On fuzzy Henstock-Stieltjes integral on time scales with respect to bounded variation function
Juan Li, Yubing Li, Yabin Shao, Angelo Marcelo Tusset, Angelo Marcelo Tusset, Angelo Marcelo Tusset
TL;DR
This paper introduces a new type of fuzzy integral on time scales, expanding the theory of fuzzy calculus.
Contribution
The paper introduces the fuzzy Henstock-Stieltjes Δ-integral on time scales with respect to bounded variation functions.
Findings
The paper defines the FHS-Δ-integral and outlines its basic properties.
It provides necessary and sufficient conditions for integrable functions.
A characterization theorem is presented using the embedding theorem of fuzzy number space.
Abstract
In present paper we will investigate the basic theory of fuzzy Henstock-Stieltjes Δ-integral with respect to a bounded variation function on time scale. Firstly, we define the notion of fuzzy Henstock-Stieltjes Δ-integral (or briefly FHS-Δ-integral) on time scales, and propose some basic properties and several necessary and sufficient conditions for fuzzy Henstock-Stieltjes Δ-integrable functions. Secondly, we present a characterization theorem of fuzzy Henstock-Stieltjes Δ-integrable function by using the embedding theorem of fuzzy number space. Therefore, this paper complements and enriches the theory of fuzzy integral, and the results of this paper will contribute to establishing discontinuous fuzzy dynamic equations on time scales.
Genes, proteins, chemicals, diseases, species, mutations and cell lines named across the full text — each resolved to its canonical identifier and authoritative record.
Click any figure to enlarge with its caption.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40
Figure 41
Figure 42
Figure 43
Figure 44
Figure 45
Figure 46
Figure 47
Figure 48
Figure 49
Figure 50Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFuzzy Systems and Optimization · Nonlinear Differential Equations Analysis · Functional Equations Stability Results