## 2 Literature Review
### Multi-Criteria Decision-Making Models (MCDM) in Construction Industry  
In the construction industry, much knowledge and the provided information are imprecise, complex or incomplete [45]. Thus, construction safety planning problems are always associated with a set of factors, such as effectiveness, feasibility and cost, which are either quantitative or qualitative, and may be in conflict with each other. Construction safety planners need to deal with information vagueness and uncertainty, and finally make the optimal decision using the ambiguous data. The Multi-criteria decision-making (MCDM) method is an effective approach in screening, prioritizing, ranking or selecting a set of alternatives with conflicting, incommensurate or independent attributes [46]. Different operational researchers and decision-making theorists have proposed many MCDM approaches and techniques, including simple additive weighting, analytical hierarchy process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian (VIKOR), and Elimination Et Choix Traduisant la Realite (ELECTRE). However, the selection and applicability of a certain MCDM method largely depends on the available and collectable information that can be provided to the decision maker and the generated structure of the decision model. AHP is a method to determine the priority weights for multiple criteria in the decision-making system based on a rational framework of quantitative comparisons [47]. This approach has been widely applied in the risk assessment and management problems in the construction industry. During the AHP decision-making process, the knowledge about goals and priorities is not necessarily required [48]. The key step is to make pairwise comparison judgements through determination of the relative importance among different criteria. TOPSIS was developed to determine the best solution for MCDM problems, which is proposed by [PERSON] and [PERSON] [46]. In the TOPSIS method, the positive and negative ideal solutions as the ideal and anti-ideal solutions, are determined, and the selected alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative-ideal solution (NIS) [49]. Given that the results from TOPSIS are stable and the calculation process is easy to apply, TOPSIS has the fewest ranking reversals compared with other MCDM methods [46]. In previous construction safety related studies, many MCDM methods have been applied in areas of safety risk assessment [50; 51; 52], safety factor weighting [53], and priority evaluation [54]. [PERSON] et al. [55] used TOPSIS to determine the priorities of safety solutions, which effectively secures the employees' health and safety performance on construction sites. [PERSON] [56] proposed a multi-criteria construction safety evaluation system based on a fuzzy TOPSIS method and further provides construction contractors and safety managers with guidelines to improve safety performance. The TOPSIS method is an effective and flexible method which can be easily understood and widely employed during safety planning in construction. Therefore, in this research, the TOPSIS method is extended and applied in the fall protection plan decision-making problem, and used in the evaluation and selection of the optimal fall protection solution for the construction project. In the proposed MCDM system, AHP and TOPSIS are integrated with fuzzy sets to evaluate and determine the best fall protection system among construction safety plan alternatives. With the application of AHP and fuzzy TOPSIS, the fuzzy sets can be used to quantitatively describe subjective preference by simultaneously using the membership and non-membership functions, and the criteria weights, the positive-ideal solution and the negative-ideal solution can be further obtained. Integrating AHP, TOPSIS and fuzzy sets can fully take advantage of each.