## 1 Introduction  
The literature has been a subject of intense research in the field of research in the field of finance, economics, economics, and finance. The literature has been a subject of intense research in the field of finance, economics, and finance. ## 1 Introduction  
The Datar-Mathews method (DM method) is a particularly interesting but still relatively underexplored area in simulation-based real option valuation (ROV). The method proposed by [PERSON] and [PERSON] in 2004 provides an easy way to determine the real option value of a project by using the average of positive outcomes [1,2]. It uses Monte Carlo simulation to propagate uncertainty and to create pay-off distribution of an investment alternative. The resulting pay-off distribution is flexible, allowing for any compounding interval and free selection of discount rates [3]. Additionally, the results of the DM method converge with the Black & Scholes result when the Monte Carlo simulation is run enough times. In this article, we propose a method for performing the DM method in a hybrid environment, which refers to a scenario where the parameters utilized for evaluating the investment cannot be precisely determined. In real option valuation, the accuracy of input parameters greatly influences the financial terms, such as cash flow and profit. Analysts frequently estimate parameters using past data and simultaneously make subjective guesses about future economic changes [4, 5, 6, 7]. It results in the additional type of uncertainty in describing parameters, which, apart from random uncertainty, arises from a lack of knowledge or inherent vagueness [7]. The exclusive reliance on probability theory in these situations can result in a false sense of precision and an incorrect assumption that outcomes are inherently predictable and repeating in nature [8]. There is therefore a natural need to distinguish between different types of uncertainty in ROV. Entrepreneurial activities encompass different levels of informational reliability, giving rise to situations where risks are linked to the probabilities of expected outcomes, while uncertainty arises when these probabilities cannot be precisely determined. It follows from the fact that valuing investment projects usually involves both types of uncertainty--aleatoric and epistemic. Aleatoric uncertainty is observed variability while epistemic uncertainty arises from incomplete knowledge. To effectively capture non-probabilistic uncertainty, it becomes crucial to incorporate to the model both probabilistic and possibilistic approaches [9]. Experts' opinions or imprecise estimates may be introduced to the model in the form of possibilistic distribution as they better express vagueness, imprecision, or ambiguity [10]. In the field of ROV, the probabilistic Black-Scholes (B-S) model provides robust framework to model aleatoric uncertainty of many variables such as market size or product prices [5,6,11,12,13,14]. Therefore, a combination of both probabilistic and possibilistic approaches is necessary for accurately modeling and evaluating the uncertainties that exist in ROV. Several factors led us to the writing of this article. The first is that a pure probabilistic approach is difficult to use in valuing investment projects using the DM method due to the inherent vagueness that investors encounter. The most widely used probabilistic real option valuation techniques--such as the analytical Black-Scholes model [15], the Cox-Ross-Rubinstein binomial lattice [16], Monte Carlo-based extensions of the Datar-Mathews framework [1], and decision-tree analysis [17]--require the analyst to specify every source of uncertainty with a precise probability distribution derived from rich historical data. This assumption is problematic when knowledge is incomplete, and parameters are only available as expert judgements or coarse intervals (epistemic uncertainty).