# Knowledge-Based Fuzzy Expert System to the Condition Assessment of Historic Road Bridges
### Expert Systems and Fuzzy Logic  
Expert systems (ES) are computer programs within a particular domain that involve a certain amount of artificial intelligence mimicking human thinking to reach the same conclusions as experts. The main goal of the ES is to provide expert advice in specific situations [29]. They are part of artificial intelligence, which is a broader research area that, in addition to ES, also includes natural language management systems and a computer perception system for sight, speech, and touch [30]. The advantage of ESs is that they can use incomplete and unreliable data in conclusions and contain explanations of their review process [31]. The knowledge base in the ES contains expert knowledge on a particular issue. It stores knowledge of a specific field and heuristic-based rules to minimize the complete search of the field of knowledge. Knowledge can be shaped by formal theories or normative models and is presented in the form of rules, semantic networks, frameworks, or cases [30]. Fuzzy logic was presented by [PERSON] [32] and even then this approach attracted a lot of attention. Although for simpler systems fuzzy logic has proven to be very effective and adapted to human understanding. For more complicated systems, it has proven to be very demanding. Namely, there are situations in which knowledge about the system cannot be presented in an absolutely precise way. To present knowledge about such systems, one must reject the classical (binary) logic in which something is either true or false and use fuzzy logic. Classical set theory starts from the fact that some element \(x\) from the observed (universal) set \(X\) belongs or does not belong to a specific set \(A\). A similar division exists in classical logic: a statement is true or false and the third possibility is excluded. Belonging is conditioned by the characteristic of the element, i.e., the condition that the element of the set \(X\) must meet in order to belong to the set \(A\). The theory of fuzzy sets introduces the membership function \(\mu_{A}(x)\). This function shows how much \(x\in X\) satisfies the condition of belonging to the set \(A\). In classical theory it can have one of two values, 1 and 0, i.e., the element belongs or does not belong to the set \(A\). In the theory of fuzzy sets, the membership function can have any value between 0 and 1. The value of \(\mu_{A}(x)\) determines how much truth is in the statement that the element \(x\) belongs to the set \(A\), i.e., the element \(x\) in a greater degree meets the conditions of belonging to the set \(A\). For the membership function there is: \(0\leq\mu_{A}(x)\leq 1\), \(\forall\ x\in A\), i.e., \(\mu_{A}\): \(X\rightarrow[0,\,1]\). A fuzzy set \(A\) is defined as a set of ordered pairs: \(A=\{(x,\,\mu_{A}(x))|x\in X,\,0\leq\mu_{A}(x)\leq 1\}\). \(X\) is a universal set or set of observations on which a fuzzy set \(A\) is defined, and \(\mu_{A}(x)\) is a function of the membership of an element \(x\) to the set \(A\). Each fuzzy set is completely and uniquely determined by its membership function. Fuzzy logic is most commonly used to model complex systems in which, by applying other methods, it is very difficult to determine the interdependencies that exist between individual variables. It was also introduced in various studies of the assessment of concrete and reinforced-concrete bridge condition assessment [33; 34; 35; 36; 37; 38; 39; 40]. Models based on fuzzy logic consist of \"If-Then\" rules. The \"If-Then\" rules are interrelated with the expression \"Else\". In the vast majority of cases, the input values are most often represented by a number, where the output value is also obtained in numerical form. On the other hand, in a fuzzy system, a given system is described linguistically (qualitatively) through given rules. Therefore, numerical values are first fuzzified in a certain way. Thereafter, the reasoning mechanism processes them in a fuzzy system through the phases of aggregation, activation, and accumulation [41].