TOPSIS may be considered as an extension of the Ideal Point Method.
TOPSIS orders a set of alternatives on the basis of their separation from the ideal and anti-ideal points (Hwang & Yoon, 1981).
These points represent hypothetical alternatives that consist of the most desirable (ideal) and the less desirable (anti-ideal)
levels of each criterion across the alternatives under consideration.
Within the TOPSIS method the following distance to the 'ideal point' is used:
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(14) |
where wj is a weight assigned to the j-th criterion, vij is the standardized criterion value of
the i-th alternative, v+j is the ideal value for the j-th criterion, p is a parameter (p=1,2,
∞ is the most often used).
The negative (anti) ideal point and distances si- are defined similarly:
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(15) |
There are several decision rules which are used within TOPSIS. The following rule is most often used:
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(16) |
(the case p=2 in (14-15) and the formula (16) are implemented in DecernsSDSS).
The Alternative(s) with the highest ci+ is considered as the "best" one.
TOPSIS is very attractive method to decision problems when the dependency among criteria is difficult to test or verify.
That is especially true in case of spatial decision problems, which typically involve complex interdependencies among
attributes.
Details and discussion of these (and some other) methods may be found in the publications indicated below.