**3.3 Risk assessment phase**

### **3.3.1 Fuzzy inference process**

The risk assessment is the phase where the fuzzy attributes related to a Case are processed according to fuzzy rules evaluating the degree of risk present in the workplace. At the end of this phase the fuzzy evaluation result is defuzzified to produce the output to present to the users. The reasoning process used is discussed in this section as well as its FMADM mathematical counterpart.

The main assumption of this fuzzy risk assessment model is that if a hazard is present in a workplace and there is a lack of adequate safety control measures and there are some potentiating factors then there is risk for accident. This can be expressed by the following generic rule:

**IF** hazard exists **AND** safety control is inadequate AND (R1) potentiating factors exist **THEN** risk exists

The fuzzy approach allows the use of fuzzy operators to numerically aggregate the different fuzzy attributes that characterize the criteria of the rule and assess the degree of truth of the conclusion. Considering the variety of fuzzy operators the ANDs expressed in the rule can be formulated using different intersection operators, according to desired aggregation behaviour. Therefore, rule [R1] can be translated into a mathematical formula such as:

$$
\mu\_r = (\mu\_h \propto \mu\_p) \* \mu\_{pf} \tag{E1}
$$

Where:

30 Fuzzy Inference System – Theory and Applications

opinions and measurements is done using the OWA operator (Yager, R. R., 1988). With this operator it is possible to assign weights to the different input data sources. This is particularly useful when the sources of information have different levels of reliability. In this case the inputs from more reliable sources have a bigger weight than the ones coming from

Fig. 5. Linguistic variable "inadequacy" used to evaluate "protection inadequacy"

adequate little

adequate

The risk assessment is the phase where the fuzzy attributes related to a Case are processed according to fuzzy rules evaluating the degree of risk present in the workplace. At the end of this phase the fuzzy evaluation result is defuzzified to produce the output to present to the users. The reasoning process used is discussed in this section as well as its FMADM

The main assumption of this fuzzy risk assessment model is that if a hazard is present in a workplace and there is a lack of adequate safety control measures and there are some potentiating factors then there is risk for accident. This can be expressed by the following

safety control is inadequate AND (R1)

The fuzzy approach allows the use of fuzzy operators to numerically aggregate the different fuzzy attributes that characterize the criteria of the rule and assess the degree of truth of the conclusion. Considering the variety of fuzzy operators the ANDs expressed in the rule can be formulated using different intersection operators, according to desired aggregation behaviour. Therefore, rule [R1] can be translated into a mathematical formula such as:

inadequate

inadequate very

less reliable sources.

**3.3 Risk assessment phase 3.3.1 Fuzzy inference process** 

0

very adequate

0,25

0,5

**Inadequacy Degree**

0,75

1

mathematical counterpart.

**IF** hazard exists **AND**

potentiating factors exist

generic rule:

**THEN** risk exists

*µr* is the Fuzzy membership degree that reflects the risk level;

*µh* is the Fuzzy membership degree that reflects the hazard level for a specific risk;

*µp* is the Fuzzy membership degree that reflects the inadequacy level of the safety control measures set in place to prevent a specific risk;

*µpf* is the Fuzzy membership degree that reflects the level of the potentiating factors for a specific risk;

represents a Fuzzy Intersection aggregation operator that produces a normalized fuzzy value, i.e., in the interval [0, 1]

\* represents a Fuzzy Intersection aggregation operator that produces a normalized fuzzy value, i.e., in the interval [0, 1]

Each criteria of the rule (the left side terms of the IF-THEN) can be the result of previous rules of an inference chain. For instance, considering that the protection provided by the safety control measures can be achieved through collective and personnel protection means the evaluation of the criteria "safety control is inadequate" can result from the use of the following rule:

**IF** collective protection is inadequate **AND** personnel protection is inadequate (R2) **THEN** safety control is inadequate

As before this rule can be translated into a mathematical formula, such as:

$$
\mu\_p = \mu\_{cp} \land \mu\_{lp} \tag{E2}
$$

Where:

*µp* is the Fuzzy membership degree that reflects the inadequacy of the safety control measures set in place to prevent a specific risk;

*µcp* is the Fuzzy membership degree that reflects the inadequacy of the collective protection measures set in place to protect a specific risk;

*µip* is the Fuzzy membership degree that reflects the inadequacy of the personnel protection measures set in place to protect a specific risk;

 represents a Fuzzy Intersection aggregation operator that produces a normalized fuzzy value, i.e., in the interval [0, 1]

Another example relates with the evaluation of the potentiating factors. These factors (e.g., work activity, and environmental, psychosocial and individual factors) do not represent risk by themselves but potentiate and may intensify the negative impact of a hazard. In this case the evaluation of the criteria "potentiating factors exist" can result from the use of the following rule:


Applications of Fuzzy Logic in Risk Assessment – The RA\_X Case 33

The Dubois and Prade Intersection operator is an operator with compensation which is controlled by the parameter. This operator was selected to aggregate two main factors, Hazard and lack of adequate Safety Control. The result of this aggregation reflects the extension of the Hazard that is not mitigated by the Safety Control (Prevention and

The Algebraic Product was selected to combine the result of the above aggregation with the Potentiating factors. The rationale behind this selection is that there is an identical

The Min operator is used in the aggregation of data regarding the levels of Collective and Personnel Protection. This operator was selected because it reflects the lack of protection that is still present in the workplace after combining all the types of protective measures set

The Dubois and Prade Union operator is an operator with compensation which is controlled by the ' parameter. This operator is used twice. It is used first to aggregate the Attributes that characterize each Potentiating factor, and a second time to aggregate the results of all individual Potentiating factors, producing a global result. The use of this operator allows the simulation of the synergistic effect resulting from the simultaneous presence of several

The risk assessment results are presented as crisp risk levels which are obtained through a defuzzification process that uses a VL like the one presented in Figure 6. Note that the definition of the defuzzification fuzzy sets has to consider the relationship between the results distribution in the [0, 1] domain and the linguistic evaluation categories. Since the evaluation process uses product operators and the terms in the interval [0, 1], the evaluation results tend to be shifted to zero; therefore, the width of the fuzzy sets that reflect each linguistic term varies to accommodate this characteristic of the evaluation process. For a

Very Low

Low

Medium

High

Very High

Fig. 6. Linguistic variable "risk level" used to defuzzify the risk assessment results

0 0,2 0,4 0,6 0,8 1

**Risk Level**

Protection) measures implemented.

in place.

Potentiating factors.

**3.3.3 Defuzzification process** 

0

0,2

0,4

0,6

**Membership Degree**

0,8

1

contribution of both terms to the risk level.

Naturally such inference chains can have multiple layers that address the information regarding a specific concept with difference levels of detail (i.e., complexity, vagueness and relevance). An example of the next level of the inference chain rules is the evaluation of the criteria "work activity is inadequate". One should note that this evaluation is risk dependent. Considering, for instance, the criteria to assess the "work activity" potentiating factor regarding the risk of "falls from height", the following rule could be used:

**IF** type of floor/tidiness is inadequate **OR**  manual materials handling exists **OR** use of tools exists **OR** (R4) handling of suspended loads exists **THEN** work activity is inadequate

This type of rule can be assessed numerically considering the respective membership degrees using a generic assessment formula such as:

$$
\mu\_{pf\_l} = \cup\_{f=1}^n \mu\_{f\_{lf}} \tag{E3}
$$

Where:

*µpfi* is the Fuzzy membership degree that reflects the inadequacy level of *ith* potentiating factor for a specific risk;

*µf ij* is the Fuzzy membership degree that reflects the inadequacy level of the *jth* factor contributing to the *ith* potentiating factor for a specific risk;

U represents a Fuzzy Union aggregation operator that produces a normalized fuzzy value, i.e., in the interval [0, 1]

#### **3.3.2 Fuzzy operators selection**

The selection of the aggregation operators was based on the eight selection criteria proposed by (Zimmermann, H.-J., 2001) mentioned above. Table 1 synthesizes the main fuzzy operators used in the RA\_X, and also the value of the parameters adopted for the parametric operators.


Table 1. Fuzzy operators adopted in the RA\_X model

The Dubois and Prade Intersection operator is an operator with compensation which is controlled by the parameter. This operator was selected to aggregate two main factors, Hazard and lack of adequate Safety Control. The result of this aggregation reflects the extension of the Hazard that is not mitigated by the Safety Control (Prevention and Protection) measures implemented.

The Algebraic Product was selected to combine the result of the above aggregation with the Potentiating factors. The rationale behind this selection is that there is an identical contribution of both terms to the risk level.

The Min operator is used in the aggregation of data regarding the levels of Collective and Personnel Protection. This operator was selected because it reflects the lack of protection that is still present in the workplace after combining all the types of protective measures set in place.

The Dubois and Prade Union operator is an operator with compensation which is controlled by the ' parameter. This operator is used twice. It is used first to aggregate the Attributes that characterize each Potentiating factor, and a second time to aggregate the results of all individual Potentiating factors, producing a global result. The use of this operator allows the simulation of the synergistic effect resulting from the simultaneous presence of several Potentiating factors.

#### **3.3.3 Defuzzification process**

32 Fuzzy Inference System – Theory and Applications

Naturally such inference chains can have multiple layers that address the information regarding a specific concept with difference levels of detail (i.e., complexity, vagueness and relevance). An example of the next level of the inference chain rules is the evaluation of the criteria "work activity is inadequate". One should note that this evaluation is risk dependent. Considering, for instance, the criteria to assess the "work activity" potentiating

use of tools exists **OR** (R4)

This type of rule can be assessed numerically considering the respective membership

���� = ⋃ ���� �

is the Fuzzy membership degree that reflects the inadequacy level of *ith* potentiating

is the Fuzzy membership degree that reflects the inadequacy level of the *jth* factor

U represents a Fuzzy Union aggregation operator that produces a normalized fuzzy value,

The selection of the aggregation operators was based on the eight selection criteria proposed by (Zimmermann, H.-J., 2001) mentioned above. Table 1 synthesizes the main fuzzy operators used in the RA\_X, and also the value of the parameters adopted for the parametric

**# Fuzzy Operator Parameter** 

���� <sup>=</sup> ����

E2 ^ Min ���� = min (��, ��) -

<sup>=</sup> ����� � ���� � ����1 � ��

product ���� = ��� �� -

��� (E3)

������, ��, �) , ���0,1� = 0.9

, ��, ��) ����1 � ��,1���, ��) , ����0,1� ' = 0.6

factor regarding the risk of "falls from height", the following rule could be used:

**IF** type of floor/tidiness is inadequate **OR**  manual materials handling exists **OR**

degrees using a generic assessment formula such as:

contributing to the *ith* potentiating factor for a specific risk;

 handling of suspended loads exists **THEN** work activity is inadequate

Where:

operators.

**Equation** 

E1

E3

factor for a specific risk;

i.e., in the interval [0, 1]

**3.3.2 Fuzzy operators selection** 

E1 \* Algebraic

Dubois and Prade Intersection

Dubois and Prade Union

Table 1. Fuzzy operators adopted in the RA\_X model

���´�

*µpfi*

*µf ij*

> The risk assessment results are presented as crisp risk levels which are obtained through a defuzzification process that uses a VL like the one presented in Figure 6. Note that the definition of the defuzzification fuzzy sets has to consider the relationship between the results distribution in the [0, 1] domain and the linguistic evaluation categories. Since the evaluation process uses product operators and the terms in the interval [0, 1], the evaluation results tend to be shifted to zero; therefore, the width of the fuzzy sets that reflect each linguistic term varies to accommodate this characteristic of the evaluation process. For a

Fig. 6. Linguistic variable "risk level" used to defuzzify the risk assessment results

Applications of Fuzzy Logic in Risk Assessment – The RA\_X Case 35

In this section it will be demonstrated the use of the RA\_X fuzzy model in support of risk management. The example presented analyzes a construction work activity, which is pouring concrete into the forms of the structure of a building. Since the activity is performed on a platform located several meters in the air, the risk analysis presented regards the risk of

Supervision

tools

loads

Work pace

 Hearing Vision

Table 2. Example of main factors and attributes considered in the assessment

 Wind Rain Cold Noise

Protection Harness/Lifeline

Security Signs/ Warnings

 Type of floor/Tidiness Manual materials handling Use of power/heavy

Handling suspended

Alcohol consumption

Extra Work Stress

Safety barriers Safe Access

 Techniques and Procedures

 Interaction with other work activities

 Vibration Illumination

Dust

Safety

behaviour Type of footwear Safety training

*"Regarding the [attribute1] of the risk of [descriptor of risk] consider the following advice* 

*Specific Recommendation1* 

*Specific Recommendationn"* 

**Risk Hazard Attributes** 

 Collective Protection (Physical)

 Collective Protection (Organizational)

Personnel

Work Activity

 Environmental Factors

 Psychosocial Factors

of the risk "falls from height"

Individual Factors

 Work at height Height **Safety Control Factors Attributes** 

**Potentiating Factors Attributes** 

**4. Application example** 

"falls from height".

**Falls from height** 

*…* 

given fuzzy risk level the linguistic term is selected from the fuzzy set with higher membership degree. For instance, a risk level of 0.5 has a membership degree of 0.2 to "Medium" and 0.8 to "High", consequently the qualifier to use will be "High".

The selected qualifier is used for building a sentence in natural language that presents the result to the user, using the generic format:

*The risk of [descriptor of risk] is [qualifier]* 

For instance, a result from a risk assessment can be "The risk of electrical shock is very high".

#### **3.3.4 Explanation process**

The system can also offer explanations about the results presented. This is done using a backward chain inference process that identifies, ranks and presents the attributes that have high values (above a specified threshold) and that more significantly contributed to the computed level of risk. The explanations use the following generic format:

```
"The risk of [descriptor of risk] is [qualifier] because: 
The [attribute1] is [qualifier] (fuzzy value) 
The [attribute2] is [qualifier] (fuzzy value) 
 … 
The [attributen] is [qualifier] (fuzzy value)"
```
Where the detailed explanations are sorted in decreasing order of the respective attributes fuzzy value.

#### **3.3.5 Advice phase**

The advice phase is performed after the conclusion of the risk assessment, and offers recommendations about safety measures adequate to control the risk for situations where the risk level is Medium or higher. The recommendations can be generic and specific. Generic recommendations refer to advice (i.e., legislation, guidelines, best practice) relating to a type of risk in general (e.g., risk of falls from height); while specific recommendations refer to advice that addresses a specific type of attribute that contributes to the risk (e.g., collective protection installed in site).

The generic recommendations use the following format:

*"Regarding the risk of [descriptor of risk] consider the following advice Generic Recommendation1* 

*Generic Recommendationn"* 

*…* 

The selection of the specific recommendations is performed using a backward chaining inference process based on the risk assessment fuzzy rules. This process identifies and ranks the key attributes that contributed to the risk assessment result (i.e., the attributes with high membership values), and provides recommendations in this order.

The specific recommendations use the following format:

*"Regarding the [attribute1] of the risk of [descriptor of risk] consider the following advice Specific Recommendation1 …* 

*Specific Recommendationn"* 
