Mathematical modeling --- distance method of superior and inferior solution (Topsis model)

Application scenario

Among the limitations of AHP,When the data of the indicators at the decision-making level are known rather than given subjectivelyWhen, you need to use the advantage and disadvantage distance method (Topsis model)

Basic process

Indicator type

1. Maximum index-benefit index
2. Minimality index-cost index
3. Intermediate indicators-the closer to a value, the better
4. Interval indicators — the best in a certain interval

Unified indicator type-indicators are positive (all converted to extremely large)

Positive indicators:

1. Change the very small index -> the very large index:
   $max-x$
2. Intermediate -> Very Large Index:
   
3. Interval -> Very Large Index:
   

MM in 2, 3$M$ can be regarded as the maximum deviation from the standard value
Each column is an indicator
One evaluation object for each behavior

Standardized processing

in order toEliminate dimension

Calculate the indicator score and normalize

1. Calculate the score:
   
   ${WITH}^{+}{Z}^{-}toeachrowof\; the\; mostlargevalueand\; themostsmallvaluesetto$
   $D^{+}{D}^{-}for\; thecolumnto\; theamount$

The score is not normalized during the above process

• When different indicators have different score weights:
  
  $w$ can be used when selecting weightsfor the corresponding weights
  : Analytic Hierarchy Process

2. Normalized:
   Finally, the score is normalized

Finally use excel for visualization

Insert in wps --> all charts
For example:

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Reference: Mathematical Modeling Breeze Video