edition, Kindle Edition
Author Gwo-Hshiung Tzeng (Author), Kao-Yi Shen...
Fuzzy VIKOR Articles
Explore academic and applied research articles that use Fuzzy VIKOR to analyze real-world decision-making problems.
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Fuzzy VIKOR Blog Posts
Read practical guides, tutorials, and case studies about applying Fuzzy VIKOR
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Fuzzy VIKOR FAQ
Answers to the most common questions about Fuzzy VIOR
What is Fuzzy VIKOR?
Fuzzy VIKOR combines the VIKOR method with fuzzy logic to rank alternatives and find a compromise solution under uncertain or linguistic expert judgments.
What are the main steps of Fuzzy VIKOR?
- Define alternatives and criteria
- Collect expert judgments using fuzzy scales
- Build the fuzzy decision matrix and criteria weights
- Normalize the matrix
- Determine the fuzzy best and worst values
- Calculate S and R values
- Calculate the Q value and defuzzify
- Rank alternatives and check acceptable advantage/stability
What do S, R, and Q mean in VIKOR?
S represents an alternative’s overall (group) utility, R represents its worst individual regret on any single criterion, and Q combines both into a final compromise ranking score.
What is the strategy weight (v) in VIKOR?
It’s a value between 0 and 1 that sets how much weight is given to group utility (S) versus individual regret (R) when calculating Q — v = 0.5 is the most common choice.
Where can Fuzzy VIKOR be applied?
In supplier selection, project evaluation, risk analysis, site selection, and other ranking problems where criteria and judgments involve uncertainty.
Can I perform Fuzzy VIKOR analysis online?
Yes, you can use the Fuzzy VIKOR online software at OnlineOutput.com.
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