topsis2

topsis2 is a well-tested, simple, and lightweight TOPSIS implementation with zero dependencies built with TypeScript.

TOPSIS, known as Technique for Order of Preference by Similarity to Ideal Solution, is a multi-criteria decision analysis method. It compares a set of alternatives based on a pre-specified criterion.

Why topsis2? because topsis already taken with no more updates, no TypeScript included, no and has unnecessary dependency. Therefore, topsis2 is expected to be a successor with easier, better use.

Install

# using npm
npm install topsis2
# using yarn
yarn add topsis2

Usage

Import

// in ESM
import topsis2 from 'topsis2';
// in CommonJS
const topsis2 = require('topsis2');

Example

const criteria = [
  { weight: 4, type: 'cost' },
  { weight: 5, type: 'benefit' },
  { weight: 4, type: 'benefit' },
  { weight: 3, type: 'benefit' },
  { weight: 3, type: 'benefit' },
  { weight: 2, type: 'benefit' },
];
const matrix = [
  [3500, 70, 10, 80, 3000, 36],
  [4500, 90, 10, 60, 2500, 48],
  [4000, 80, 9, 90, 2000, 48],
  [4000, 70, 8, 50, 1500, 60],
];
const ranked = topsis2.rank(criteria, matrix);
console.log(ranked);

API

topsis2.rank(criteria: CriteriaAttribute[], matrix: number[][], verbose?: boolean): number[]

This method will rank the alternatives with TOPSIS calculations and return the order of the best alternatives as an array. The parameters of this method are:

• criteria

Criteria are usually in the form of measures or rules or standards used as benchmarks in decision-making. The property of CriteriaAttribute are:

Name	Type	Description
weight	number	A number to estimate the relative importance of criterion. Can be any positive number, including float (required)
type	'benefit' | 'cost'	The benefit criterion is desired to be maximized, i.e. the higher the alternative scores in terms of this criterion, the better the alternative; in contrast, for the cost criterion, a lower value is preferred. Default: 'benefit'

Example use case:

// Criteria / attributes for selection of smartphones
const criteria = [
  { weight: 15, type: 'cost' }, // C1 = Price (lower score better)
  { weight: 25, type: 'benefit' }, // C2 = RAM (higher score better)
  { weight: 25, type: 'benefit' }, // C3 = Storage (higher score better)
  { weight: 15, type: 'benefit' }, // C4 = Battery (higher score better)
  { weight: 20, type: 'benefit' }, // C5 = AnTuTu (higher score better)
];

• matrix

Decision matrix that contains score data from all alternatives. The columns of the matrix must match the number of criteria and the rows of the matrix are the number of alternatives.

Example use case:

	C1 (Price)	C2 (RAM)	C3 (Storage)	C4 (Battery)	C5 (AnTuTu)
A1 (Xiaomi Poco M4 Pro)	$201	6 GB	128 GB	5000 mAh	318444
A2 (Google Pixel 6a)	$283	6 GB	128 GB	4410 mAh	502773
A3 (OnePlus Nord N20 5G)	$200	6 GB	128 GB	4500 mAh	380672
A4 (Samsung Galaxy A54)	$374	6 GB	128 GB	5000 mAh	506678
A5 (Samsung Galaxy A33 5G)	$269	6 GB	128 GB	5000 mAh	394918

The values above are for illustration purposes only taken from GSMArena.com. The table above can be written as follows:

// Alternative scores for smartphone
const matrix = [
  [201, 6, 128, 5000, 318444], // A1 = Xiaomi Poco M4 Pro
  [283, 6, 128, 4410, 502773], // A2 = Google Pixel 6a
  [200, 6, 128, 4500, 380672], // A3 = OnePlus Nord N20 5G
  [374, 6, 128, 5000, 506678], // A4 = Samsung Galaxy A54
  [269, 6, 128, 5000, 394918], // A5 = Samsung Galaxy A33 5G
];

• verbose

Used to generate detailed logging of TOPSIS calculations. Default: false, see the example below.

Example:

const ranked = topsis2.rank(criteria, matrix, true); // using verbose mode
console.log('ranked =', ranked);

Output:

decision matrix (M)
┌─────────┬─────┬────┬─────┬──────┬────────┐
│ (index) │ C1  │ C2 │ C3  │  C4  │   C5   │
├─────────┼─────┼────┼─────┼──────┼────────┤
│   A1    │ 201 │ 6  │ 128 │ 5000 │ 318444 │
│   A2    │ 283 │ 6  │ 128 │ 4410 │ 502773 │
│   A3    │ 200 │ 6  │ 128 │ 4500 │ 380672 │
│   A4    │ 374 │ 6  │ 128 │ 5000 │ 506678 │
│   A5    │ 269 │ 6  │ 128 │ 5000 │ 394918 │
└─────────┴─────┴────┴─────┴──────┴────────┘
normalized decision matrix (R)
┌─────────┬──────┬──────┬──────┬──────┬──────┐
│ (index) │  C1  │  C2  │  C3  │  C4  │  C5  │
├─────────┼──────┼──────┼──────┼──────┼──────┤
│   A1    │ 0.33 │ 0.45 │ 0.45 │ 0.47 │ 0.33 │
│   A2    │ 0.46 │ 0.45 │ 0.45 │ 0.41 │ 0.53 │
│   A3    │ 0.33 │ 0.45 │ 0.45 │ 0.42 │ 0.4  │
│   A4    │ 0.61 │ 0.45 │ 0.45 │ 0.47 │ 0.53 │
│   A5    │ 0.44 │ 0.45 │ 0.45 │ 0.47 │ 0.41 │
└─────────┴──────┴──────┴──────┴──────┴──────┘
weighted normalized decision matrix (WR)
┌─────────┬──────┬───────┬───────┬──────┬───────┐
│ (index) │  C1  │  C2   │  C3   │  C4  │  C5   │
├─────────┼──────┼───────┼───────┼──────┼───────┤
│   A1    │ 4.94 │ 11.18 │ 11.18 │  7   │ 6.67  │
│   A2    │ 6.95 │ 11.18 │ 11.18 │ 6.18 │ 10.53 │
│   A3    │ 4.91 │ 11.18 │ 11.18 │ 6.3  │ 7.97  │
│   A4    │ 9.19 │ 11.18 │ 11.18 │  7   │ 10.61 │
│   A5    │ 6.61 │ 11.18 │ 11.18 │  7   │ 8.27  │
└─────────┴──────┴───────┴───────┴──────┴───────┘
positive ideal solution matrix (A+)
┌─────────┬──────┬───────┬───────┬────┬───────┐
│ (index) │  C1  │  C2   │  C3   │ C4 │  C5   │
├─────────┼──────┼───────┼───────┼────┼───────┤
│    0    │ 4.91 │ 11.18 │ 11.18 │ 7  │ 10.61 │
└─────────┴──────┴───────┴───────┴────┴───────┘
positive negative solution matrix (A-)
┌─────────┬──────┬───────┬───────┬──────┬──────┐
│ (index) │  C1  │  C2   │  C3   │  C4  │  C5  │
├─────────┼──────┼───────┼───────┼──────┼──────┤
│    0    │ 9.19 │ 11.18 │ 11.18 │ 6.18 │ 6.67 │
└─────────┴──────┴───────┴───────┴──────┴──────┘
alternative distance to positive ideal solution matrix (D+)
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│   A1    │  3.94  │
│   A2    │  2.2   │
│   A3    │  2.73  │
│   A4    │  4.28  │
│   A5    │  2.89  │
└─────────┴────────┘
alternative distance to negative ideal solution matrix (D-)
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│   A1    │  4.33  │
│   A2    │  4.46  │
│   A3    │  4.47  │
│   A4    │  4.03  │
│   A5    │  3.15  │
└─────────┴────────┘
preference values (V)
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│   A1    │  0.52  │
│   A2    │  0.67  │
│   A3    │  0.62  │
│   A4    │  0.49  │
│   A5    │  0.52  │
└─────────┴────────┘
sorted preference values (V)
┌─────────┬────────┐
│ (index) │ Values │
├─────────┼────────┤
│   A2    │  0.67  │
│   A3    │  0.62  │
│   A1    │  0.52  │
│   A5    │  0.52  │
│   A4    │  0.49  │
└─────────┴────────┘

ranked = [ 1, 2, 0, 4, 3 ]

The results above indicate an alternative with index 1 or A2 (Google Pixel 6a) is the best smartphone from the TOPSIS calculation followed by A3, A1, A5 and A4.

topsis2.best(criteria: CriteriaAttribute[], matrix: number[][], verbose?: boolean): number[]

Same as the topsis2.rank method but immediately returns the index of the best ranking alternative.

Example:

const best = topsis2.best(criteria, matrix, false);
console.log('best =', best);

Output:

best = 1

Testing

This library is well tested. You can test the code as follows:

# use npm
npm test
# use yarn
yarn test

Contribute

If you have anything to contribute, or functionality that you lack - you are more than welcome to participate in this!

Additions to unit testing are very welcome.

License

Feel free to use this library under the conditions of the MIT license.