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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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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DOI: https://doi.org/10.1007/s00477-006-0042-9