# shannon entropy

An entropy method is one of the methods based on the existence of information in the decision table. So, in order to solve an issue in an entropy manner, we must make a decision table. In the following, the steps of the entropy method are explained first and, in the next step, an entropy method is given as a fully functional example.

**Entropy method steps**

Step 1: Set up a decision table: The first step in the process of entropy is the formation of a decision table. Therefore, in order to calculate the weight of the indices using the entropy method, the problem decision table must first be formed, since, as stated, the decision table is considered as the input of the entropy method. Matters indicate the decision making as follows.

Step 2) Normalizing the decision table: The second step is the normalization of the entropy procedure or the non-scaleing of the decision table. Normalization uses a simple normalization method, the same as the arithmetic mean. The simple normalization relation is as follows.

Step 3: Calculate the entropy of each index: At this stage, the entropy of each indicator should be calculated using the following equation.

Note: The K value will cause the entropy value of each index to remain between zero and one.

Step 4: Calculate the distance of each index from its entropy (dj): at this stage, we must find the distance of each of the indicators from the amount of entropy that was calculated in the previous step. To do this, use the following equation.

Step 5: Calculate the weight of each indicator: At this stage we calculate the weight of each indicator using the following equation.

Note: Because the credibility of the weight derived from the entropy method depends on the validity of the data, so to increase the weight of the weight, this method can be combined with one another.

Example) A dam construction project has been delegated to the “A” ministry. This project can be carried out by executive personnel in the ministry (option A1), internal contractor (option A2), or external contractor (option A3). The ministry is looking to select the best contractor (option) to give it a dam construction project.

To assess contractors, five indicators of “labor hardness”, “capacity”, “national reputation”, “strength” and “cost” have been used. Calculate the weight of each index using the entropy method.

Step 1: Formulate a decision table: As stated, the first stage of the entropy process is the formation of a decision table. Using the questionnaire, the data related to the decision table was obtained as follows.

Step 2: Normalization of the decision table: Using the relationship expressed to normalize the problem-solving table.

Step 3: Calculate the entropy of each index: At this stage, we calculate the entropy of each of the indices using the proposed relationship. The table below gives the entropy value of each indicator in each option.

Note: To calculate the entropy of each index, the entropy of each indicator must be combined for all the options presented in the table above (sum of the above table columns).

By calculating the entropy of each index, we can calculate the degree of diversion of each indicator, the weight of each indicator and the rating of each payment index (stages 4 and below) by comparing the ratios presented. The following table provides the results of these calculations.

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