## 1 Introduction  
Dealing with uncertainties is an unavoidable challenge of every project. The effect of uncertainties on project objectives, which may be positive or negative, can be controlled by implementing a risk management process. Risk management starts with developing the risk management plan, which determines how risk management activities will be structured, funded, and performed. Subsequently, the risk events must be identified and documented. Then, these events must be analyzed qualitatively and quantitatively in order to be prioritized based on their probability and impact, and to determine the contingency reserve. Response strategies must be identified, assessed, and implemented in order to control the probability of occurrence and/or the impacts of the events. Finally, the effectiveness of the risk management process throughout the project must be evaluated and controlled. In this paper, to highlight the importance of uncertainties with positive effects, \"risk event\" and \"opportunity event\" are defined as uncertain events or conditions that can negatively or positively affect the project objectives, respectively. To deal with uncertain events, there are two types of reserves in a project, namely management and contingency reserves, that must be calculated and considered in the project budget. Contingency reserve is defined as the money or time allocated in the cost or schedule baseline to reduce the overruns of project objectives due to known risks and opportunities [1,2]. The management reserve is an amount of project budget that is reserved to handle unforeseen events [2]. The project budget is the summation of the cost baseline and management reserve. The cost baseline is made up by adding the cost estimates of all work packages with contingency reserve [2]. [PERSON] et al. [3] categorized uncertain events into two main groups: (1) unknown unknowns that must be addressed with management reserve, and (2) known unknowns that must be addressed proactively (i.e., by employing avoiding, mitigating, and transferring strategies for risks and also exploiting, enhancing, and sharing strategies for opportunities) or reactively (i.e., by employing active and passive accepting strategies). Those events that are addressed by applying proactive response strategies or active acceptance response strategies are dealt with using contingency reserve. Risk and opportunity events addressed with passive acceptance response strategies are dealt with using management reserve [1,4]. Contingency reserve is a key tool for the decision makers of a project for controlling and responding to risks and opportunities. Allocating too little or too much for the contingency reserve amounts required for a project may result in significant losses and inefficient resource management [5]. The accurate estimation of contingency leads to achieving project objectives (e.g., schedule and cost objectives) [5,6]. Moreover, different uncertainties need to be considered in calculating contingency reserve. [PERSON] [7] first defined the dual nature of uncertainty by categorizing it into \"objective uncertainty\" and \"subjective uncertainty.\" Objective uncertainty refers to the variability that comes from the stochastic characteristic of an environment and its concepts rooted in probability theory. Subjective uncertainty stems from employing approximate reasoning and linguistically expressed expert knowledge. [PERSON] and [PERSON] [8] break down subjective uncertainty into vagueness, ambiguity, and subjectivity. Vagueness results from the lack of sharpness of relevant distinctions. Ambiguity stems from the lack of certain distinctions characterizing an object, from conflicting distinctions, or from both. Subjectivity results from the influence of personal beliefs or feelings rather than facts [9]. Classic techniques of calculating the contingency reserve have serious drawbacks and fail to consider vagueness, ambiguity, and subjectivity uncertainties.