Autor/innen
Julian Behrend, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; Tom Könecke, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; Mario Rosenfelder, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; Jan Schneider, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; Michael Hanss, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; Peter Eberhard, Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
Über dieses Buch
The quantification of sparse, imprecise knowledge using possibility theory traditionally forces a compromise between computational efficiency and geometric accuracy. Standard interval arithmetic over axis-aligned hyperrectangles ignores parameter dependencies and yields overly conservative bounds, while sampling-based techniques capture these dependencies but remain computationally intensive and fail to deliver guarantees. By leveraging geometric properties of ellipsoids, we address these challenges by providing a comprehensive operational calculus for possibilistic uncertainty representation using hyperellipsoids. This framework provides methodologies to construct ellipsoidal possibility distributions from data, fuse multiple knowledge sources, propagate distributions analytically through affine functions, and extract both marginal and joint distributions. Furthermore, we demonstrate the practical efficacy of these ellipsoidal possibility distributions by applying them to a filtering application for a mobile robot localization problem.
Veröffentlicht
21.08.2026
Copyright (c) 2026 Matthias Faes, Michael Beer, Julian Behrend, Marco Broccardo, Guohai Chen, Hanshu Chen, Jieyu Chen, Fang Cong, Henrik Ebel, Peter Eberhard, Andrea Franchini, Zhuojia Fu, Yanzhao Gu, Michael Hanss, Hui Huang, Md Maidul Islam, Jafar Jafari-Asl, Balsa Jovanovic, Tom Könecke, Olga Kosheleva, Vladik Kreinovich, Hao-Ming Li, Pei-Pei Li, Qinghe Li, Ruikun Li, Stefano Marelli, Rafi L. Muhanna, Robert L. Mullen, Chiara Nardin, Lukáš Novák, Shenghao Piao, Mario Rosenfelder, Styfen Schär, Jan Schneider, Wei Shi, Panagiotis Spyridis, Bruno Sudret, Ruben Van Coile, Bo-Yu Wang, Dixiong Yang, Xuan-Yi Zhang, Zi-Xin Zhang, Bo-Qi Zhao, Yan-Gang Zhao, Zhibao Zheng, Baihong Zhong, Zhaowei Zhou, Marcos A. Valdebenito, Chao Dang, Lan-Xin Li, Marius Bittner, Parth Tambat, Marco Behrendt, Zhao Liu, Ping Zhu, Zlatan Dimitrov, Petar O. Hristov, Meng-Ze Lyu, Yang-Yi Liu, Jian-Bing Chen, Qitian Lu, Miroslav Vořechovský, Ekaterina Auer, Lorenz Gillner, Julien Alexandre dit Sandretto, Binod K. Yadav, Ghifari Adam Faza, Hans Hallez, David Moens, Reza Naeimaei, Steffen Schön, Elisabeth Ötsch, Hans Neuner, Zhanhua Liang, Jingwen Song, Michael Desch, Mehdi Modares, Valentin Nikolov, Paulo Lucas Figueiredo, José Torres Farinha, Hugo Raposo, António J. Marques Cardoso, Alice do Carmo Duarte Rodrigues, Paula Gonçalves, Peihan Chen, Xinyu Zhu, Pengfei Wei, Kaiwen Li, Mansoureh Shahabi, Y. F. Cui, Johannes O. Royset, Salvatore Russotto, Mario Di Paola, Antonina Pirrotta, Til Lux, Johannes Sundheim, Tania Feiri, Udo Wiens, Marcus Ricker, F. Niklas Schietzold, Felix Harazin, Yoshi Diepelt, Wolfgang Graf, Michael Kaliske, Rongyao Song, Changcong Zhou, Xuanyi Zhao, Weiping Zhang, Juntao Hu, Yu Chen, Edoardo Patelli, Tingting Sun, Jianbing Chen, Bouwe Verkens, L. Bogaerts, Patrick Van Rymenant, Maximilian Schweizer, Marc Fina, Werner Wagner, Steffen Freitag, George Stefanou, Dimitros Savvas, Panagiotis Gavalas, Luigi Schiano, Razhan S. Ahmed, Oleksandr Al-Shboul, David Ringeloth, Vladislav Gudžulić, Stefanie Schoen, Jelena Bijeljić, Ernst Niederleithinger, Iurie Curoşu, Gerrit E. Neu, Jia-Hui Fu, Yi Luo, De-Cheng Feng, Xiao-Qiu Ai, Luyi Li, Hao Wang, Tairan Wang, Sifeng Bi, Emily Zeller (Kapitelautor/in)
Zitationsvorschlag
Possibilistic uncertainty modeling with hyperellipsoids. (2026). In
REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World (pp. 204-218). TUDObooks.
https://doi.org/10.17877/tudobooks-11.155
