List

Entropy Weight Topsis

Entropy Weight Topsis is a multi-attribute decision analysis method that combines the entropy method with the TOPSIS method. It essentially follows the TOPSIS approach but applies entropy-based weighting before performing TOPSIS calculations. It is located in SPSSAU -> Comprehensive Evaluation -> Entropy Weight Topsis.

SPSSAU Operations

To begin, drag the analysis items to the right-side box and click 'Start'. The research objects can be dragged to the 'Label' box for analysis. SPSSAU includes the parameter Save Process Values.

Save Process Values: When selected, SPSSAU saves 'Distance to Positive Ideal', 'Distance to Negative Ideal', and Relative Closeness (C) as new titles similar to "DPlus_****", "DMinus_****", and "C_****".

SPSSAU Data Format

Entropy Method determines the weight of indicators, where each indicator corresponds to one column of data. Sample IDs are identifiers only and are generally year-based data that do not need to be included in the analysis

Algorithm

Steps for Entropy Weight Topsis:

1.Prepare the Matrix

Prepare the data matrix as follows:

$X = (\begin{matrix} x_{11} & x_{12} & x_{13} & \dots & x_{1 n} \\ x_{21} & x_{22} & x_{23} & \dots & x_{2 n} \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ x_{m 1} & x_{m 2} & x_{m 3} & \dots & x_{m n} \end{matrix})$

Note:

Researchers may need to standardize the data. This can be done by SPSSAU -> Data Processing -> Generate Variables.

2.Non-negative Shift

If any column in the original data matrix X contains values <= 0, SPSSAU automatically applies a 'non-negative shift' of 0.01 to get X_new:

$x_{i j} = | min (x_{* j}) | + 0.01$

When x_*j <= 0, the system applies the above processing.

Note:

Researchers can also manually apply this shift by SPSSAU -> Data Processing -> Generate Variables.

3.Entropy-Based Weight Calculation

Calculate weights using the entropy method:

$W = (\begin{matrix} w_{1} \\ w_{2} \\ w_{3} \\ ⋮ \\ w_{n} \end{matrix})$

4.Obtain Weighted Data

Apply the entropy-based weights to obtain the weighted data matrix:

$X_{n e w} 2 = (\begin{matrix} x_{11} \cdot w_{1} & x_{12} \cdot w_{2} & x_{13} \cdot w_{3} & \dots & x_{1 n} \cdot w_{n} \\ x_{21} \cdot w_{1} & x_{22} \cdot w_{2} & x_{23} \cdot w_{3} & \dots & x_{2 n} \cdot w_{n} \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ x_{m 1} \cdot w_{1} & x_{m 2} \cdot w_{2} & x_{m 3} \cdot w_{3} & \dots & x_{m n} \cdot w_{n} \end{matrix})$

5.Conduct the TOPSIS analysis using X_new2.

6.SPSSAU also outputs average evaluation indicators based on , which may include data after 'non-negative shift'.

References

【1】The SPSSAU project (2024). SPSSAU. (Version 24.0) [Online Application Software]. Retrieved from https://www.spssau.com.

【2】周俊,马世澎. SPSSAU科研数据分析方法与应用.第1版[M]. 电子工业出版社,2024.

【3】Chen C T. Extensions of the TOPSIS for group decision-making under fuzzy environment[J]. Fuzzy Sets & Systems, 2000, 114(1):1-9.

【4】孙振球,徐勇勇. 医学统计学.第4版[M]. 人民卫生出版社,2017.