Some Result on Fuzzy Integration

Subject Areas : Transactions on Fuzzy Sets and Systems

Reza Chaharpashlou ¹ , Ehsan Lotfali Ghasab ²

1 - Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran.
2 - Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran.

Received: 2024-06-09 Accepted : 2024-09-12 Published : 2024-11-05

Keywords: Fuzzy measure space, Fuzzy measure, Fuzzy measurable function, Fuzzy integral.,

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.

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