Some Result on Fuzzy Integration
محورهای موضوعی : 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.
کلید واژه: Fuzzy measure space, Fuzzy measure, Fuzzy measurable function, Fuzzy integral.,
چکیده مقاله :
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.
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.
[1] Altenbach H, Eremeyev V. Advances in Linear and Nonlinear Continuum and Structural Mechanics. Springer; 2023. DOI: https://doi.org/10.1007/978-3-031-43210-1
[2] Bass RF. Real Analysis for Graduate Students: Measure and Integration Theory. CreateSpace, 2011.
[3] Chaharpashlou R, Saadati R, Abdeljawad T. Existence, uniqueness and HUR stability of fractional integral equations by random matrix control functions in MMB-space. Journal of Taibah University for Science. 2021; 15(1): 574-578. DOI: https://doi.org/10.1080/16583655.2021.1994787
[4] Chaharpashlou R, ORegan D, Park C, Saadati R. C*-Algebra valued fuzzy normed spaces with application of HyersUlam stability of a random integral equation. Advances in Difference Equations. 2020; 2020(1): 326. DOI: https://doi.org/10.1186/s13662-020-02780-0
[5] Hadzic O, Pap E. Fixed Point Theory in Probabilistic Metric Spaces. Dordrecht: Kluwer Academic Publishers; 2001. DOI: https://doi.org/10.1007/978-94-017-1560-7
[6] Nazarianpoor M, Rassias JM, Sadeghi Gh. Solution and stability of quatturvigintic functional equation in intuitionistic fuzzy normed spaces. Iranian Journal of Fuzzy Systems. 2018; 15(4): 13-30. DOI: https://doi.org/10.22111/IJFS.2018.4112
[7] Saadati R, Vaezpour SM. Some results on fuzzy Banach spaces. Journal of Applied Mathematics and Computing. 2005; 17(1-2): 475-484. DOI: https://doi.org/10.1007/BF02936069
[8] Vijayakumar S, Karthikeyan S, Rassias JM, Baskaran B. A quartic functional equation originating from the sum of the medians of a triangle in fuzzy normed space. In: American Institute of Physics Conference Series. 2020. p.020006. DOI: https://doi.org/10.1063/5.0028290
