Multi-class granular approximation by means of disjoint and adjacent fuzzy granules
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multi-class granular approximations for {\L}ukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.
Code (0)
등록된 구현이 없습니다.
Tasks
AttributeBinary ClassificationMulti-class ClassificationSimilar Papers 제목 키워드 기반
Diversity-aware clustering: Computational Complexity and Approximation Algorithms
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen c…
ClusteringDiversity$(O,G)$-granular variable precision fuzzy rough sets based on overlap and grouping functions
Since Bustince et al. introduced the concepts of overlap and grouping functions, these two types of aggregation functions have attracted a lot of interest in both theory and applications. In this paper, the depiction of …
Fuzzy granular approximation classifier
In this article, a new Fuzzy Granular Approximation Classifier (FGAC) is introduced. The classifier is based on the previously introduced concept of the granular approximation and its multi-class classification case. The…
Binary ClassificationClassificationMulti-class ClassificationClassification with Nearest Disjoint Centroids
In this paper, we develop a new classification method based on nearest centroid, and it is called the nearest disjoint centroid classifier. Our method differs from the nearest centroid classifier in the following two asp…
Classificationfeature selectionStochastic spectral embedding
Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classica…
Uncertainty Quantification