The fuzzy VIKOR method was first developed by Opricovic (2007), which has been applied to rank the alternatives in a fuzzy environment.

The Steps of the Fuzzy VIKOR Method

Step 1: Create a decision matrix

In this study there are 5 criteria and 5 alternatives that are ranked based on FUZZY VIKOR method. The table below shows the type of criterion and weight assigned to each criterion.

Characteristics of Criteria

The following table shows the fuzzy scale used in the model.

Fuzzy Scale

The alternatives in terms of various criteria are evaluated and the results of the decision matrix are shown as follows. Note that if multiple experts participate in the evaluation, then the matrix below represents the arithmetic mean of all experts.

Decision Matrix

Step 2: Determine the positive ideal solution and negative ideal solution

Positive and negative ideal solutions of each criterion can be obtained as follows.

If the criterion is positive, the positive ideal solution ( ) and negative ideal solution ( ) can be obtained using the following relations:

i =1, 2, …., n

i=1, 2, …., n

If the criterion is negative, the positive ideal solution ( ) and negative ideal solution ( ) can be obtained using the following relations:

i=1, 2, …., n

i=1, 2, …., n

The table below shows the positive and negative ideal values.

Positive and negative ideal solutions of the criteria

Step 3: Compute the normalized decision matrix

Based on the positive and negative ideal solutions, a normalized decision matrix can be calculated by the following relation:

Positive ideal solution

Negative ideal solution

Where

The table below shows the normalized values of the evaluation matrix.

The normalized decision matrix

Step 4: Compute the values and :

First, the normalized matrix is transformed into weighted normalized decision matrix and then the values and can be calculated as follows:

If and

Step 5: Calculate the VIKOR index (Q)

The value of Q can be calculated as follows.

If

Where,

The variable v representing the maximum group utility is equal to 0.5 in this study.

The fuzzy numbers S, R and Q can be transformed into crisp numbers using the following formula.

If ( is expreseed as a fuzzy number)

table below shows the fuzzy values S, R, and Q.

The Fuzzy Values S, R, And Q

table below shows the crisp values S, R and Q and Ranking the alternatives based on R, S and Q.

The crisp values S, R, Q and alternatives ranking

Step 6: Proposing a Compromise solution

In this step, a decision is made based on the values R, S and Q for the alternatives sorted in descending order. There are two conditions that need to be made a decision, and a set of compromise solutions can be proposed following these two conditions.

Condition 1 . Acceptable advantage: where is the alternative with first position and is the alternative with second position in the ranking list by Q. m is number of alternatives.

Condition 2 . Acceptable stability in decision making: The alternative must also be the best ranked by S or/and R.

If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of:

Solution 1. Alternatives if Condition 1 is not satisfied; Alternative is determined by for maximum M (the positions of these alternatives are ‘‘in closeness’’).

Solution 2. Alternatives and if only condition 2 is not satisfied.

Solution 3. Alternative with the minimum Q value will be selected as the best Alternative if both conditions are satisfied.

result of the conditions survey is shown in the following table.

result of the conditions survey

Therefore, Communicative Approach,Grammar-Translation\n Method,Audio-Lingual Method,Task-Based Learning,Total Physical\n Response (TPR), are selected as the final alternatives.