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Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS)

Fast quantum algorithms for handling probabilistic, interval, and fuzzy uncertainty

M. Martinez, Luc Longpré, Владик Крейнович, Scott A. Starks, Hung Tan Nguyen

Published Jun 22, 2004• 12 citations
Publisher

Abstract

We show how quantum computing can speed up computations related to processing probabilistic, interval, and fuzzy uncertainty.
DOI
10.1109/nafips.2003.1226817

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Among clustering algorithms, fuzzy clustering stands out for its ability to offer a nuanced representation of the data by assigning degrees of membership to clusters, providing a more flexible and adaptive approach than the rigid partitioning of hard clustering algorithms. This has proved highly advantageous, particularly for image segmentation problems. Numerous approaches have been proposed to improve the Fuzzy C-means (FCM) algorithm using quantum computing, some are quantum-inspired and others can be run on quantum simulators. In this paper, a study was conducted on Quantum Fuzzy Means (QFCM) approaches. Then, a novel QFCM algorithm is introduced to address the challenges associated with these current algorithms, particularly in handling large datasets and incorporating genuine fuzzy system principles. Using concepts from quantum computing, our approach aims to improve distance calculations between data points by using a quantum distance measure. This method enables significant acceleration of the clustering process especially when dealing with extensive datasets. Moreover, our proposed algorithm integrates a structured fuzzy system framework into the membership matrix calculation, enhancing the precision and interpretability of the clustering results. Furthermore, unlike other FCM algorithms, which often lack explicit representation of fuzzy logic principles, our approach incorporates a well-defined fuzzy system to capture the inherent uncertainty and ambiguity in real-world data.