Ecology and Development Series No. 10, 2003 - ZEF

Conservation of the wild Coffea arabica populations in situOrder-weighted averageThe order-weighted average (OWA) is similar to the WLC except that a second set ofweights is used. The second set of weights, order weights, control the manner in which theweighted criteria are aggregated (Jiang and Eastman 2000). The OWA is given by theequation (Eastman 2001):∑S = w . x . woEquation 6.4ijiiwhere S is the suitability as in WLC (Equation 6.3), w ij is the weight of class j from map i, x iis the criterion scale of map i and wo i is the order weight of the map i. The OWA also usescriterion weights similar to the WLC beside the order weights. Criterion weights are applieduniformly to specific criterion maps. However, order weights are applied to the criterionscores on a pixel-by-pixel basis as determined by their rank ordering across criteria at eachlocation (pixel). Order weight 1 is assigned to the lowest-ranked criterion for that pixel (i.e.,the criterion with the lowest score), order weight 2 to the next higher-ranked criterion for thatpixel, and so forth. Thus, it is possible that a single order weight be applied to pixels fromany of the various criteria depending upon their relative rank order in that particular pixel.Both WLC and OWA are available in the MCE module of IDRISI.The advantage of using OWA is that the decision maker can get several alternativesolutions, and can choose one that best fits the objectives of the decision making process.Because, order weights can produce several aggregate solutions that fall anywhere betweenthe ‘minimum’ and ‘maximum’ along the risk continuum. The concept of risk in decisionmakingoriginates from the Boolean approaches. The Boolean approaches are extremefunctions that result either in very risk-averse solutions when the AND operator is used or inrisk-taking solutions when the OR operator is used (Eastman 2001). In the risk-aversesolution, a high aggregate suitability score for a given location (pixel) is only possible if allcriteria have high scores. In the risk-taking solution, a high score in any criterion will yield ahigh aggregate score, even if all the other criteria have very low scores. The AND operationcan be described as the ‘minimum’, since the minimum score for any pixel determines thefinal aggregate score. Similarly, the OR operation can be called the ‘maximum’, since themaximum score for any pixel determines the final aggregate score. The AND solution is riskaversebecause we can be sure that the score for every criterion is at least as good as the finalaggregate score. The OR solution is risk-taking because the final aggregate score only tells us110