Project selection and formation of an optimal portfolio of selected projects are among the main challenges of project management. For this purpose, several factors and indicators are simultaneously examined considering the terms and conditions of the decision problem. Obviously, both qualitative and quantitative factors may influence the formation of a portfolio of projects. In this study, the projects were first ranked using grey relational analysis to form an optimal portfolio of projects and to create an expert system for the final project selection. Because of the fuzzy nature of the environmental risk of each project, the environmental risk was predicted and analyzed using the fuzzy inference system and failure mode and effect analysis based on fuzzy rules. Then, the rank and risk of each project were optimized using a two-objective zero-one mathematical programming model considering the practical constraints of the decision problem through the nondominated sorting genetic algorithm-II (NSGA-II). A case study was used to discuss the practical methodology for selecting a portfolio of projects. 1. Introduction Project selection is among important issues in industrial management, industrial engineering, and governmental, nonprofit, and commercial organizations [1]. The selection of the best portfolio or project to achieve full satisfaction in an organization has been considered in previous studies [2]. The project selection process can be defined as follows: it is started by continuous collecting, analyzing, and judging the available information on the project leading to project selection considering the factors influencing the selection process [3]. The project portfolio selection is a multicriteria decision problem which considers multicriteria quantitative and qualitative factors simultaneously [4]. In the multicriteria decision-making model, the solution may already exist and therefore the purpose is to select the best solution from the available solution set. This class of decision problems is called multicriteria decision models. On the other hand, the solution may be unknown. In this case, the purpose is to find the optimal Pareto solution of the problem in the continuous or discrete space [5]. Such decision models are called multiple objective decision-making models. The multicriteria decision models are formed based on utility theory and human pressures in dealing with the behavior of max finder [6]. In 1945, John Newman published his famous book Theory of Games and Economic Behavior and proposed a mathematical theory for game theory-based
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