TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) is a multi-criteria decision-making (MCDM) method used to determine the best alternative among a set of alternatives based on their similarity to an ideal solution. It is widely used in fields such as engineering, management, environmental studies, and economics where decisions need to be made considering multiple conflicting criteria.

**Here’s how TOPSIS works:**

Criteria Identification : Identify a set of criteria (attributes) that are relevant to the decision problem. These criteria should represent different aspects of the alternatives being evaluated.

Normalization : Normalize the decision matrix. This involves transforming the raw data for each criterion (which might have different scales and units) into dimensionless scores that are comparable. Normalization is typically done to convert criteria values into a common scale (e.g., using min-max normalization or standardization).

Weight Assignment : Assign weights to the criteria based on their relative importance in the decision. The weights reflect the relative significance or priority of each criterion in relation to the others.

Ideal and Anti-Ideal Solution : Determine the ideal and anti-ideal solutions for each criterion:

– Ideal Solution: For benefit criteria (where larger values are better), the ideal solution is the maximum value observed across all alternatives for each criterion.

– Anti-Ideal Solution : For cost criteria (where smaller values are better), the anti-ideal solution is the minimum value observed across all alternatives for each criterion.

Similarity Calculation: Calculate the similarity of each alternative to the ideal solution and the anti-ideal solution using a distance measure (often Euclidean distance or other distance metrics):

– Similarity to Ideal Solution : Measure the distance of each alternative from the ideal solution.

– Similarity to Anti-Ideal Solution : Measure the distance of each alternative from the anti-ideal solution.

TOPSIS Score : Compute the TOPSIS score (performance index) for each alternative based on its proximity to the ideal solution and its distance from the anti-ideal solution Alternatives with higher TOPSIS scores are considered better choices as they are closer to the ideal solution and farther from the anti-ideal solution.

Ranking : Rank the alternatives based on their TOPSIS scores in descending order. The alternative with the highest TOPSIS score is considered the most preferred solution.

TOPSIS is favored for its simplicity and intuitive appeal in decision-making scenarios involving multiple criteria. It provides a systematic way to rank alternatives by balancing their closeness to the ideal and their distance from the anti-ideal solutions across multiple dimensions.