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Risk-based environmental decision-making using fuzzy analytic hierarchy process (F-AHP)

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Abstract

Environmental risk management is an integral part of risk analyses. The selection of different mitigating or preventive alternatives often involve competing and conflicting criteria, which requires sophisticated multi-criteria decision-making (MCDM) methods. Analytic hierarchy process (AHP) is one of the most commonly used MCDM methods, which integrates subjective and personal preferences in performing analyses. AHP works on a premise that decision-making of complex problems can be handled by structuring the complex problem into a simple and comprehensible hierarchical structure. However, AHP involves human subjectivity, which introduces vagueness type uncertainty and necessitates the use of decision-making under uncertainty. In this paper, vagueness type uncertainty is considered using fuzzy-based techniques. The traditional AHP is modified to fuzzy AHP using fuzzy arithmetic operations. The concept of risk attitude and associated confidence of a decision maker on the estimates of pairwise comparisons are also discussed. The methodology of the proposed technique is built on a hypothetical example and its efficacy is demonstrated through an application dealing with the selection of drilling fluid/mud for offshore oil and gas operations.

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Abbreviations

(a, b, c):

Triangular fuzzy number

CI:

Consistency index

CR:

Consistency ratio

\(\tilde{F}_{{Ai}}\) :

Final fuzzy AHP score

\(\tilde{G}_{k}\) :

Fuzzy global preference weights

\(\tilde{J}\) :

Fuzzy judgment matrix

\(\tilde{j}_{{ij}}\) :

Pairwise comparison index in fuzzy judgment matrix

RI:

Random index

\(R_{\alpha}^{{\lambda _{{\rm RI}}}}\) :

Risk index value

U T (A i ):

Total utility or ordering value (Chen’s method)

\({\tilde{w}}_{i}\) :

Fuzzy weight (where i =1 to n)

W :

Eigenvector value

X k i,j :

Risk item, where i is the order of the child in the level/layer k of hierarchical structure, and j is the parent of the child

x O (A i ):

Geometric center of an alternative (Yager centroid index)

α:

Alpha cut of fuzzy number

λ:

Eigenvalue

λmax :

Maximum eigenvalue

λRI :

Risk attitude

μ x :

Membership function of x

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Correspondence to Solomon Tesfamariam.

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Tesfamariam, S., Sadiq, R. Risk-based environmental decision-making using fuzzy analytic hierarchy process (F-AHP). Stoch Environ Res Ris Assess 21, 35–50 (2006). https://doi.org/10.1007/s00477-006-0042-9

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