*3.5. Fuzzy Logic Based Techniques*

Fuzzy logic is one of the multi-value logic, i.e., one in which more than two logical values are adopted. This term is closely related to the fuzzy set theory. In the fuzzy logic, a series of intermediate values extend between state 0 (e.g., false) and state 1 (e.g., true), which determine the degree of belonging of an element to a set. The fuzzy logic is very useful in engineering applications, because the classical truth/false logic cannot effectively deal with many ambiguous problems [70]. The problem of this type in the cement composites technology is precisely the digital identification of cracks using an image analysis. The problem of ambiguous identification of cracks on the surface of a cement composite using the fuzzy logic has been shown in Figure 7. The fuzzy logic techniques are often used in combination with genetic algorithms and artificial neural networks, which may result in the creation of an intelligent system with the ability to generalize knowledge in a given area.

**Figure 7.** Model scheme of the fuzzy logic in an application to identify cracks on the surface of cement composites, where the input variable is the value on the gray-scale histogram.

Choudhary and Dey [71] used a fuzzy logic model in which they used "area" and "ratio" as input variables and the output variable was the "class" of the object. The class in this case was the pixel belonging to the crack or noise. Each variable consisted of two or more fuzzy subsets and corresponding trapezoidal membership functions. A total of 205 different images representing a cracked concrete surface were examined and it was found that the overall accuracy of the model was estimated at 90–94%. The fuzzy logic technique was also used to identify cracks on road pavements [72]. The whole developed method was based on the assumption that the crack is a continuous element and is darker on the histogram compared to its surroundings. The developed algorithm allowed positive identification of very thin cracks, even on very noisy pavement images. Yan et al. [73] developed an adaptive fuzzy image enhancement algorithm that effectively identified the cracking patterns on pavement surface.
