# An Integrated Decision Support System for Low-Disturbance Surface Mining
## 2 Methodology
### Integrated Methodological Approach
#### 2.2.1 F-AHP  
The most acceptable solutions can be obtained in a shorter period through information systems for sound decision support systems [24]. Decision support systems based on multicriteria decision-making methodology (MCDM) have great potential to enhance the work of research scholars and policymakers. MCDM is gaining popularity in sustainable energy planning because it provides decision-makers with a rational multi-criteria framework [25; 26; 27]. The analytical hierarchy Process (AHP) is one of the MCDM tools widely used for rational decision-making in renewable energy planning, water resource management, and other areas [28; 29]. AHP is widely accepted because it provides a way to transform complex problems into hierarchical structures [30]. However, the following weaknesses exist in the traditional hierarchical analysis approach: (i) Does not take into account the uncertainty of  
Figure 3: Flowchart for analyzing the integrated method. natural language's subjective judgment of numbers; (ii) AHP results are strongly influenced by the subjective judgment of the decision maker; (iii) AHP's ranking is not precise enough. Therefore, to overcome these problems and improve the uncertainty of decision-making, F-AHP was proposed by combining fuzzy theory with hierarchical analysis [31]. In F-AHP, the expert evaluates the importance of the indicator and takes into account the uncertainty of its judgment using fuzzy numbers. (1) Determination of the fuzzy number  
A fuzzy set is a collection of elements with degrees of membership, and fuzzy methods deal with the concept of attribution from a single perspective. It describes its elements through the concept of a fuzzy membership function that assigns each element a degree of membership. 1 denotes absolute belonging, 0 denotes absolute exclusion, and [0, 1] denotes some degree of partial inclusion, all relative to its set. Fuzzy theory is designed to help people make decisions in situations where information is imprecise, and fuzzy numbers are an ideal way to describe linguistic phenomena where the detailed description of their state is unknown. Fuzzy numbers and fuzzy intervals are two terms used interchangeably [32]. A triangular fuzzy number is defined by a triad (\(a^{l}\), \(a^{m}\), \(a^{u}\)) that has a triangular membership function [33; 34]. The mathematical and graphical concepts are shown in Equation (1) and Figure 4, respectively. \[\mu_{\vec{a}}(x)=\left\{ \begin{array}{cc}0&x\leq a^{l}\\ \left(x-a^{l}\right)/\left(a^{m}-a^{l}\right)&a^{l}<x<a^{m}\\ \left(a^{u}-x\right)/\left(a^{u}-a^{m}\right)&a^{m}<x<a^{u}\\ 0&x>a^{l}\end{array} \right. \tag{1}\]  
From Equation (1), The \(a^{l}\) and \(a^{u}\) denote the lower and upper bounds of the fuzzy number, respectively. \(a^{m}\) is the modal value of \(\vec{a}\). As shown in Figure 4, the triangular fuzzy number (TFN) can be expressed as, where \(a^{l}>0\), \(a^{m}>0\), and \(a^{u}>0\). (2) Identification of linguistic variables  
The process of identifying linguistic variables begins with the construction of a two-by-two comparison matrix between all the indicators in the hierarchical framework, and the membership functions of the linguistic variables are shown in Figure 5. Each expert acted as a decision maker to compare the indicators two by two by assigning linguistic terms through [PERSON]'s 1-9 scale method [35]. The nine linguistic terms compared and their respective triangular fuzzy numbers (TFN) are: \"Perfect (8,9,10)\", \"Absolute (7,8,9)\", \"Very good (6,7,8)\", \"Fairly good (5,6,7)\", \"Good (4,5,6)\", \"Preferable (3,4,5)\", \"Not bad (2,3,4)\", \"Weak advantage (1,2,3)\" and \"Equal (1,1,1)\". Figure 4: The membership function of triangular fuzzy numbers. (3) Define the fuzzy hierarchical analysis comparison matrix  
Constructing a two-by-two comparison matrix of all indicators in the dimensions of the hierarchy system and assigning linguistic terms to the two-by-two comparison by investigating which of each two indicators is more important.