Some Result on Fuzzy Integration

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Chaharpashlou Reza; Lotfali Ghasab Ehsan

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Journal Paper

Paper Information

Journal: Transactions on Fuzzy Sets and Systems Year:2024 | Volume:2 | Issue:3 Page(s): 100-107

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Information Journal Paper

Title

Some Result on Fuzzy Integration

Author(s)

Chaharpashlou Reza | Lotfali Ghasab Ehsan | Issue Writer Certificate

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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