The selection of FWSs in building construction projects has been the focus of several studies from 1989 until 2022. The majority of these studies fall into two main categories: (1) studies that focus on identifying and/or ranking the quantitative and qualitative FWS selection criteria, e.g., [24,37], and (2) studies that propose solutions to select the most appropriate FWS, which is affected by various compromising and conflicting criteria, e.g., [10,38]. The studies related to the identification and/or ranking of FWS selection criteria have been summarized in a single body of knowledge in Terzioglu et al.’s [27] study, which is a critical review of the relevant literature for building construction projects. Since the main objective of this study is to propose an integrated MCDM approach for selecting FWSs, this section will focus mainly on studies that attempted to solve the FWS selection problem. Value engineering, knowledge-based guidelines, rule-based expert systems, neural networks (NNs), and several MCDM methods are among the proposed solutions for the FWS selection problem. The following is a brief review of these studies in chronological order:

Hanna and Sanvido [39] developed a knowledge-based systematic guideline, specifically for the contractor’s formwork planner, to select vertical FWSs based on Hanna’s factors and FWS alternatives [37]. In this study, five vertical FWS alternatives, including conventional FWS, ganged FWS, jump FWS, slip FWS, and self-raising FWS, were identified for building construction projects in the USA. Hanna et al. [26] presented a rule-based expert system to assist decision-makers and formwork design engineers in selecting vertical and horizontal FWS alternatives for building construction projects in the USA. This study considered traditional wood FWS, conventional metal FWS, flying truss FWS (i.e., Table FWS), column-mounted shoring FWS, and tunnel FWS as horizontal FWS alternatives. Kamarthi et al. [40] and Hanna and Senouci [41] proposed Neural Network (NN) models for the vertical and horizontal FWSs selection problem, respectively, using the previously identified factors and FWS alternatives. Abdel-Razek [42] utilized a value engineering approach to guide decision-makers in the FWS selection process for building construction projects. Elazouni et al. [43] proposed an integrated approach to estimate the acceptability of new horizontal FWSs (e.g., telescopic beam and prop FWS, telescopic beam and shore-brace FWS, shore-brace FWS, s-beam and prop FWS, drop-head FWS), by combining the Analytical Hierarchy Process (AHP) method with NN models. Based on previously developed NN models for the FWS selection problem, e.g., [41], Tam et al. [44] and Shin [45] introduced a probabilistic NN model and an artificial NN model, respectively, to select the most appropriate FWS. In Shin’s [32] study, horizontal FWS alternatives such as aluminium panel FWS, conventional FWS, Table FWS, and drop-head FWS were identified as the most commonly utilized FWSs in Korea’s high-rise building construction projects. Elbeltagi et al.’s [46] study for the selection of horizontal FWS (e.g., conventional FWS, Table FWS, shore-brace FWS, and drop-head FWS), and Elbeltagi et al.’s [29] study for the selection of vertical FWS (e.g., traditional FWS, panel FWS, single-sided FWS, crane-climbing FWS, and self-climbing FWS) both used a knowledge-based systematic guideline and fuzzy logic to determine the most appropriate FWS in building construction projects in Egypt. It should be noted that, in these studies, fuzzy logic was applied to convert linguistic input and output variables associated with FWS selection criteria and FWS alternatives, respectively, to their fuzzy forms. Shin et al. [10] employed a boosted decision tree (BDT) model to select horizontal FWSs in high-rise building construction projects in Korea, based on the most important FWS alternatives and factors affecting the FWS selection identified by Shin [45]. Several studies have proposed well-known MCDM methods to solve the FWS selection problem using experts’ evaluations based on crisp numbers. For instance, Krawczyska-Piechna [47] proposed the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to select the most appropriate FWS for building construction projects in Poland. Martinez et al. [48] proposed the Choosing by Advantages (CBA) method for the FWS selection problem in Ecuador. However, in these studies, information regarding the various types of FWS alternatives was not provided. Basu and Jha [38] applied the AHP method to solve the FWS selection problem in the Indian building construction sector, based on the FWS selection criteria identified by Hanna et al. [26]. Likewise, Hansen et al. [30] employed the AHP method to select among two FWS alternatives (e.g., conventional FWS and aluminium FWS) based on Indonesia’s most significant FWS selection criteria. Teja et al. [49] developed a fuzzy rule-based system to select vertical FWSs by combining fuzzy logic with the rule-based expert system introduced by Hanna et al. [26]. This study determined that traditional FWS, conventional FWS, panel FWS, crane-climbing FWS, self-climbing FWS, and plastic FWS are the most frequently utilized FWSs in the Indian building construction sector.

In summary, most studies addressing the FWS selection problem employed techniques such as rule-based expert systems, NNs, and other MCDM methods. However, no study has integrated the subjective judgments of the decision-makers into the FWS selection process or considered the vagueness in the collected data from the experts in their evaluation to select the most appropriate FWS. The FWS selection is a group decision-making process [29]. In addition, the early involvement of different stakeholder groups (e.g., the contractor and the formwork fabricator (FWF)) in the planning and design stages of the FWS may improve the time and the cost performance of a building construction project [50,51]. On the other hand, the perspectives and perceptions regarding the FWS alternatives and the importance level of FWS selection criteria of different construction professionals (i.e., experts in the decision-making team) may vary [52]. However, uncertainty arises when decision-makers have varying opinions on alternatives [53]. This might result from inadequate information or the different backgrounds of the decision-makers [53]. Therefore, the subjective judgments and the vagueness in data obtained from the experts should be considered when using MCDM methods for the FWS selection problem. In this regard, using the mathematical tools provided by uncertainty theories such as fuzzy set theory and rough set theory may improve the objectivity of the decision-making process [54,55]; in this case, for evaluating FWS alternatives. To the authors’ knowledge, no study involving MCDM methods to solve the FWS selection problem has incorporated uncertainty into the decision-making process.