Exponential Fuzzy Sets and Applications of AI-Powered Investment Decision-Making Using the Weighted Mean Method

The exponential fuzzy set ($\mathcal{EFS}$) is a new modification that allows for a more flexible representation of uncertainty by using an exponential function to define membership degree. In this work, we define basic operations on $\mathcal{EFS}$, such as complement, union, intersection, simple difference, and limited difference functions. The equivalency formula, symmetrical difference formula, disjoint sets, disjoint sum, and disjunctive sum are further important qualities that we examine. We analyse essential laws in the exponential fuzzy framework, such as the idempotent law of union. In addition, we present a few theorems that govern the relational and algebraic structures of $\mathcal{EFS}$. $\mathcal{EFS}$ has been compared against traditional approaches and the resulting studies showcase its advantages in modeling uncertainty, artificial intelligence, and decision making. This paper studies the use of exponential fuzzy sets in AI driven investment decision processes using the weighted mean method of multifactor investment analysis.