**3. Ambiguity in diagnosis and decision making**

Recently it is become obvious that although BMS and BHMS can be precisely used for managerial issues but there is an important fact about the collected data. Data is not perfect. It is found that the results and data-driven interpretations are prone to some degree of vagueness. Therefore, the obtained data that should be altered to information has inherently some degrees of uncertainty and vagueness (Tarighat & Miyamoto, 2009).

In managing a bridge we are concerned about condition state or standard level of a requirement. For example we want to know what the current condition state of a bridge is and to how it has been deviated from the previous and known condition state (Washington State Bridge Inspection Manual, 2010).

Fuzzy Inference System as a Tool for Management of Concrete Bridges 451

**A** Deck 5.8 0.81 3 7 6 49 5 **B** Deck 4.9 0.94 2 7 5 48 4 **C** Deck 5.2 0.92 3 7 6 49 4 **D** Deck 4.8 0.94 2 6 5 48 5 **E** Deck 4.5 0.74 3 6 5 48 4 **F** Deck 7.1 0.53 6 8 7 49 7 **G** Deck 5.8 0.92 4 7 5 24 7 Table 1. Statistical information from routine inspection for deck condition rating (Phares et

The range of the results between min and max show the stochastic nature of the inspector's judgment. These stochastic representations show the fuzzy nature of the inspectors'

While current rating systems of concrete structures may give a fundamental understanding of structural deterioration conditions, their application is more or less limited in reflecting actual conditions. In some cases it is often difficult to cover complex structural behavior and environment in the real world. Uncertainties and fuzziness, along with complexity, add more difficulty to the estimation of condition rating by conventional methods. Therefore a better method may be a combination of logics and statistics. To take advantage of this approach in dealing with qualitative issues such as human factors, the influence of inspectors' judgment on structural condition rating and the effects of weather conditions on inspectors' judgment should be considered (Harris, 2006; Ma, 2006; Stephens, 2000; Wang et

Since the bridge inspection results are subjected to some degrees of imprecision and vagueness it is a good idea to use fuzzy set theory to overcome the shortcomings and problems of ordinary methods for prediction of condition of bridges. Fuzzy information or fuzzy data can be encountered in managing bridges. The main reasons for fuzzy data are

Knowledge engineering methods for dealing with uncertainty in many aspects of condition prediction are used to produce expert systems. Expert systems are expected to be effective for ill-defined problems (problems in which it is either difficult or impossible to define a

In most cases, either the clear knowledge of ill-defined problems cannot be obtained, or completion of the knowledge set must be approached gradually. In other words, there are many cases in which knowledge is *ambiguous*. Meaning of the word *ambiguous* is also ambiguous and vague. Just as knowledge must be formulated and written down for a user to understand it, ambiguity must take some form before it can be dealt with technically. Therefore, ambiguity that is dealt with in knowledge engineering is classified and written

**Deviation Minimum Maximum Mode <sup>N</sup>Reference** 

**Rating** 

**Bridge Element Average Standard** 

al., 2001).

judgments.

al., 2007; Yen & Langari, 1999).

method of approach).

down as follows:

 Nondeterminism Multiple meanings Uncertainty

imprecision in measured data and subjective judgments.

In most cases diagnosis is necessary to make decision for next action to return to a standard bridge condition state. Whenever we are going to diagnose, it is common to have circumstances in which we must make decision via ambiguous data and information. Practical diagnosis in managing bridges is the making of judgments about a bridge's condition state or damage detection using expert knowledge, but the observation of symptoms includes results of visual inspection and non destructive testing methods, bridge's history, and the circumstances of the diagnosis. For example, if we think about diagnosis during a regular inspection versus before a repairing operation, indications of possible deterioration or damage and need for retesting are important in the former, but in the latter, importance is placed on certainty rather than possibility. Normally a repairing operation is not performed without confirmation of the existence of deterioration or damage in the affected element of a bridge.

The words we use concerning symptoms often contain expressions of frequency and probability, such as *sever cracks* or *high corrosion*. In contrast to this kind of linguistic ambiguity, ambiguous circumstances exist in the distinguishing of the symptom, such as different inspectors' reporting differing symptoms.

When thinking about the ambiguity that originates in the characteristics discussed above, we must also consider the ambiguity that arises from the participation of experts in the bridge evaluation. In general, there is a large dependence on visual inspection results, which are subjective judgments. Since visual inspection is cheaper, faster and sometimes simpler than other inspecting methods it is more probable to have more ambiguity levels in data and interpretations (Terano et al., 1992).

Here are some more detailed explanations of the ambiguity in managing bridges. Condition rating is a judgment of a bridge component condition in comparison to its original as-built condition at a given time (Wang & Hu, 2006). Condition rating and damage detection are crucial methods and tools to conduct efficient maintenance and managing bridges. Condition rating indices are also useful for predicting future states which are completely time dependent. Based on the periodic inspections data at different time intervals deterioration rate of the material, elements and sometimes whole structure can be modeled. These models can be good tools for decision makers in future (Zadeh, 1976).

Related to condition rating definition there is another problem: what is the exact meaning of condition or health for material or bridge element in the structure? From practical point of view deterioration or damage symptoms should be easily distinguished. But in practice symptoms as signs of deteriorations cannot be easily distinguished and be reported or categorized in well-defined manner. Here, it becomes clear what the *subjective data* means. In other words the encoding of symptoms into condition rating is imprecise and involves *subjective judgments*.

Of greatest importance is the amount of variability found in the assignment of condition ratings at a given time. As an example results of the deck delamination survey conducted during some investigations indicate that this type of inspection does not consistently provide accurate results. In a case study the condition rating results analysis and the data revealed that the condition ratings were normally distributed. Table 1 shows the summary of statistical information from routine inspection for deck condition rating (Phares et al., 2000, 2001; Graybeal et al., 2001; Moore et al., 2001).

In most cases diagnosis is necessary to make decision for next action to return to a standard bridge condition state. Whenever we are going to diagnose, it is common to have circumstances in which we must make decision via ambiguous data and information. Practical diagnosis in managing bridges is the making of judgments about a bridge's condition state or damage detection using expert knowledge, but the observation of symptoms includes results of visual inspection and non destructive testing methods, bridge's history, and the circumstances of the diagnosis. For example, if we think about diagnosis during a regular inspection versus before a repairing operation, indications of possible deterioration or damage and need for retesting are important in the former, but in the latter, importance is placed on certainty rather than possibility. Normally a repairing operation is not performed without confirmation of the existence of deterioration or damage

The words we use concerning symptoms often contain expressions of frequency and probability, such as *sever cracks* or *high corrosion*. In contrast to this kind of linguistic ambiguity, ambiguous circumstances exist in the distinguishing of the symptom, such as

When thinking about the ambiguity that originates in the characteristics discussed above, we must also consider the ambiguity that arises from the participation of experts in the bridge evaluation. In general, there is a large dependence on visual inspection results, which are subjective judgments. Since visual inspection is cheaper, faster and sometimes simpler than other inspecting methods it is more probable to have more ambiguity levels in data and

Here are some more detailed explanations of the ambiguity in managing bridges. Condition rating is a judgment of a bridge component condition in comparison to its original as-built condition at a given time (Wang & Hu, 2006). Condition rating and damage detection are crucial methods and tools to conduct efficient maintenance and managing bridges. Condition rating indices are also useful for predicting future states which are completely time dependent. Based on the periodic inspections data at different time intervals deterioration rate of the material, elements and sometimes whole structure can be modeled.

Related to condition rating definition there is another problem: what is the exact meaning of condition or health for material or bridge element in the structure? From practical point of view deterioration or damage symptoms should be easily distinguished. But in practice symptoms as signs of deteriorations cannot be easily distinguished and be reported or categorized in well-defined manner. Here, it becomes clear what the *subjective data* means. In other words the encoding of symptoms into condition rating is imprecise and involves

Of greatest importance is the amount of variability found in the assignment of condition ratings at a given time. As an example results of the deck delamination survey conducted during some investigations indicate that this type of inspection does not consistently provide accurate results. In a case study the condition rating results analysis and the data revealed that the condition ratings were normally distributed. Table 1 shows the summary of statistical information from routine inspection for deck condition rating (Phares et al.,

These models can be good tools for decision makers in future (Zadeh, 1976).

in the affected element of a bridge.

interpretations (Terano et al., 1992).

*subjective judgments*.

different inspectors' reporting differing symptoms.

2000, 2001; Graybeal et al., 2001; Moore et al., 2001).


Table 1. Statistical information from routine inspection for deck condition rating (Phares et al., 2001).

The range of the results between min and max show the stochastic nature of the inspector's judgment. These stochastic representations show the fuzzy nature of the inspectors' judgments.

While current rating systems of concrete structures may give a fundamental understanding of structural deterioration conditions, their application is more or less limited in reflecting actual conditions. In some cases it is often difficult to cover complex structural behavior and environment in the real world. Uncertainties and fuzziness, along with complexity, add more difficulty to the estimation of condition rating by conventional methods. Therefore a better method may be a combination of logics and statistics. To take advantage of this approach in dealing with qualitative issues such as human factors, the influence of inspectors' judgment on structural condition rating and the effects of weather conditions on inspectors' judgment should be considered (Harris, 2006; Ma, 2006; Stephens, 2000; Wang et al., 2007; Yen & Langari, 1999).

Since the bridge inspection results are subjected to some degrees of imprecision and vagueness it is a good idea to use fuzzy set theory to overcome the shortcomings and problems of ordinary methods for prediction of condition of bridges. Fuzzy information or fuzzy data can be encountered in managing bridges. The main reasons for fuzzy data are imprecision in measured data and subjective judgments.

Knowledge engineering methods for dealing with uncertainty in many aspects of condition prediction are used to produce expert systems. Expert systems are expected to be effective for ill-defined problems (problems in which it is either difficult or impossible to define a method of approach).

In most cases, either the clear knowledge of ill-defined problems cannot be obtained, or completion of the knowledge set must be approached gradually. In other words, there are many cases in which knowledge is *ambiguous*. Meaning of the word *ambiguous* is also ambiguous and vague. Just as knowledge must be formulated and written down for a user to understand it, ambiguity must take some form before it can be dealt with technically. Therefore, ambiguity that is dealt with in knowledge engineering is classified and written down as follows:


Fuzzy Inference System as a Tool for Management of Concrete Bridges 453

modes of reasoning that play an essential role in the human ability to make decisions in an

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

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)

Decision-Making Unit

(Fuzzy) (Fuzzy)

Mamdani's method is the most commonly used in applications, due to its simple structure fuzzy calculations. This method as a simple FIS method is used to solve almost general

Let *X* be the universe of discourse and its elements be denoted as *x*. In the fuzzy theory, fuzzy set *A* of universe *X* is defined by function *μA(x)* called the membership function of set.

*<sup>A</sup>*() 1 *x* if *x* is totally in *A*;

*<sup>A</sup>*() 0 *x* if *x* is not in *A*;

*<sup>A</sup> x* if *x* is partly in *A.* 

**Knowledge Base**

**Database Rule Base**

**Input Output**

Defuzzification Interface

(Crisp)

environment of uncertainty and imprecision.

Fuzzification Interface

Fig. 2. Fuzzy Inference System (FIS)

decision making problems for practical issues.

**4.1.1 Mamdani's method** 

*mxX <sup>A</sup>*( ) : [0,1] , where

0 () 1

input variable.

(Jang, 1993).

(Crisp)


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 knowledge engineering (Terano et al., 1992).

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 development of practical BMS and BHMS.

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