Incorporating the LCIA concept into fuzzy risk assessment as a tool for environmental impact assessment

Abstract

Environmental impact assessment (EIA) is a procedural tool for environmental management that identifies, predicts, evaluates and mitigates the environmental impact of development proposals. In the process of EIA, EIA reports, prepared by developers, are expected to delineate the environmental impact, but in practice they usually determine whether the amounts or concentrations of pollutants comply with the relevant standards. Actually, many analytical tools can improve the analysis of environmental impact in EIA reports, such as life cycle assessment (LCA) and environmental risk assessment (ERA). Life cycle impact assessment (LCIA) is one of steps in LCA that takes account of the causal relationships between environmental hazards and damage. Incorporating the concept of LCIA into an ERA as an integrated tool for the preparation of EIA reports extends the focus of the reports from the regulatory compliance of the environmental impact, to determine the significance of the environmental impact. Sometimes, when using integrated tools, it is necessary to consider fuzzy situations, because of a lack of sufficient information; therefore, so ERA should be generalized to a fuzzy risk assessment (FRA). Therefore, this paper proposes the integration of a LCIA and a FRA as an assessment tool for the preparation of EIA reports, whereby the LCIA clearly identifies the causal linkage for hazard–pathway–receptor–damage and then better explain the significance of the impact; furthermore, a FRA copes with fuzzy and probabilistic situations in the assessment of pollution severity and the estimation of exposure probability. Finally, the use of the proposed methodology is demonstrated in a case study of the expansion plan for the world’s largest plastics processing factory.

Appendices

Appendix 1: Fuzzy Logic

Fuzzy logic (Zadeh 1996) has the ability to compute with words, to model qualitative human thought processes in the analysis of complex systems and decisions. Fuzzy logic represents qualitative perception-based reasoning by ‘IF-THEN’ fuzzy rules. An example of fuzzy logic, in which a new fuzzy value is derived on the basis of a fuzzy rule (i.e., the ith rule in a fuzzy-rule base) with three antecedents and three fuzzy facts, is represented as follows:

$$ \frac{\begin{gathered} \hfill {\text{If}}\,{\text{X}}_{1} \,{\text{is}}\,{\text{F}}_{\text{i1}} \,{\text{AND}}\,{\text{X}}_{2} \,{\text{is}}\,{\text{F}}_{{{\text{i}}2}} \,{\text{AND}}\,{\text{X}}_{3} \,{\text{is}}\,{\text{F}}_{{{\text{i}}3}} \,{\text{THEN}}\,{\text{Y}}\,{\text{is}}\,{\text{G}}_{\text{i}} \\ \hfill {\text{X}}_{1} \,{\text{is}}\,{\text{F}}_{1}^{\prime } \,{\text{AND}}\,{\text{X}}_{2} \,{\text{is}}\,{\text{F}}_{2}^{\prime } \,{\text{AND}}\,{\text{X}}_{3} \,{\text{is}}\,{\text{F}}_{2}^{\prime } \,{\text{AND}}\,{\text{X}}_{3} \,{\text{is}}\,{\text{F}}_{3}^{\prime } \\ \end{gathered} }{{{\text{Y}}\,{\text{is}}\,{\text{G}}_{1}^{\prime } }} $$

(7)

where X_j and Y are linguistic variables, F_ij and ${\text{F}}_{\text{j}}^{\prime }$ are fuzzy sets of U_j and G_ij and ${\text{G}}_{\text{j}}^{\prime }$ are fuzzy sets of V. In the framework of the compositional rule of inference (Zadeh 1975), ${\text{G}}_{\text{j}}^{\prime }$ is computed by

$$ {\text{G}}_{\text{i}}^{\prime } = \left( {{\text{F}}_{1}^{\prime } \wedge {\text{F}}_{2}^{\prime } \wedge {\text{F}}_{3}^{\prime } } \right) \circ \left( {\left( {{\text{F}}_{{{\text{i}}1}} \wedge {\text{F}}_{{{\text{i}}2}} \wedge {\text{F}}_{{{\text{i}}3}} } \right) \to {\text{G}}_{\text{i}} } \right) $$

(8)

where ∧ denotes a t-norm operator, ∘ is a composition operator and → indicates an implication operator.

The selection of operators is important for the calculation of G′. If ‘sup-min’ is chosen as the composition operator (Zadeh 1975), the membership function of G′ is computed by:

$$ \mu_{{{\text{G}}_{\text{i}}^{\prime } }} ({\text{v}}) = \mathop {\max }\limits_{{{\text{u}}1,{\text{u}}2,{\text{u}}3}} \min \left[ {\mu_{{{\text{F}}_{1}^{\prime } \wedge {\text{F}}_{2}^{\prime } \wedge {\text{F}}_{3}^{\prime } }} \left( {{\text{u}}_{1} ,{\text{u}}_{2} ,{\text{u}}_{3} } \right),\mu_{{{\text{F}}_{{{\text{i}}1}} \wedge {\text{F}}_{{{\text{i}}2}} \wedge {\text{F}}_{{{\text{i}}3}} \to {\text{G}}}} \left( {{\text{u}}_{1} ,{\text{u}}_{2} ,{\text{u}}_{3} ,{\text{v}}} \right)} \right] $$

(9)

Furthermore, if ‘min’ is the t-norm operator (i.e., a ∧ b = min (a, b)) and the Mamdani’s implication operator (i.e., a → b = min(a, b)), Eq. 9 becomes the well-known ‘Mamdani’s fuzzy reasoning’, which can be expressed as

$$ \mu_{{G_{i}^{\prime } }} (v) = \mathop {\max }\limits_{u1,u2,u3} \min \left[ {\mu_{{F_{1}^{\prime } }} (u_{1} ),\mu_{{F_{2}^{\prime } }} (u_{2} ),\mu_{{F_{3}^{\prime } }} (u_{3} ),\mu_{{F_{i1} }} (u_{1} ),\mu_{{F_{i2} }} (u_{2} ),\mu_{{F_{i3} }} (u_{3} ),\mu_{G} (v)} \right] $$

(10)

Equation 10 can be further depicted in another form:

$$ \mu_{{G_{i}^{\prime } }} (v) = \min \left[ {\mathop {\max }\limits_{u1} \mu_{{F_{1}^{\prime } \wedge F_{i1} }} (u_{1} ),\mathop {\max }\limits_{u2} \mu_{{F_{2}^{\prime } \wedge F_{i2} }} (u_{2} ),\mathop {\max }\limits_{u3} \mu_{{F_{3}^{\prime } \wedge F_{i3} }} (u_{3} ),\mu_{G} (v)} \right] $$

(11)

where $F_{j}^{\prime } \wedge F_{ij}$ denotes the intersection of fuzzy sets $F_{j}^{\prime }$ and F _ij ; $\mathop {\max }\limits_{uj} \mu_{{F_{j}^{\prime } \wedge F_{ij} }} (u_{j} )$ is the highest degree of membership of the intersection and can be interpreted as the compatibility C_ij between $F_{j}^{\prime }$ and F _ij ; $\min \left[ {\mathop {\max }\limits_{u1} \mu_{{F_{1}^{\prime } \wedge F_{i1} }} (u_{1} ),\mathop {\max }\limits_{u2} \mu_{{F_{2}^{\prime } \wedge F_{i2} }} (u_{2} ),\mathop {\max }\limits_{u3} \mu_{{F_{3}^{\prime } \wedge F_{i3} }} (u_{3} )} \right]$ can be viewed as the overall compatibility C_i between the facts and the rule; and C_i is used to truncate G_i to obtain ${\text{G}}_{\text{i}}^{\prime }$. Moreover, if ${\text{F}}_{\text{j}}^{\prime }$ is a precise value (i.e., say ū_j), Eq. (11) becomes:

$$ \mu_{{G_{i}^{\prime } }} (v) = \min \left[ {\mu_{{F_{i1} }} \left( {\overline{u}_{1} } \right),\mu_{{F_{i2} }} \left( {\overline{u}_{2} } \right),\mu_{{F_{i3} }} \left( {\overline{u}_{3} } \right),\mu_{G} (v)} \right] $$

(12)

where $\min \left[ {\mu_{{F_{i1} }} \left( {\overline{u}_{1} } \right),\mu_{{F_{i2} }} \left( {\overline{u}_{2} } \right),\mu_{{F_{i3} }} \left( {\overline{u}_{3} } \right)} \right]$ can be viewed as the overall compatibility C_i between the facts and the rule; C_i is used to truncate G_i to obtain ${\text{G}}_{\text{i}}^{\prime }$.

Appendix 2: Analysis of the sensitivity of operators in fuzzy logic

The sensitivity analysis of this study’ fuzzy logic system with different operators is expressed by three-dimensional surfaces, which represent the dependency of the output (severity) on any two of the three inputs (magnitude, spatial extent and temporal duration), as shown in Fig. 8. When any horizontal plane exists it implies that both of the inputs are not sensitive to the output; in other words, any change in the inputs within the plane does not alter the output. The selection of operators (‘product’ for the ‘and operator’ and the ‘implication operator’; ‘centroid’ for the ‘defuzzification operator’) is acceptable in the sensitivity analysis, as shown in Fig. 8a, b. Even if either the ‘and operator’ or the ‘implication operator’ uses ‘min’, the sensitivity analysis is still acceptable, as shown in Fig. 8c, d. However, it is unacceptable, due to the existence of horizontal planes, if the ‘defuzzification operator’ uses other settings (‘bisector’, ‘mom’, ‘lom’, or ‘som’), or if the membership functions are changed from ‘triangular’ into ‘trapezoidal’ or ‘Gaussian’.

Fig. 8

Sensitivity analysis of the fuzzy logic system with different operators. a Our selection (E&M vs. S), b our selection (D&M vs. S), c And operator: min, d Implication operator: min, e Defuzzification: Bisector, f Defuzzification: Mom, lom, som, g Membership function: trapezoid, h Membership function: Gaussian