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Multicriteria decision analysis (MCDA) involves techniques which relatively recently have received great increase in interest for their capabilities of solving spatial decision problems. One of the most frequently used techniques of MCDA is Analytic Hierarchy Process (AHP). In the AHP, decision-makers make pairwise comparisons between different criteria to obtain values of their relative importance. The AHP initially only dealt with crisp numbers or exact values in the pairwise comparisons, but later it has been modified and adapted to also consider fuzzy values. It is necessary to empirically validate the ability of the fuzzified AHP for solving spatial problems. Further, the effects of different levels of fuzzification on the method have to be studied. In the context of a hypothetical GIS-based decision-making problem of locating a dam in Costa Rica using real-world data, this paper illustrates and compares the effects of increasing levels of uncertainty exemplified through different levels of fuzzification of the AHP. Practical comparison of the methods in this work, in accordance with the theoretical research, revealed that by increasing the level of uncertainty or fuzziness in the fuzzy AHP, differences between results of the conventional and fuzzy AHPs become more significant. These differences in the results of the methods may affect the final decisions in decision-making processes. This study concludes that the AHP is sensitive to the level of fuzzification and decision-makers should be aware of this sensitivity while using the fuzzy AHP. Furthermore, the methodology described may serve as a guideline on how to perform a sensitivity analysis in spatial MCDA. Depending on the character of criteria weights, i.e. the degree of fuzzification, and its impact on the results of a selected decision 1 rule (e.g. AHP), the results from a fuzzy analysis may be used to produce sensitivity estimates for crisp AHP MCDA methods.

Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.