**4. Fuzzy inference systems and managing bridges**

Fuzzy logic is an interesting and easy-to-use method for practical inference problems in engineering. It relates significance and precision to each other very well. Fuzzy logic-based inference systems enable the use of engineering judgment, experience and scarce field data to translate the level of deterioration or damage to condition rating (Rajani et al., 2006).

One of the best methods to deal with decision making problems such as condition rating of bridges is application of Fuzzy Inference System (FIS). In order to diagnose deterioration type or damage detection in concrete bridges and to increase accuracy and errors reduction caused by subjective human judgment fuzzy inferring is the appropriate choice (Wang & Hu 2006). Fuzzy sets can be used for modeling uncertainty of detection and imprecision of symptoms.

Detection support systems operate on rules with fuzzy premises, which represent imprecise symptoms. During inference fuzzy relations or implications are used, so conclusions are also represented in the form of fuzzy sets (Straszecka, 2006).

#### **4.1 Fuzzy inference system**

System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with ill-defined and uncertain systems. By contrast, a fuzzy inference system employing fuzzy *if-then* rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A Fuzzy Inference System (FIS) is a way of mapping an input space to an output space using fuzzy logic. A FIS tries to formalize the reasoning process of human language by means of fuzzy logic (that is, by building fuzzy IF-THEN rules). This *fuzzy modeling* or *fuzzy identification*, first explored systematically by Takagi and Sugeno, has found numerous practical applications in control different engineering application and fields.

*Fuzzy if-then rules* or *fuzzy conditional statements* are expressions of the form *IF A THEN B*, where A and B are labels of *fuzzy sets* characterized by appropriate membership functions. Due to their concise form, fuzzy if-then rules are often employed to capture the imprecise

Uncertainty and fuzziness have a particularly close relationship with each other and systems that handle knowledge with fuzziness have been created even in the field of

One of the best ways of dealing with this kind of problems is the application of fuzzy inference system. Fuzzy inference system is capable of dealing with imprecise, imperfect, uncertain and vague data and information. Thus, it can be good candidate toward

A measure of imprecision is advantageous for symptoms representation. Uncertainty characterizes a relation between symptoms and deteriorations/damages, while imprecision

Fuzzy logic is an interesting and easy-to-use method for practical inference problems in engineering. It relates significance and precision to each other very well. Fuzzy logic-based inference systems enable the use of engineering judgment, experience and scarce field data to translate the level of deterioration or damage to condition rating (Rajani et al., 2006).

One of the best methods to deal with decision making problems such as condition rating of bridges is application of Fuzzy Inference System (FIS). In order to diagnose deterioration type or damage detection in concrete bridges and to increase accuracy and errors reduction caused by subjective human judgment fuzzy inferring is the appropriate choice (Wang & Hu 2006). Fuzzy sets can be used for modeling uncertainty of detection and imprecision of

Detection support systems operate on rules with fuzzy premises, which represent imprecise symptoms. During inference fuzzy relations or implications are used, so conclusions are also

System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with ill-defined and uncertain systems. By contrast, a fuzzy inference system employing fuzzy *if-then* rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A Fuzzy Inference System (FIS) is a way of mapping an input space to an output space using fuzzy logic. A FIS tries to formalize the reasoning process of human language by means of fuzzy logic (that is, by building fuzzy IF-THEN rules). This *fuzzy modeling* or *fuzzy identification*, first explored systematically by Takagi and Sugeno, has found numerous

*Fuzzy if-then rules* or *fuzzy conditional statements* are expressions of the form *IF A THEN B*, where A and B are labels of *fuzzy sets* characterized by appropriate membership functions. Due to their concise form, fuzzy if-then rules are often employed to capture the imprecise

practical applications in control different engineering application and fields.

Incompleteness

symptoms.

**4.1 Fuzzy inference system** 

Fuzziness or imprecision

knowledge engineering (Terano et al., 1992).

development of practical BMS and BHMS.

is associated with the symptoms representation.

**4. Fuzzy inference systems and managing bridges** 

represented in the form of fuzzy sets (Straszecka, 2006).

modes of reasoning that play an essential role in the human ability to make decisions in an environment of uncertainty and imprecision.

Another form of fuzzy if-then rule has fuzzy sets involved only in the premise part. By using Takagi and Sugeno's fuzzy if-then rule, we can use a relationship among variables or simply a formula. However, the consequent part is described by a nonfuzzy equation of the input variable.

Both types of fuzzy if-then rules have been used extensively in both modeling and control. Through the use of linguistic labels and membership functions, a fuzzy if-then rule can easily capture the spirit of a "rule of thumb" used by humans. From another angle, due to the qualifiers on the premise parts, each fuzzy if-then rule can be viewed as a local description of the system under consideration. Fuzzy if-then rules form a core part of the fuzzy inference system. Fig. 2 shows the general form of a Fuzzy Inference System (FIS) (Jang, 1993).

Fig. 2. Fuzzy Inference System (FIS)
