Abstract

Natural neighbors, inspired by human friendship, define a relationship in which two individuals consider each other mutual neighbors. Based on this concept, Zhu et al. (2016) introduced the Natural Neighbor Search Algorithm to automatically determine the optimal number of neighbors in the K-Nearest Neighbors (KNN) algorithms. Although this method has been applied in various data mining tasks, it faces limitations with datasets of varying density. Specifically, points in dense regions may be incorrectly flagged as outliers, while those in sparse regions may go undetected. In this paper, we extend the concept of Boolean natural neighbors into a fuzzy framework, offering a more nuanced understanding of neighborhood relations. This leads to the development of four novel outlier detection algorithms. One of these integrates the ideas of having few friends and being far away from other data points, providing a robust solution to the ambiguity inherent in outlier detection. Since both concepts (few and far) are fuzzy by nature, their aggregation using fuzzy operators is a natural choice, improving both the flexibility and the accuracy of detecting outliers. Benchmarking on 18 datasets demonstrates that our proposed methods outperform state-of-the-art techniques in terms of AUC and Precision.