Topsis-Sparsh-Gupta-102317228 1.0.0

A Python implementation of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method.

Topsis-Sparsh_Gupta-102317228

A Python implementation of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method for multi-criteria decision making.

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📌 What is TOPSIS?

TOPSIS is a Multi-Criteria Decision Making (MCDM) technique used to rank alternatives based on:

• Distance from the Ideal Best solution
• Distance from the Ideal Worst solution

The best alternative is:

• Closest to the Ideal Best
• Farthest from the Ideal Worst

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⚙️ Mathematical Steps

1. Normalize the decision matrix
2. Multiply by weights
3. Determine Ideal Best and Ideal Worst
4. Compute Euclidean distances
5. Calculate relative closeness score
6. Rank alternatives

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📊 Algorithm Flow (Mermaid Diagram)

flowchart TD
    A[Start] --> B[Read Input File]
    B --> C[Validate Data]
    C --> D[Normalize Matrix]
    D --> E[Apply Weights]
    E --> F[Find Ideal Best & Worst]
    F --> G[Compute Distances]
    G --> H[Calculate TOPSIS Score]
    H --> I[Rank Alternatives]
    I --> J[Save Output File]
    J --> K[End]

📥 Installation

Install from PyPI:

pip install Topsis-Sparsh Gupta-102317228

Or install locally:

pip install .

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🚀 Usage (Command Line)

topsis <InputFile> <Weights> <Impacts> <OutputFile>

Example

topsis data.xlsx "1,1,1,2" "+,+,-,+" result.csv

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📄 Input Format

The input file must:

• Contain at least 3 columns
• First column: Identifier (Name/ID)
• Remaining columns: Numeric values only
• Weights must be comma-separated
• Impacts must be '+' or '-'

Example Input

Fund	P1	P2	P3	P4
M1	0.67	0.45	5.6	12.56
M2	0.6	0.36	3.5	14.47

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📤 Output Format

The output file contains:

• Original data
• Topsis Score column
• Rank column

Higher score = Better rank

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🧮 Mathematical Formula

Normalization

[ R_{ij} = \frac{x_{ij}}{\sqrt{\sum x_{ij}^2}} ]

Weighted Matrix

[ V_{ij} = w_j \cdot R_{ij} ]

Distance Measures

[ S_i^+ = \sqrt{\sum (V_{ij} - A_j^+)^2} ]

[ S_i^- = \sqrt{\sum (V_{ij} - A_j^-)^2} ]

Topsis Score

[ C_i = \frac{S_i^-}{S_i^+ + S_i^-} ]

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🛑 Error Handling

The program checks for:

• File not found
• Incorrect number of parameters
• Less than 3 columns
• Non-numeric values
• Mismatch in weights and impacts
• Invalid impacts

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🧠 Requirements

• Python 3.7+
• numpy
• pandas
• openpyxl

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👤 Author

Sparsh Gupta
102317228

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📜 License

MIT License