In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, t...In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.展开更多
In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions...In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.展开更多
Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft fn（t）dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Hensto...Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft fn（t）dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Henstock-Kurzweil. Necessary and sufficient conditions are given for Ф to be the indefinite integral of a Henstock Kurzweil-Pettis （or Henstock, or variational Henstock） integrable function f ： [0, 1] → X.展开更多
文摘In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.
文摘In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.
基金Supported by the MURST of Italy(Prin2008)(Grant No.2008EEZ4N7)the Polish Ministry of Science and Higher Education of Poland(Grant No.N N201416139)
文摘Let X be a Banach space with a Schauder basis （en）, and let Ф（I） =∑^∞n=1 en ft fn（t）dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Henstock-Kurzweil. Necessary and sufficient conditions are given for Ф to be the indefinite integral of a Henstock Kurzweil-Pettis （or Henstock, or variational Henstock） integrable function f ： [0, 1] → X.
