## 3 Methodology
### Neutrosophic Classifier  
All real-world information has some degree of imprecision due to many factors. As used here, \"imprecise\" might mean anything from vagueness to a lack of detail. Such fuzzy information may be handled by a number of different theories, such as fuzzy set theory, probability theory, intuitionistic fuzzy set theory, and paraconsistent logic theory. These ideas can explain certain aspects of a complicated problem, but not all of them. For instance, partial and inconsistent data are outside the scope of fuzzy set theory. Mathematical models of ambiguity, vagueness, inconsistency, contradiction, redundancy, and incompleteness were the impetus for the creation of neutrosophic logic [14; 15; 16]. Due to its focus on membership and non-membership of an element to a particular class, fuzzy logic and related logics fail to address the indeterminate nature of data acquired due to factors such as incomplete knowledge, stochasticity, or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures). The non-membership value must be equal to one minus the membership value for the fuzzy logic notion to hold [38]. Neutrosophic logic is a non-traditional approach to tripartition analysis that takes into account qualifications like degree of truthiness (\(T\)), degree of indeterminacy (\(I\)), and degree of falsity (\(F\)) [47; 48]. A comparison of neutrosophic and fuzzy classifiers is shown in Figure 6[14]. Figure 5: Discrete wavelet transform (with different decomposition level) of the simulated ultrasonic signal. A single-valued neutrosophic set \(N\) through \(X\) taking the form \(N=\{\)x, \(T_{N}(x),I_{N}(x)\), \(F_{N}(x):x\in X\}\), where \(X\) be a universe of discourse, \(T_{N}(x):X\rightarrow[0,\,1]\), \(I_{N}(x):X\rightarrow[0,\,1]\) and \(F_{N}(x):X\rightarrow[0,\,1]\) with \(0\leq T_{N}(x)+I_{N}(x)+F_{N}(x)\leq\ 3\) for all \(x\in\ X\). \(T_{A}(x)\), \(I_{A}(x)\) and \(F_{A}(x)\) represent truth membership, indeterminacy membership and falsity membership degrees of \(x\) to \(N\). A linear trapezoidal neutrosophic number is defined as \(\widetilde{\text{A}}_{Neu}=(a,b,\,c,\,d;\,e,\,f,\,g,\,h;\,i,\,j,\,k,\,l)\) whose truth, indeterminacy and falsity membership is defined as [49; 50; 51]:  
\[T_{\widetilde{\text{A}}_{Neu}}=\left\{ \begin{array}{ll}0&x<a\\ \frac{x-a}{b-a}&a\leq x<b\\ 1&b\leq x<c\\ \frac{d-x}{d-c}&c\leq x\leq d\\ 0&x>d\end{array} \right. \tag{1}\]  
Figure 6: A look at how NS is like fuzzy logic. (**a**) The triangular fuzzy membership function of classes I and II; (**b**) a fuzzy verification; (**c**–**e**) are the neutrosophic truth, falsehood, and indeterminacy parts, respectively. \[I_{\widetilde{\Lambda},Neu}=\left\{ \begin{array}{ll}1&x<e\\ \frac{f-x}{f-e}&e\leq x<f\\ 0&f\leq x<g\\ \frac{x-g}{h-g}&g\leq x\leq h\\ 1&x>h\end{array} \right. \tag{2}\]  
\[F_{\widetilde{\Lambda},Neu}=\left\{ \begin{array}{ll}1&x<i\\ \frac{i-x}{f-i}&i\leq x<j\\ 0&j<x<k\\ \frac{x-k}{1-k}&k\leq x\leq l\\ 1&x>l\end{array} \right. \tag{3}\]  
where \(0\leq T_{\widetilde{\Lambda}_{Neu}}(x)+I_{\widetilde{\Lambda}_{Neu}}(x)+I_{ \widetilde{\Lambda}_{Neu}}(x)\leq 3,x\in\widetilde{\Lambda}_{Neu}\). The pictorial view is shown in Figure 7.  
The suggested neutrosophic rule-based indoor obstacle detection expands upon the fuzzy rule-based system by making use of neutrosophic logic. Statements of neutrosophic logic, rather than fuzzy logic, are used as antecedents and consequences of \"IF-THEN\" rules in the proposed paradigm. It has three steps: First, there is neutrosophication, which entails transforming crisp inputs into the neutrosophic knowledge base through the truth-membership, falsity-membership, and indeterminacy-membership functions. In the second stage, the neutrosophic \"IF-THEN\" rules leverage the knowledge base to generate neutrosophic results. The third stage, \"deneutrosophication,\" uses three functions similar to those used in \"neutrosophication\" to transform the neutrosophic results produced in the previous phase into a crisp one. 1.