Fuzzy Sets and Systems 158 (2007) 1546 – 1560 www.elsevier.com/locate/fss Evaluating probabilistic data with a possibilistic criterion in land-restoration decision-making: Effects on the precision of results Burak Güneralp a , ∗, 1 , George Gertner a , Guillermo Mendoza a , Alan Anderson b a Department of Natural Resources and Environmental Sciences, University of Illinois at Urbana-Champaign, W503 Turner Hall, 1102 S. Goodwin Avenue, Urbana, IL 61801, USA b US ACE, CERL, P.O. Box 9005, Champaign, IL, USA Received 13 September 2005; received in revised form 13 February 2007; accepted 26 February 2007 Available online 12 March 2007 Abstract Many decision-making settings incorporate both possibilistic and probabilistic uncertainty. In this study, entropy is used as a common measure in quantifying both types of uncertainty. This measure facilitates the direct comparison of the “amounts” of the two types of uncertainty in a given situation. The main objective of this study is, however, to illustrate how, in a decision-making setting, incorporating fuzzy membership function to represent possibilistic uncertainty leads to a more realistic assessment of the decision-making problem at hand. A methodology for the evaluation of land condition and for aiding the decision on restoration allocation and a case study is presented. The methodology enables handling both types of uncertainty: probabilistic uncertainty from the spatial simulation data and possibilistic uncertainty due to vagueness in land condition factor. Erosion status is selected as the land condition factor. Restoration allocation decision is based on fuzzy logic to reflect the continuous transition between different land conditions. The analysis is done six times, each time using a membership function with a different degree of fuzziness. Insights gathered from this study would relate to the risks associated with taking a decision in the presence of both types of uncertainty. The comparison of the output of the analysis (i.e. the loss associated with misclassification) from six different trials reveals that the variance in the loss values decreases as more fuzziness is incorporated into the analysis. In other words, there is an inverse relation between the coefficient of variance of the loss values and the fuzziness incorporated into the analysis. A more in-depth analytical investigation is needed to understand if this observation is specific to this case study or a more general phenomenon. © 2007 Elsevier B.V. All rights reserved. Keywords: Decision analysis; Measures of information; Land restoration; Geography; Uncertainty; Entropy; Vagueness 1. Background Uncertainty is pervasive in many real-world problems. Therefore, proper representation and accommodation of uncertainty is important in order to better represent the actual situation in the analyses. Although applicable only for dealing with a very special type of uncertainty, probability theory has historically been the only tool in dealing with uncertainty until the introduction of the theory of fuzzy sets by Zadeh [26]. Uncertainty in the context of fuzzy sets implies inexactness or imprecision, not in terms of randomness or probabilistic terms. Various types of uncertainty can ∗ Corresponding author. E-mail address: guneralp@stanford.edu (B. Güneralp). 1 Present address: Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305, USA. 0165-0114/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2007.02.021