Advances in Fuzzy Statistics and Uncertainty Analysis

Dear Colleagues,

The analysis of uncertainty remains one of the central challenges of modern science. While probability theory provides a powerful framework for modelling randomness, many real-world phenomena involve forms of uncertainty that arise because of imprecision, vagueness, incomplete knowledge, subjective assessments, or linguistic information. In such contexts, fuzzy set theory offers a natural and mathematically rigorous framework for representing and analysing information that cannot be adequately described through probabilistic models alone.

In recent decades, considerable efforts have been devoted to the development of fuzzy methods in engineering, artificial intelligence, and decision sciences. However, the statistical treatment of fuzzy data has received comparatively less attention. As increasingly complex datasets contain measurements, evaluations, and observations affected by ambiguity and imprecision, there is a growing need for a coherent statistical framework that is capable of describing, modelling, and analysing fuzzy information.

The objective of this Special Issue is to highlight recent advances contributing to the development of fuzzy statistics as a genuine branch of statistical science. Particular emphasis is placed on methodologies that extend the classical goals of statistics—description, inference, prediction, and decision-making—to situations involving fuzzy observations and fuzzy uncertainty.

We welcome original contributions addressing theoretical, methodological, computational, and applied aspects of fuzzy statistics and uncertainty analysis, including (but not limited to):

* Modelling and analysis of fuzzy and imprecise data;

* Fuzzy probability distributions and empirical fuzzy distributions;

* Statistical inference, estimation, and hypothesis testing under fuzzy uncertainty;

* Regression, classification, clustering, and statistical learning for fuzzy data;

* Ranking, ordering, and comparison of fuzzy quantities;

* Uncertainty quantification and propagation in fuzzy systems;

* Fuzzy risk analysis, reliability assessment, and decision-making;

* Hybrid probabilistic–possibilistic and fuzzy statistical frameworks;

* Explainable AI and machine learning under fuzzy uncertainty;

* Applications of fuzzy statistical methods in science, engineering, economics, finance, and the social sciences.

In addition to works that showcase methodological innovation, submissions that contribute to establishing robust statistical principles for the analysis of fuzzy data and that clarify the role of fuzzy uncertainty within modern statistical reasoning are of particular interest. Papers presenting real-world applications are welcome—especially those that illustrate how fuzzy statistical methods provide insights that cannot be obtained through conventional approaches alone.

By uniting researchers whose work focuses on theory, methodology, and applications, this Special Issue aims to showcase the current state of the art in fuzzy statistics and to stimulate further developments in the modelling, inference, and analysis of uncertain information.

We look forward to receiving your contributions.

Prof. Dr. Laurent Donzé
Dr. Rédina Berkachy
Guest Editors

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