## 3 Proposed Methodology
### Fuzzy Logic Principles  
This section presents the fundamental definitions and principles of fuzzy logic, in contrast to \"crisp\" sets. The latter are defined by strict membership criteria, where an element either fully belongs to a set or does not. In contrast, fuzzy logic allows the value of a variable to be described through degrees of membership to a concept, using a continuous scale from 0 to 1.  
There are various types of membership functions, including triangular, trapezoidal, gamma, and rectangular, among others. Triangular Membership Functions (TMF) are particularly popular due to their simplicity and effectiveness in modeling imprecise data. For instance, TMFs are well-suited for representing vague or incomplete information. A typical example is describing a mean time to repair as \"approximately 1.5 h\" or \"somewhere between 1 and 2 h\", where exact precision is either unavailable or unnecessary.  
Triangular fuzzy numbers are defined by three values: (m\({}_{1}\), m\({}_{2}\), m\({}_{3}\)). Along with their respective \(\alpha\)-cuts, this variable is expressed as M\({}_{\alpha}\) = [m\({}_{1}(\alpha)\), m\({}_{3}(\alpha)\)]. TMFs not only capture the behavior of various system parameters but also accurately reflect data dispersion. This dispersion accounts for both the inherent variations of any process and the vagueness of the system. As a result, the decision-making process becomes more intuitive for engineers, even when dealing with imperfect information.  
Imprecisely defined events are often described using linguistic terms such as \"low\", \"very low\", \"high\", or \"very high\". These linguistic variables are employed to model and understand such events by leveraging fuzzy membership functions. In the context of this study, terms like low, medium, high, and very high are used to characterize the probability of occurrence or frequency of a given failure mode, its severity, and, consequently, the associated level of difficulty or ease in its recovery or repair. These linguistic terms are integral to expressing the expert knowledge underlying the decision-making process, forming the basis of what is known as a fuzzy inference system.  
Fuzzy inference systems derive output fuzzy sets based on rules (combinations) and input variables, often expressed in an \"If-Then\" format: \"If x is Mi, then y is Ni\", where xx is the input linguistic variable, Mi represents antecedent linguistic constants, y is the output linguistic variable, and Ni refers to consequent linguistic constants. The two most common types of inference methods are the max-min inference method (Mamdani implication) and the max-prod inference method (Larsen implication). In this study, the [PERSON] max-min inference method is used.  
To make decisions regarding RAM analysis experiments, the fuzzy outputs must be converted into crisp values. This requires a defuzzification process. Several defuzzification techniques exist, such as the centroid, bisector, middle of maximum, and weighted-average methods. The most used method is the centroid method, due to its computational simplicity and plausible results. This process is represented as follows:  
\[Defuzzy\,fied\,Value=\frac{\int\,y\,\cdot\,m_{B0}(y)\,dy}{\int\,m_{B0}(y)\,dy}\]