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Trends and applications of multi-criteria decision analysis in environmental sciences: literature review

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Abstract

Approximately 3000 papers concerning multi-criteria decision analysis (MCDA) in the environmental field were identified through a series of queries in the Web of Science database and classified by MCDA method and environmental application using text mining in R. Stemming and stop word removal techniques were used to remove irrelevant text from the literature. Trends in MCDA methods (AHP/ANP, TOPSIS, outranking, MAUT/MAVT) associated with specific environmental applications (water, air, energy, natural resources, and waste management) or interventions/tools applications (stakeholders, strategies, sustainability, and GIS) were identified. The results show a linear growth in the share of MCDA papers in environmental science across all application areas. Furthermore, the results show that AHP/ANP and MAUT/MAVT are the most frequently mentioned MCDA methods in the literature. For environmental applications, the results showed that natural resource and waste management keywords were, respectively, the most and least commonly discussed applications within the MCDA papers. For intervention/tool applications, we found that keywords associated with ‘strategy’ and ‘GIS’ applications are, respectively, the most and least commonly discussed keywords within the MCDA papers. The authors found that MCDA method keywords were evenly distributed across the environmental and intervention/tool applications, indicating a lack of preference in the environmental field for use of specific MCDA methods. This paper demonstrates that text mining is an applicable tool to assess specific textual trends and patterns when analyzing larger bodies of MCDA literature.

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Notes

  1. A list of the 2837 publications used in this analysis is provided in a supplemental online appendix.

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Correspondence to Igor Linkov.

Appendix

Appendix

1.1 MCDA methods

MCDA involves applying scores or ranks to multiple criteria for each alternative, weighting each criterion based on priorities, and then aggregating criteria scores to determine the best alternative. The specifics of each step and final products used to compare alternatives vary based on the method of selection. Some basic approaches to calculating a total score (V) in MCDA application incorporate linear weighted sums, often in combination with hierarchical structure. A simple equation for the linear weighted sum is V = Σ (wixi) where Σ (wi) = 1. The hierarchical structure subdivides the criteria, where V = Σ (wivi) and vi = Σ (wijxij). Most MCDA methods use some variant of these equations. The methods included in this analysis are AHP/ANP, TOPSIS, Outranking, MAUT/MAVT.

1.1.1 MAUT/MAVT

Multi Attribute Utility Theory (MAUT) and Multi Attribute Value Theory (MAVT) are built around a set of axioms of rationality. They do not involve interaction between alternatives. Value functions in MAVT are constructed to ensure consistency with preferences involving tradeoffs the decision maker is willing to make for performance across attributes. While value functions are often linear and additive, neither of these properties is required. MAUT extends MAVT, incorporating utility functions which are constructed to ensure that uncertainty is treated in a manner consistent with the decision maker’s attitude toward risk. Single attribute value and utility functions range from 0 (worst case) to 1 (best case), and multi-attribute value and utility functions, also ranging from 0 to 1, are constructed as sums or other aggregation of the single attribute utility functions. Multi-attribute utility and value functions are constructed so that the alternative which has the highest value or expected utility based on the inputs provided must be the one preferred by a rational decision maker.

MAVT with linear additive value functions is a type of MCDA (while MAUT in general is not). In this case, alternatives are scored on their attributes, these scores (xi) are normalized to the 0-1 scale by the value function, and the alternative’s value is the weighted sum V = Σi wivi (xi).

This method is useful when the management team of a project can clearly identify the priorities for weightings and the scores for each alternative.

1.1.2 Outranking

PROMETHEE and ELECTRE are similar so are often grouped together and referred to as outranking. PROMETHEE stands for Preference Ranking Organization Method for Enrichment Evaluation and ELECTRE stands for Elimination and Choice Expressing Reality. Weights are assigned to and alternatives scored on a set of criteria. Alternatives are then ranked on the different criteria, and scores based on these rankings and the criteria weights are calculated and analyzed. In essence, each criterion gets a vote.

1.1.3 AHP/ANP

The Analytic Hierarchy Process (AHP) and the closely related Analytic Network Process (ANP) both start by identifying and structuring criteria. Both methods use simple pairwise comparisons of the importance of criteria at each level of the structure to fit criteria weights. Scores (possibly derived from pairwise comparisons) of alternatives on the different criteria at the bottom level are then weighted and summed and measures of the consistency of the pairwise comparisons are calculated. Alternatives are prioritized by their total scores. Advanced versions of this method incorporate uncertainty in weights and scores.

1.1.4 TOPSIS

The Technique for Order Preference by Similarity (TOPSIS) also involves assigning weights to and scoring alternatives on multiple criteria. First each alternative is assigned a raw score on each criterion. For each criterion, these scores are normalized across alternatives using a formula which smooths out extreme values. Using these normalized scores and accounting for the weights of the different criteria, a distance is calculated between each alternative and a hypothetical point which includes the best possible value for each criterion. Alternatives are thus scored against each other in terms of how close they are to that hypothetical best alternative. By relying on intenal comparisons among alternatives, this method has the benefit of producing reasonable results without requiring participants to define explicit scales for the criteria and or to know in advance the range of possible criteria scores.

1.2 Additional charts: methods breakdown by application

Another way to classify the papers is by first determining which papers mention specific applications, and then further subdivide each application bin according to mentioned methods (AHP/ANP, MAUT/MAVT, Outranking, and TOPSIS). This breakdown is shown in Fig. 8 for environmental keywords and Fig. 9 for Intervention/Tool keywords.

Fig. 8
figure 8

Breakdown of methods by environmental keywords

Fig. 9
figure 9

Breakdown of methods by intervention/tool keywords

The proportion in the y-axis is determined by the following equation:

$${\text{Proportion}} \left( \% \right) = \frac{{{\text{Count}}_{m,a} }}{{{\text{Count}}_{a} }}$$

where \({\text{Count}}_{m,a}\) represents the number of publications that mention both the method and application (e.g., AHP/ANP and waste management) and \({\text{Count}}_{a}\) represents the number of publications that mention a specific application (e.g., waste management). Note that in Sect. 3.2.1, the denominator of the equation is \({\text{Count}}_{m}\) as opposed to \({\text{Count}}_{a}\) used in this ratio.

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Cegan, J.C., Filion, A.M., Keisler, J.M. et al. Trends and applications of multi-criteria decision analysis in environmental sciences: literature review. Environ Syst Decis 37, 123–133 (2017). https://doi.org/10.1007/s10669-017-9642-9

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