Abstract

A common research topic has been the search of an optimal center, according to some objective function that considers the distance between the potential solutions and a given set of points. For crisp data, closed form expressions obtained are the median center, for the Manhattan distance, and the min-max center, for the Chebyshev distance. In this paper, we prove that these closed form expressions can be extended to fuzzy sets by modeling data points with fuzzy numbers, obtaining centers that, through their membership function, model the "appropriateness" of the final location.