The Heterogeneous Fuzzy Clustering Problem: Models and Heuristics
Heterogeneous Clustering Problem, Fuzzy Environments, Consumer Segmentation.
This work proposes formulations for the Fuzzy Heterogeneous Clustering Problem
and proposes 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 distinct fuzzy partitions of objects for each
group of individuals. The second level is based on the p-median problem, whose objective is to separate 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 it’s 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.