Transactions on Fuzzy Sets and Systems (Nov 2024)
Some Result on Fuzzy Integration
Abstract
In this article, we introduce a new concept of fuzzy measurement, the space of fuzzy measurable functions and fuzzy integral, which has a dynamic position and is different from previous approaches. With this concept, we create a new version of measurement theory and fuzzy integral. The main goal of this paper is to define the fuzzy integral in the fuzzy size space. First, we introduce fuzzy measurable functions and $L^{+}$ essential and related concepts in fuzzy space. In the continuation of the work, with the help of fuzzy measurable functions, we define the fuzzy integral in the fuzzy measurement space and examine the theorems related to it and the relationship between them in the fuzzy measurement space. The next step is to establish one of the fundamental convergence theorems with the uniform convergence theorem in the fuzzy measurement space and prove it. Finally, we prove Fatou's lemma as an application of the theorems raised in the fuzzy measurement space.
