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| MCDM method | Description | Advantages | Disadvantages |
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| AHP | Saaty created it to enable the decision-makers make more organized decisions [34, 35]. A multilevel hierarchical structure of objectives, criteria and alternatives is used [36]. Evaluate the significance of key measurements before correlating possible options with regard to each factor. Eventually, calculate the utmost preference of each decision option and also the overall score of the decision options [37] | Simple to be adopted, and its scale can be adapted to meet the needs of various decision-making situations [38]. Its popularity arises from the belief that it requires less data than other MCDM methods and can manage evaluation criteria [39]. When data are measured on different scales, it can be normalized and aggregated later [40]. It is accurate in taking decisions because of its potential to prove the consistency of the independent expert assessment [41] | As the list of considerations to be matched grows, calculations can become challenging. The ultimate determination (overall score of options) may be impacted by increasing the scale of relative importance [38]. As stated earlier in the section, AHP is only valid with positive reciprocal matrices [40] |
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| PROMETHEE | In 1982, it was firstly created by Brans and Vincke [42]. The PROMETHEE, for each alternative, calculates both positive and negative flows (Ф+, Ф−), respectively, based on the weight assigned to each criterion [43]. PROMETHEE I through VI was created to serve as outranking methods. In each criterion, alternatives are compared in pairs [44] | Can compare a finite set of alternatives to competing criteria [45]. Pair-wise comparison is no longer necessary once options are removed or provided during the assessment. It is employed to select the optimal underground ore transportation and mining method [46]. Calculations are very complicated; therefore, the method is only suitable for experts | Because of the scarcity of selection guidelines, decision-makers find it hard to set up preference limits and thresholds [47]. The uncertainty of the set up limits is also not wholly responsible for, despite the fact that a parametric analysis is then conducted [48]. The subjective input of preferences adds to the uncertainty [49] |
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| TOPSIS | In 1981, Hwang and Yoon addressed TOPSIS, which stands for order preferences by similarity to ideal solution [50]. Ranks the alternatives according to the distance between the ideal positive and negative solutions [51, 52]. The TOPSIS method’s best alternative is the one that comes closest to the positive ideal solution [53, 54] | TOPSIS allows to reach the right solution faster than most MCDM methods. Its logic is sound and easy to grasp. Furthermore, the significance of weight vectors could be incorporated into the comparative process [55]. A polyhedron could be used to depict the effectiveness of options and metrics, and the estimation process is then straightforward [56]. The method is suitable when the indicators of alternatives do not vary very strongly | TOPSIS lacks a component that checks for inconsistency between judgment and expressed preferences [57]. Because TOPSIS cannot elicit weights, it must focus solely on alternative measuring strategies such as AHP [58]. TOPSIS application might be invalid if the weights are not accurate [59]. Simple computational steps, solid mathematical foundations, and a method that is simple to understand [60] |
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| TODIM | Tomada de Decisao interactive multicriteria have been developed in the early 1990s by Gomes and Lima to assist throughout the list of options in which the selection should successfully maintain a choice in the event of a crisis [61]. Main idea has to use the overall value to determine each alternative’s dominance over the others and then evaluate and rank the alternatives [62] | In terms of behavioral decision-making, it is effective since it considers the decision-psychological maker’s virtues and therefore can catch damage and lack of certainty [63]. The attenuation parameter, that would be adjusted, will portray the decision-maker’s risk tolerance [64]. Even professionals with no prior knowledge of MCDM describe the method as an easy-to-implement tool [65, 66] | Inability to acknowledge the uncertainty associated and imprecision in decision-making [67]. In the TODIM method, any two alternatives must be compared, which results in high computational complexity [68]. Interactive attributes can be used with positive or negative criteria interactions and crisp values [69] |
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| VIKOR | Opricovic [70] proposed this method to solve situations with contradictory and quasi requirements [71]. Presuming that agreement is reasonable for dealing with conflict, the selection seeks the fairly close answer to the perfect, and all defined requirements are used to take active steps [72, 73] | It is very simple because it has the fewest steps for calculating the ranking order [74]. Could go with the expansion functionality of the “most of” and the least specific remorse of the “competitor” [75, 76]. A helpful aid, especially once the choice has not yet addressed his or her priorities at the outset of the method [77]. Enables to calculate the distance between the second-best option and the first | Looking for a compromise ranking order, i.e., a compromise between pessimistic and expected solutions. Another flaw is the use of complex-linear normalization in the calculation formula [78]. The use of complex normalization is required for all of the matrix’s elements, which typically have different metrics, to be obtained as dimensionless units [79] |
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| ELECTRE | Roy invented it in 1968. Various ELECTRE methods have since been developed [80] used to classify a number of options by analyzing data in a decision matrix [81]. In the pair-wise correlation of alternatives, consistency and disharmony are used [82] | Capable of dealing with both qualitative and quantitative criteria [83]. ELECTRE was employed in civil and environmental engineering [84]. Examples of these applications include power efficiency, sustainable use of natural resources, environment protection, nutrition, security, healthcare, design, and mechatronics. To select the best surface mining technology [85] | ELECTRE occasionally fails to sort the alternatives into different ranks [86]. The weakness of ELECTRE's normal ranking arises from the need of supplemental limit, and the ranking of the alternative is dependent on the size of this limit, so there is no “correct value” [87] |
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| GRA | Deng proposed it in 1982 to find solutions involving uncertainty and missing information [88]. Grey prediction model, grey relational analysis (GRA), grey decision, grey programming, and grey control are the five components of the grey prediction model [89]. This method treats each alternative as a data sequence. It then looks at how similar each alternative is to the reference sequence [90] | The analyzed results are reliant on the raw data, and the calculation procedure is simple and straightforward [91, 92]. There are no restrictions on sample size or normally distributed data, and the computational method is simple [93]. Ability to provide methods for ranking alternatives that do not necessitate a large sample size or any sample distribution. Very popular and useful tools for analyzing various relationships among discrete information and making decisions in various situations | There is a lack of mathematical principles to discuss its history, rules, and restrictions [94]. The most relative relational degree from the probabilistic linguistic positive ideal solution is used to select an alternative [95] |
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| OCRA, ARAS, COPRAS, SAW, CP | | Rapid development of methods for dealing with real-world problems [32] | The method has seen limited application in mining engineering [32] |
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