Authors:
Julio Rojas-Mora
;
Didier Josselin
and
Marc Ciligot-Travain
Affiliation:
Université d’Avignon (UAPV), France
Keyword(s):
Location problem, Median center, Min-max center, Fuzzy sets, Distance.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Systems
;
Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic
;
Soft Computing
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.