The Fuzzy Future: Embracing the Potential of Fuzzy Functions

الملخص

Most of the tools we've used in the past for formal modeling, reasoning, and computing are clear, predictable, and precise. By crisp, we mean that the answer is either yes or no, not more or less. In traditional dual logic, for example, a statement can either be true or false but not both. In set theory, an element either belongs to a set or it doesn't. In optimization, a solution is either possible or it isn't. Precision means that the parameters of a model exactly represent either how we see the phenomenon being modeled or how the real system being modeled works. Most of the time, precision also means that the model is clear or that it has no ambiguities.

This study mostly talks about: 1) a generalized treatment of fuzzy sets of type n, where n is an integer greater than or equal to 1, with an example, mathematical discussions, and real-life interpretations of the given mathematical concepts; 2) the potentials and links between fuzzy logic and probability logic that haven't been talked about in one document; and 3) the representation of random and fuzzy uncertainties and ambiguities that come up in data-driven systems.