Fuzzy median and min-max centers: An spatiotemporal solution of optimal location problems with bidimensional trapezoidal fuzzy numbers

Abstract

The calculation of the center of a set of points in an open space, subject to a given metric, has been a widely explored topic in operations research. In this paper, we present the extension of two of these centers, the median and the min-max centers, when there is uncertainty in the location of the points. These points, modeled by two-dimensional trapezoidal fuzzy numbers (TrFN), induce uncertainties in the distance between them and the center, causing that the resulting center may also be a two-dimensional TrFN. The solution gives flexibility to planners, as the value of the membership function at any given coordinate can be seen as a degree of "appropriateness" of the final location of the center. We further consider how to model the existing space constraints and what is their effect on the calculated centers. Finally, in the case of temporal analysis, we can determine the durability of the location of the center at a given point of the study area. © Springer-Verlag Berlin Heidelberg 2013.