Multi-Criteria Evaluation (MCE) has widely been coupled with GIS to solve the spatial decision-making problems where there are several measures to be compared and screened for decision alternatives. There is an extensive body of literature and application for over 20 years which was summarized in . In order to aid a multi-criteria decision-making process, criteria value and criteria weight should be defined whatever the preferred MCE method (including weighted linear combination (WLC) , analytical hierarchy process (AHP), reference point methods , and outranking methods ).
Uncertainty Analysis and GIS
Uncertainty is an unavoidable part of spatial data due to an approximation of real-world phenomena. Moreover, many real-world decision makings involve some aspects of uncertainty due to the unpredictable and unknowable nature of the problem. Spatial decision making is subjected to uncertainty, due to its operations which involves discretization and generalization on the geographical data set. The influence of uncertainty may be visible in the form of original data and measurement, assumptions or in the model structure. An uncertainty analysis helps us to define and understand the possible sources. Following an uncertainty analysis, a sensitivity analysis completes the picture by helping us to relate the amount of uncertainty and its relation to input variables. The potential sources of uncertainty could be multiple; however, criteria weights usually considered the foremost source of controversy and certainty in MCE . In this article, the most outstanding application of uncertainty and sensitivity analysis possibilities of MCE can be discussed under renewable energy site selection, land-use evaluation and flood vulnerability.
Multi-criteria evaluation is becoming popular in energy supply systems since it is effective to rank or order different alternatives. In some cases, decision making is highly affected by the subjective judgment of experts and stakeholders. Therefore, sensitivity analysis is also a necessary step to enhance the transparency of the procedure for renewable energy planning . Interval Shannon’s entropy, a widely used concept in determining the dominant role in information theory, is used to determine criteria weights in MCE. However, in order to have an understanding of how different cutting levels affect the results, a sensitivity analysis might be performed to provide an optimal resource allocation for decision and policy makers. Therefore, some scholars applied one-at-a-time (OAT) approach (mostly known as local sensitivity analysis) to observe the variation in the results by changing each criteria weight one by one; namely, changing one for each time while keeping the rest unchanged . The dominating criterion in the selection of wind project is closely related to the potential of the wind resource, therefore, excluding the low potential places. However, in these places, the exploitation of a potential wind project could be valuable to reduce the cost of electricity generation. For such an effort, sensitivity analysis has been used to assess wind resources in less abundant places for a case study in Tabasco, Mexico . In this study, equations that relate the cost of energy with the capacity factor of wind turbines are developed. As a result, they found that the necessity to develop a national wind industry even at sites with poor wind potential.
Land use evaluation
Land use evaluation is a process of concern from present to future. It focuses on change and its effects while considering the economic and social consequences for people and the environment . Considering this characteristic of land use evaluation process, multi-criteria decision making is a proper approach to solve decision-making problems related to land use evaluation. However, due to the complex nature of the many spatial decision-making problems in land-use, a local sensitivity approach is not always preferred since it doesn’t lay out the interaction effect among criteria weights. , ,  are among the examples where global sensitivity analysis has been applied to address the interaction among preferences in complex decision-making problems. These approaches are useful guides for modelling effort since it helps to differentiate which data is more influential. Moreover, the spatial approach helps to visualize the sources of uncertainty spatially along with the influential criteria weights in the areas of high uncertainty.
Assessment of robust vulnerability indices is crucial in flood vulnerability studies . An application of uncertainty and sensitivity analysis applied for a flood vulnerability case study for Brazil. In this study effect of variability in criteria weights (preference of each participant) are analyzed for a flood vulnerability model and the resulting map showed the highly vulnerable areas with high uncertainty . As an outcome of this kind study, a decision maker can define (i) the most sensitive vulnerability criteria to any criteria weight change, (ii) if there are any criteria that do not impact the final results, (iii) the limits of variation of criteria weights for stable results, and finally (iv) how these changes vary spatially.
To conclude, MCE, when coupled with sensitivity analysis helps to identify the uncertainty in the decision-making process and increase the confidence in the final decision-making output.
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