Interval-based, nonparametric approach for resampling of fuzzy numbers

• Published in: Soft computing (Berlin, Germany) Vol. 23; no. 14; pp. 5883 - 5903
• Main Authors: Romaniuk, Maciej, Hryniewicz, Olgierd
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2019; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computational Intelligence; Control; Engineering; Epistemology; Expected values; Fuzzy sets; Hilbert space; Mathematical Logic and Foundations; Mechatronics; Methodologies and Application; Monte Carlo simulation; Numbers; Probability distribution; Random variables; Resampling; Robotics; Statistical tests; Simulations; Bootstrap; Resampling method; Fuzzy numbers; Alpha-cuts; Generation of fuzzy numbers
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-018-3251-5

In this paper, we propose two new nonparametric resampling methods for the simulation of bootstrap-like samples of fuzzy numbers. The generated secondary samples are based on an input set (i.e., a primary sample) consisting of left–right fuzzy numbers. The proposed approaches utilize random simulations in a way which, to some extent, resembles a bootstrap. However, contrary to the classical bootstrap approach, the proposed methods are based on alpha-cuts of fuzzy numbers, which are generated in a new nonparametric way. Therefore, these procedures give us an opportunity to create ”not exactly the same as previous” fuzzy numbers and also lead to greater diversity of the obtained output. Moreover, we check whether the introduced methods can be successfully applied in two statistical tests about the mean value of a population of fuzzy numbers.