## 4 Image Fusion Applications in NDT Inspection
### Learning-Based Approaches
#### 4.5.2 Fuzzy Sets  
Fuzzy logic is another technique that uses ambiguous or imprecise statements to simulate logical thinking. Fuzzy logic stems from the idea of fuzzy sets [103] and assigns a degree of membership to the elements of a system, often a real integer in the range of \([0,1]\) (where 0 denotes \"completely false\", 1 denotes \"completely true\", and values in between the range denote \"partial truth\"). This indicates a set of many-valued logics in which the truth values are viewed as levels of truth. The general workflow of a fuzzy logic approach is as follows [104]:  
* Fuzzification: transform the data in the form of an uncertain language into the linguistic variables (fuzzy set or a membership function) together with the fuzzy components. In this way, the data can be processed using a classical binary method of \"zero\" and \"one\". * Inference: refer to a rule-based inference that the membership functions are combined with the fuzzy control rules, such as the mean of the maximum or minimum distance, to find the control outcome [105]. * Defuzzification: the fuzzy control outcome must be converted from linguistic variable to classical variable format. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sources** & **Material** & **Defect Types** & **Aim** & **Base Algorithm** & **Reference** \\ \hline Ultrasonic (US) and & & & & To overcome & \\ eddy current (EC) & Aluminum & Holes & individual sensor & ANNs & [90] \\  & & & problems & & \\ \hline Vibro-thermography & & & To use the & & \\ (VT) and pulse & Aluminium- & & synergistic effect of & Shearlet transform & \\ thermography (PT) & BFRP/GFRP & Impact & multi-excitation & and a pulse-coupled & \\  & & & infrared fusion & neural network & \\ \hline Magnetic flux & & & To avoid & Neural networks & \\ leakage and active & High-carbon steel & & & single-sensor low & and k-nearest & \\ thermography & wire rope & & precision & neighbour & \\ \hline Accelerometer, & & & To optimise feature & & \\ microphone, current & & & & extraction and & \\ sensor and optical & & & selection at fusion & neural networks & \\ encoder & & & level & & \\ \hline Pulsed & Plant & & To overcome the & & \\ thermography and & fibre-reinforced & Impact & structural & Unsupervised deep & \\ terahertz inspections & polymer (PFRP) & & complexity of plant & residual network & \\ \hline Industrial camera & Stainless steel & & & & \\ images & (reflective material) & & & & \\  & & & deformations, & illumination effect & \\  & & & on detection & & \\ \hline Line scan active & & & To provide NDT & & \\ thermography and & & & & inspection for & \\ terahertz inspections & & & & preserving cultural & residual network & \\  & & & heritage objects & & \\ \hline Continuous-wave & & & & & \\ terahertz and & & & & & \\ long-wave infrared & & & & & \\ (LWIR) & & & & & \\ thermography & & & & inspection method & \\ inspections & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: A summary of the recent neural network-based fusion studies for NDT methods. From the point of view of NDT, defect characterisation is the primary implementation field to use entire methodologies, whether it is data collection or processing that data. An early study which introduced a fuzzy logic-based pixel fusion for three tomographic techniques that characterise different shape properties was presented at the end of the nineties [106]. Cylindrically shaped aluminium specimens that included two different thicknesses for the drilled side holes and a planar flaw were used. Here, the set was utilised to define the pixel's membership level in a generated defect image. To be precise, the member pixels had a weight of 1, while others were between 0 and 1 according to the membership function. The weighted pixel amplitudes were summed to form a fused defect image. The study showed that the holes were clearly visible in the fused images, but the planar flaw was not evident in terms of size and shape. It was explained that the data acquisition configurations might change with the orientation of the defect.