*3.1. Fuzzy AHP and Fuzzy Logic*

Multi-criteria decision-making (MCDM) techniques are extremely beneficial for project selection problems when considering different selection criteria. These techniques use mathematical models and simulations to aid in the project selection process. AHP, introduced by Saaty [22], is one of the most common and established MCDM techniques in project selection [15]. However, for these techniques to yield meaningful results, they need crisp and specific input data, which are usually difficult to obtain in project selection situations due to the subjective and uncertain nature of experts' judgments. Fuzzy AHP was developed to handle such uncertain and subjective input data more effectively than conventional MCDM techniques [7]. Fuzzy AHP applies the fuzzy set theory to allow researchers and decision makers to convert uncertain and vague linguistic input information from experts, such as the phrase "A lot more important", for example, to specific decisions intervals that are a lot more convenient to deal with by decision makers [15,23]. As project selection becomes increasingly global, this is a critical dimension to evaluate effectively. most common and established MCDM techniques in project selection [15]. However, for these techniques to yield meaningful results, they need crisp and specific input data, which are usually difficult to obtain in project selection situations due to the subjective and uncertain nature of experts' judgments. Fuzzy AHP was developed to handle such uncertain and subjective input data more effectively than conventional MCDM techniques [7]. Fuzzy AHP applies the fuzzy set theory to allow researchers and decision makers to convert uncertain and vague linguistic input information from experts, such as the phrase "A lot more important", for example, to specific decisions intervals that are a lot more convenient to deal with by decision makers [15,23]. As project selection becomes increasingly global, this is a critical dimension to evaluate effectively.

The concept of fuzzy numbers used in the FAHP represents a range of possible values for a specific variable or rating. This means that a single ambiguous linguistic rating will be translated into a fuzzy number consisting of a range of numbers [24]. In fuzzy theory, it is more convenient to use triangular fuzzy numbers (TFNs) because of their computational simplicity and usefulness in representing information in a fuzzy environment [25]. TFNs are represented as three numbers (*l*, *m*, *u*) where the variables *l*, *m*, and *u* indicate the lowest possible value, the modal or most likely value, and the upper or highest possible value, respectively [7]. The mathematical representation of a fuzzy number *A* with a membership function µ*A*(*x*) is depicted in Equation (1), as shown in Shukla et al. [24] and Hsieh et al. [26]. The concept of fuzzy numbers used in the FAHP represents a range of possible values for a specific variable or rating. This means that a single ambiguous linguistic rating will be translated into a fuzzy number consisting of a range of numbers [24]. In fuzzy theory, it is more convenient to use triangular fuzzy numbers (TFNs) because of their computational simplicity and usefulness in representing information in a fuzzy environment [25]. TFNs are represented as three numbers (, , ) where the variables , , and indicate the lowest possible value, the modal or most likely value, and the upper or highest possible value, respectively [7]. The mathematical representation of a fuzzy number with a membership function () is depicted in Equation (1), as shown in Shukla et al. [24] and Hsieh et al. [26].

$$\mu\_A(\mathbf{x}) = \begin{cases} 0 & \mathbf{x} < l; \\ \frac{\mathbf{x} - l}{m - l} & l \le \mathbf{x} \le m; \\\\ \frac{\mathbf{u} - \mathbf{x}}{u - m} & m \le \mathbf{x} \le u; \\\\ 0 & \mathbf{x} > u. \end{cases} \tag{1}$$

The geometric representation of the fuzzy number *A* from Equation (1) is shown in Figure 1, adapted from Lespier et al. [7] and Sun [27]. The geometric representation of the fuzzy number from Equation (1) is shown in Figure 1, adapted from Lespier et al. [7] and Sun [27].

**Figure 1.** A triangular fuzzy number (TFN), *A* [7,27].

### **Figure 1.** A triangular fuzzy number (TFN), [7,27] *3.2. FAHP Selection Criteria*

*3.2. FAHP Selection Criteria* Alyamani and Long [21] and Alyamani et al. [10] identified four common key project characteristics that are used to evaluate sustainable projects in different institutional environments. This research extends their work by utilizing the characteristics they identified in addition to project cost as a fifth characteristic. The five characteristics are then used as selection criteria in evaluating multiple sustainable project alternatives. Using these characteristics as selection criteria develops a selection tool that can be used to evaluate projects in different environments regardless of location. Alyamani and Long [21] and Alyamani et al. [10] identified four common key project characteristics that are used to evaluate sustainable projects in different institutional environments. This research extends their work by utilizing the characteristics they identified in addition to project cost as a fifth characteristic. The five characteristics are then used as selection criteria in evaluating multiple sustainable project alternatives. Using these characteristics as selection criteria develops a selection tool that can be used to evaluate projects in different environments regardless of location. Consequently, this research aims to rank novelty, uncertainty, skill and experience, technology information transfer,

and project cost from the context of sustainability as part of project selection in different environments and locations.

Novelty describes the degree to which a project differs from what is considered standard and established in terms of sustainable practices, processes, and technologies. In other words, this refers to the originality of the project and the maturity of the selected sustainable practices and technologies [28]. Undertaking a novel project that is utilizing completely new sustainable technologies or practices presents its own set of challenges and requires a certain level of resources and capabilities to ensure the successful implementation of such projects as opposed to more mature sustainable projects using standard and established sustainable practices and technologies [10,29].

Project uncertainty is generally defined in the literature as negative events for which both the consequence and probability of occurrence is unknown [30,31]. Different projects have different levels and sources of uncertainty [10]. In any case, however, these different sources of uncertainty, whether it be technological, financial, environmental, political, or any other source, should be outlined and addressed with appropriate mitigation plans to reduce their potential impact on the project should they occur.

The skill and experience criterion describes the level of skill and experience a project team is required to possess to be able to complete the project tasks effectively and efficiently, thus ensuring the successful completion of the project [10]. This criterion essentially addresses matching workforce capabilities with the project requirements [32]. Some sustainable projects require a highly skilled and experienced project team to be able to successfully complete the project, while other sustainable projects require relatively lower levels of skill and experience. The availability of the required workforce capabilities within the location of the evaluated project alternatives is an important component of this criterion. Project tasks can range from being trivial and standard all the way to complex and unusual. Consequently, choosing a project team with the appropriate know-how and sufficient level of experience to undertake these tasks and implement the chosen sustainable technology or practice is crucial in achieving project success and ensuring that project goals are met.

Technology information transfer, originally presented by Stock and Tatikonda [32], describes the amount of sustainable technology information being exchanged between the supplier of the sustainable technology and the project team implementing that technology. In other words, it describes the amount of interaction required between a supplier of a technology and the recipient of that technology to ensure the successful integration and implementation of said technology in the project. Selecting the appropriate technology and making sure it is correctly implemented in the project is one of the major steps towards achieving project goals. The level of information sharing between the two parties can vary significantly from project to project depending on the type of technology implemented. Stock and Tatikonda [32] explain that the level of information sharing between the supplier of the technology and the project team can range from a simple "arms-length" purchase requiring trivial information sharing, all the way to a "co-development" type of technology information sharing where both the supplier of the technology and the project team work closely together on the details of the design and specifications to ensure successful integration of the technology in the project [10].

Project cost essentially describes the total cost of the project including the initial investment cost and subsequent annual project costs. This criterion was added because it is considered one of the major driving factors in sustainable development and sustainable project selection [11]. One of the major challenges facing sustainable energy projects is competing with conventional energy sources in financial cost. However, the reduction in sustainable development costs in recent years in addition to the consideration of the indirect costs associated with conventional energy sources has somewhat balanced the scales between sustainable and conventional energy sources from the economic perspective [20]. Nonetheless, the costs associated with sustainable energy development in the international stage remain one of the major driving forces in sustainable energy project development.

A summary of the criteria explained above and their notations as used in this research are presented in Table 1.


**Table 1.** Key sustainable project selection criteria used in fuzzy analytic hierarchy process (FAHP). *Sustainability* **2020**, *12*, x FOR PEER REVIEW 6 of 15

Based on these criteria, a typical hierarchy model of the sustainable project selection process is created, as shown in Figure 2, which consists of three levels: the goal of evaluating sustainable project alternatives, the criteria used to evaluate these alternatives as presented in Table 1, and the sustainable project alternatives to be evaluated using these criteria. As such, the prioritization of weights for the presented criteria using fuzzy analytic hierarchy process (FAHP) will aid in the selection process when presented with different sustainable project alternatives. Based on these criteria, a typical hierarchy model of the sustainable project selection process is created, as shown in Figure 2, which consists of three levels: the goal of evaluating sustainable project alternatives, the criteria used to evaluate these alternatives as presented in Table 1, and the sustainable project alternatives to be evaluated using these criteria. As such, the prioritization of weights for the presented criteria using fuzzy analytic hierarchy process (FAHP) will aid in the selection process when presented with different sustainable project alternatives.

**Figure 2.** The hierarchy model for sustainable project selection. **Figure 2.** The hierarchy model for sustainable project selection.
