Some Result on Fuzzy Integration

‎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.