A note on the potentials of probabilistic and fuzzy logic
This work addresses the representation of uncertainties in data-driven problems, but it appears incremental as it consolidates existing ideas without introducing new methods.
The paper tackles the generalization of fuzzy sets and explores the connections between fuzzy logic and probability logic, providing mathematical discussions and real-life interpretations of these concepts.
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical concepts; (2) the potentials and links between fuzzy logic and probability logic that have not been discussed in one document in literature; (3) representation of real-life random and fuzzy uncertainties and ambiguities that arise in data-driven real-life problems, due to uncertain mathematical and vague verbal terms in datasets.