## 4 AHP/TOPSIS-Based Multi-Criteria Decision-Making  
The AHP (Analytic Hierarchy Process)/TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution)-based hybrid approach is proposed in this research to compare a number of factors/criteria (in the following, criteria and factors are used interchangeably) and provides the rank based on those factors for each candidate. Many researchers have used either AHP or TOPSIS to find the best alternative from several potential candidates [3; 4; 5], since they are two different multi-criteria decision-making (MCDM) methods [1; 2]. With the assistance of the approaches mentioned above, a set of criteria can be evaluated to rank the alternatives. The purpose of using AHP is to determine the criteria weights, and TOPSIS employs the weights obtained from AHP in order to rank the alternatives; however, on many occasions, the two approaches are combined to obtain optimal results [27]. AHP/TOPSIS refers to the mechanism where TOPSIS uses AHP weights. The reasons behind the use of this hybrid approach in this article, are as follows:  
* It helps lower the computational complexity. * It eases the manual effort needed for the construction of the AHP pairwise comparison matrices. Although AHP alone is a very flexible and powerful MCDM tool, the computations made by AHP are always guided by the decision maker's experience, and AHP can thus be considered a tool that is able to translate the evaluations made by the decision maker into a multi-criteria ranking. However, if the decision maker's understanding about the alternatives is not good enough, it can lead to inaccurate results. On the other hand, AHP alone requires a large number of evaluations by the user, especially for problems with many criteria and alternatives [11]. In fact, the number of pairwise comparisons grows quadratically with the number of criteria and options. Let us discuss the following example to understand the proposed approach. **Example 1**. : _In this example, the best alternative is computed from a set of 10 alternatives using five criteria. Only two alternatives are taken at a time by AHP and a comparison matrix is constructed by comparing their criteria one by one. As a result, the best one is found among the 10 alternatives via AHP. A total of \(\binom{10}{2}=55\) combinations are generated, i.e., a total of 55 comparison matrices need to be constructed. Each criteria is given some weight based on its importance. Hence, a comparison matrix of the criteria is necessary to obtain criteria weights. In total, 56 comparison matrices are required and each matrix has to be made with careful selection of the degree of importance for each matrix cell [11]. This process takes a lot of time, and the problem intensifies when the number of alternatives are increased. Once TOPSIS is applied after given the criteria weights, a single decision matrix is generated with the assistance of all of the alternatives simultaneously. The best alternative or ranking of the alternatives is generated with the help of this decision matrix._  
The TOPSIS approach drastically reduces the computational complexity and the manual effort required in the AHP approach, but it does not assist in the formulation of a mechanism to compute the criteria weights. Several researchers have adopted hybrid MCDM approaches to increase the overall efficiency. In [28], the authors suggested that the hybrid between AHP and Complex Proportional Assessment (COPRAS) to rank seven sustainable hydrogen production options helped reduce uncertainties in all phases of the task. In another research [13], AHP and SRF were combined to determine precast concrete panels for building retrofitting. They defined six criteria and evaluated seven visual rankings within 15 min, making it easier even for non-expert users to carry out the procedures. [PERSON] et al. in [29] ranked seven alternatives of renewable energy sources with AHP, TOPSIS, and Simple Additive Weighting (SAW).