TOPSIS
A method for ranking and selecting the best alternative among multiple options based on their closeness to an ideal solution, using precise numerical judgments across multiple criteria.
Understanding TOPSIS
What is TOPSIS?
A method that ranks alternatives by how close they are to an ideal solution and how far from a negative-ideal (worst-case) solution, using precise numerical data.
When to Use TOPSIS
- Ranking or selecting among several alternatives with multiple criteria
- When data is precise (not fuzzy/uncertain)
- When you want a clear, easy-to-interpret ranking
Why Choose TOPSIS
- Simple, intuitive distance-based logic
- Produces a complete ranking of all alternatives
- Handles many criteria and alternatives well
- Pairs easily with weighting methods like AHP
Where TOPSIS Is Applied
- Supplier/vendor selection
- Product and technology evaluation
- Investment and project prioritization
- Site selection
- Personnel evaluation
How to Calculate TOPSIS — Step by Step
Step 1: Build the Decision Matrix
List alternatives as rows and criteria as columns, with performance values for each alternative against each criterion.
Step 2: Normalize the Decision Matrix
Convert raw values into a comparable scale, typically using vector normalization, so criteria measured in different units can be compared fairly.
Step 3: Construct the Weighted Normalized Matrix
Multiply each normalized value by the weight assigned to its criterion, reflecting the criterion's relative importance.
Step 4: Determine the Ideal and Negative-Ideal Solutions
Identify the best value (ideal solution) and worst value (negative-ideal solution) for each criterion, based on whether it's a benefit or cost criterion.
Step 5: Calculate Separation Measures
Compute the Euclidean distance of each alternative from the ideal solution and from the negative-ideal solution.
Step 6: Calculate the Relative Closeness to the Ideal Solution
Use the two distance measures to calculate a closeness coefficient for each alternative, ranging from 0 to 1.
Step 7: Rank the Alternatives
Sort alternatives by their closeness coefficient, from highest to lowest, to get the final ranking — the alternative with the highest score is the best choice.
See It in Action
See TOPSIS applied to a real decision-making problem, step by step.
No installation required
Advantages and Limitations of TOPSIS
| Advantages | Limitations |
| ✓ Simple, intuitive logic based on geometric distance | ! Requires precise numerical data — struggles with vague or qualitative judgments |
| ✓ Produces a complete ranking of all alternatives | ! Sensitive to the choice of normalization method |
| ✓ Handles a large number of criteria and alternatives efficiently | ! Rank reversal can occur when alternatives are added or removed |
| ✓ Easy to combine with weighting methods like AHP | ! Assumes criteria weights are known and fixed in advance |
How TOPSIS Compares to Other Methods
TOPSIS vs. Fuzzy TOPSIS
Fuzzy TOPSIS uses fuzzy numbers to handle vague or uncertain judgments, while classical TOPSIS relies on precise, crisp numerical data.
TOPSIS vs. VIKOR
Both rank alternatives by closeness to an ideal solution, but VIKOR focuses on finding a compromise solution by balancing group utility and individual regret, while TOPSIS ranks based purely on geometric distance.
TOPSIS vs. AHP
AHP is primarily used to derive criteria weights through pairwise comparisons, while TOPSIS uses those weights (or others) to rank alternatives based on distance from ideal solutions — the two are often used together.
TOPSIS Books
Books that cover TOPSIS's theory and practical applications.
TOPSIS and its Extensions: A Distance-Based MCDM Approach
Author Hsu-Shih Shih, David L. Olson A Brief...
TOPSIS Algorithms for Multiple Objectives Decision Making: Large Scale Programming Approach Illustrated Edition
Author Tarek Abou-El-Enien A Brief Description...
New Concepts and Trends of Hybrid Multiple Criteria Decision Making 1st Edition, Kindle Edition
Author Gwo-Hshiung Tzeng (Author), Kao-Yi Shen...
TOPSIS Articles
Academic and industry articles on TOPSIS's methodology and use cases.
Application of AHP and G-TOPSIS for prioritizing capabilities and related practices for a mature and resilient supply chain during disruption
Safety assessment of existing subgrade retaining wall based on a combined Weighting-TOPSIS evaluation method
Comparison of the criteria affecting the digital innovation performance of the European Union (EU) member and candidate countries with the entropy weight-TOPSIS method and investigation of its importance for SMEs
TOPSIS Blog Posts
Blog posts about TOPSIS, from basics to practical tips.
Introduction to Multi-criteria decision-making (MCDM): A Comprehensive Overview of MCDM
Understanding the Basics of MCDM In the area of...
what is topsis method/
TOPSIS (Technique for Order of Preference by...
Application of TOPSIS Method
The TOPSIS (Technique for Order Preference by...
TOPSIS FAQ
Answers to the most common questions about TOPSIS
What is TOPSIS used for?
TOPSIS is used to rank and select the best alternative among multiple options based on multiple criteria, by measuring closeness to an ideal solution.
How is TOPSIS different from Fuzzy TOPSIS?
Classical TOPSIS uses precise numerical data, while Fuzzy TOPSIS uses fuzzy numbers to handle uncertain or vague judgments.
What are the main steps in TOPSIS?
Normalizing the decision matrix, weighting the criteria, identifying the ideal and negative-ideal solutions, calculating distances, and ranking alternatives by their closeness coefficient.
Can TOPSIS be combined with other methods?
Yes, TOPSIS is often paired with AHP or other weighting methods to determine criteria weights before ranking alternatives.
Can I run TOPSIS online?
Yes, you can perform TOPSIS calculations online for free using the TOPSIS tool on onlineoutput.com.
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