## 7 Comparison with Other Multi-Criteria Decision-Making Techniques
### Brief Discussion of Other MCDM Techniques  
Some previous studies employed other MCDM techniques for the turbine selection problem. These techniques include the weighted sum method (WSM) [22], fuzzy logic (FL) [18; 19; 20], and goal programming (GP) [21; 23]. This study adapted the approaches presented in the above studies according to the model presented in Section 5 consisting of five selection criteria. A brief discussion of the aforementioned three methods in the context of the turbine selection problem is presented below for the sake of comprehensiveness. Detailed discussion can be found in the references mentioned above. The weighted sum method has been widely applied to MCDM problems, since it is simple and time efficient [41]. The basic approach of WSM is the aggregation of criteria to form an overall decision function. A precondition of the aggregation is that the decision criteria are normalized so as to overcome the incommensurability issue. Once the criteria are normalized, weights are assigned to each decision criterion as per the aspirations of the decision-maker. Following this, the weighted normalized criteria are aggregated using an aggregation function, which generates the output in the form of a scalar value. A necessary requirement is that the sum of all weights should not exceed 1. The weighted sum approach using the five turbine selection criteria requires that upper limit for each criterion is defined. These upper limits are required for the purpose of normalization of criteria. Note that in the context of turbine selection problem, the weighted sum approach deals with the problem as a maximization problem. That is, the interest is in finding the turbines where hub height and zero percentage are minimized, while wind speed, rated percentage, and annual energy production are maximized. Accordingly, the following equation is used for the decision. \[W(t)=w_{1}[1-(\frac{HH}{max\;HH})]+w_{2}(\frac{WS}{max\;WS})+w_{3}[1-(\frac{ZP }{max\;ZP})]+w_{4}(\frac{RP}{max\;RP})+w_{5}(\frac{AEP}{max\;AEP}) \tag{8}\]  
In the above equation, \(W(t)\) defines the weighted sum of turbine \(t\). Each fraction in Equation (1) represents the normalized value of a selection criterion. The higher the value of \(W(t)\), the better the turbine. Furthermore, in order to be consistent with the weights in the TOPSIS approach, \(w_{1}=w_{2}=w_{3}=w_{4}=w_{5}=0.2\) in Equation (8). The application of fuzzy logic to wind turbine selection problem requires that the five selection criteria are aggregated to form an overall decision function. This decision function is first formulated as a rule, which is then transformed into a mathematical function. For the turbine selection problem, the following fuzzy rule can be formulated. Rule 1: If a turbine has low hub height, high wind speed, low zero output percentage, high rated output percentage, and high annual energy production, then it is a good turbine. In the above rule, the terms \"low hub height\", \"high wind speed\", \"low zero output percentage\", \"high rated output percentage\", \"high annual energy production\", and \"good turbines\" are linguistic variables, each of which defines a fuzzy subset of solutions. For example, high wind speed is the fuzzy subset of solutions of high wind speeds. For each fuzzy subset, a membership function \(\mu\) is defined. The membership function returns a value in the interval [0, 1]. This value signifies the degree of satisfaction with the decision criterion under consideration [20]. Rule 1 can be mathematically represented using the fuzzy arithmetic mean operator [42] as follows:  
\[\mu_{t}=\frac{1}{5}(\mu_{HH}+\mu_{WS}+\mu_{ZP}+\mu_{RP}+\mu_{AEP}) \tag{9}\]where \(\mu_{t}\) is the membership function for good turbine. Similarly, \(\mu_{HH}\), \(\mu_{WS}\), \(\mu_{ZP}\), \(\mu_{RP}\), and \(\mu_{AEP}\) are the membership functions for hub height, wind speed, zero output percentage, rated output percentage, and annual energy production, respectively. The solution for the \(\mu_{t}\) nearest to 1 is declared as the best solution.