On the Measures of Possibility and Probability of Uncertainty: A Fuzzy Theoretical Approach
DOI:
https://doi.org/10.65150/EP-gjetr/V1E4/2025-02Keywords:
Fuzzy logic, possibility theory, probability theory, uncertainty modeling, epistemic uncertainty, risk analysisAbstract
Uncertainty remains one of the most fundamental challenges in science, philosophy, and artificial intelligence (AI). Classical probability theory provides a means to quantify randomness, while possibility theory offers a way to describe vagueness and incomplete information. This paper explores the theoretical measures of possibility and probability within the fuzzy theoretical framework, focusing on their conceptual distinctions, mathematical relationships, and integrative potential. Drawing on developments in fuzzy set theory, this study recognizes the complementary roles of possibility and probability measures in modelling uncertainty and decision-making systems. It therefore, proposes a hybrid uncertainty representation that unites probabilistic and possibilistic reasoning. Applications in environmental risk analysis and decision systems demonstrate how fuzzy theory that bridges the gap between quantitative and qualitative uncertainty. The results contribute to a unified understanding of uncertainty representation and reasoning under imprecise conditions. The analysis highlights the implications of these measures of uncertainty in reasoning, risk assessment and intelligent system design.
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Copyright (c) 2025 David E. Nwanze, Cletus Onwubuoya, Ken Onyneike (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
