Implementation of TOPSIS decision making
Inspired by TOPSIS-Python (python2).
Our python 3 code follows the same strucutre, definign a topsis class, but uses numpy linear algebra in order to modernise, optimise, and remove redundant code.
What is TOPSIS
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) originated in the 1980s as a multi-criteria decision making method. TOPSIS chooses the altenrative of shortest Euclidean distance from the idael solution, and fartherst distance from the negative-ideal solution. More details at wikipedia. The TOPSIS algorithm is succintly explained in this paper comparing TOPSIS and VIKOR methods
TOPSIS-Python can be run as in the following example:
>>> import numpy as np >>> from topsis import topsis >>> a = [[7, 9, 9, 8], [8, 7, 8, 7], [9, 6, 8, 9], [6, 7, 8, 6]] >>> w = [0.1, 0.4, 0.3, 0.2] >>> I = np.array([1, 1, 1, 0] >>> decision = topsis.topsis(a, w, I)
The decision matrix (
a) should be constructed with each row representing
an alternative, and each column representing a criterion. We have used an
example given in TOPSIS Method in MADM (Dr. Farhad Faez)
w) is not already normalised will be normalised upon
initialisation. Information on benefit (1) cost (0) criteria should be provided
By default, the optimisation (TOPSIS calculation) does not take place. No values
are stored in
These can be calculated, either by calling
decision.calc(), or by calling a
representation of the decision (which will itself call
>>> decision Alternatives ranking C: [0.74269409 0.40359933 0.17586999 0.44142927] Best alternative a: [7. 9. 9. 8.]
The rankings are saved in
decision.C, with the highest ranking $
offering us the best decision, and lowest ranking $
0.17586999$ offering the
worst decision making, according to TOPSIS method.
We are also then shown the best alternative index (which happens to be index 0 in this example), and the associated criteria coefficients of this alternative.
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