O problema de clustering heterogêneo fuzzy: modelos e heurísticas

Abstract

This work proposes formulations for the Fuzzy Heterogeneous Clustering Problem, as well as a heuristic method of Variable Neighborhood Search to solve it. The Fuzzy Heterogeneous Clustering Problem is a clustering problem that is formulated in two levels. The first identifies groups of individuals whose perceptions about the objects involved are similar. The second level identifies fuzzy partitions of objects for each group of individuals. The second level is based on the p-median problem, whose objective is to partition a set of objects into smaller subsets and to define an object as median for each subset, such that the sum of dissimilarities between each object and its median is minimal. The Fuzzy Heterogeneous Clustering Problem generalizes the p-median problem to fuzzy environments, allowing the degrees of membership between each object and each cluster to be fractionary. This generalization allows new interpretations about the results, such as the identification of simultaneous relationships of objects with different clusters.