Characterization of Matrix Classes Transforming Between Almost Sure Convergent Sequences of Complex Uncertain Variables

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Birojit Das ◽  
Piyali Debnath ◽  
Binod Chandra Tripathy
Keyword(s):  
Uncertainty Theory ◽  
Matrix Transformation ◽  
Matrix Classes ◽  
Uncertain Variables ◽  
Convergent Sequences

The study of uncertainty theory evolved and developed largely in the last decade. In this paper, we introduce the concept of summability and absolutely summability with respect to almost surely through matrix transformation of complex uncertain sequences and establish the interrelationship between these two concepts. In this context, applications of matrix transformation of complex uncertain sequences are also presented.

scholarly journals Lacunary sequences of complex uncertain variables defined by Orlicz functions

2021 ◽  
Vol 40 (2) ◽  
pp. 355-370
Author(s):  
Pranab Jyoti Dowari ◽  
Binod Chandra Tripathy
Keyword(s):  
Uncertainty Theory ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Uncertain Variables ◽  
Lacunary Sequences ◽  
New Class ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Convergent Sequences

Using the concept of Orlicz function and uncertainty theory, some new class of lacunary convergent sequences defined by Orlicz functions have been introduced with the lacunary convergence concepts in this paper. Some topological properties of the defined sequence spaces along with the inclusion relations have been investigated.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

scholarly journals On the Characterization of Some Classes of Four-Dimensional Matrices and Almost B-Summable Double Sequences

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Orhan Tug
Keyword(s):  
Double Sequence ◽  
Sequence Spaces ◽  
Double Sequences ◽  
Matrix Classes ◽  
Related Literature ◽  
Double Sequence Spaces

We firstly summarize the related literature about Br,s,t,u-summability of double sequence spaces and almost Br,s,t,u-summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf, BLs′:Cf, and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞, and we complete this work with some significant results.

scholarly journals Dunford-Pettis and strongly Dunford-Pettis operators on L1(μ)

1989 ◽  
Vol 31 (1) ◽  
pp. 49-57 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Positive Operator ◽  
Finite Measure ◽  
Regular Operator ◽  
Mathematical Economics ◽  
Canonical Injection ◽  
Do So ◽  
Convergent Sequences

Motivated by a problem in mathematical economics [4] Gretsky and Ostroy have shown [5] that every positive operator T:L1[0, 1] → c0 is a Dunford-Pettis operator (i.e. T maps weakly convergent sequences to norm convergent ones), and hence that the same is true for every regular operator from L1[0, 1] to c0. In a recent paper [6] we showed the converse also holds, thereby characterizing the D–P operators by this condition. In each case the proof depends (as do so many concerning D–P operators on Ll[0, 1]) on the following well-known result (see, e.g., [2]): If μ is a finite measure, an operator T:L1(μ) → E is a D–P operator is compact, where i:L∞(μ) → L1(μ) is the canonical injection of L∞(μ) into L1(μ). If μ is not a finite measure this characterization of D–P operators is no longer available, and hence results based on its use (e.g. [5], [6]) do not always have straightforward extensions to the case of operators on more general L1(μ) spaces.

scholarly journals Characterization of matrix classes involving some sets of sequences of fuzzy numbers

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6101-6112 ◽  
Author(s):  
Hemen Dutta ◽  
Jyotishmaan Gogoi
Keyword(s):  
Level Sets ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
New Approach ◽  
Matrix Classes ◽  
Sequences Of Fuzzy Numbers

In 1996, M. Stojakovic and Z. Stojakovic examined the convergence of a sequence of fuzzy numbers via Zadeh?s Extension Principle, which is quite difficult for practical use. In this paper, we utilize the notion ?-level sets to deal with convergence and summable related notions and adopted a relatively new approach to characterize matrix classes involving some sets of single sequences of fuzzy numbers. The approach is expected to be useful in dealing with characterization of several other matrix classes involving different kinds of sets of sequences of fuzzy numbers, single or multiple

scholarly journals EXISTENCE OF MODELING LIMITS FOR SEQUENCES OF SPARSE STRUCTURES

2019 ◽  
Vol 84 (02) ◽  
pp. 452-472 ◽  
Author(s):  
JAROSLAV NEŠETŘIL ◽  
PATRICE OSSONA DE MENDEZ
Keyword(s):  
Relative Size ◽  
Convergent Sequence ◽  
List Type ◽  
Sparse Graphs ◽  
First Order ◽  
Graph Modeling ◽  
Image Position ◽  
Standard Probability ◽  
Convergent Sequences

AbstractA sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a standard probability space, with the property that every definable set is Borel. It was known that FO-convergent sequence of graphs do not always admit a modeling limit, but it was conjectured that FO-convergent sequences of sufficiently sparse graphs have a modeling limits. Precisely, two conjectures were proposed:1.If a FO-convergent sequence of graphs is residual, that is if for every integer d the maximum relative size of a ball of radius d in the graphs of the sequence tends to zero, then the sequence has a modeling limit.2.A monotone class of graphs ${\cal C}$ has the property that every FO-convergent sequence of graphs from ${\cal C}$ has a modeling limit if and only if ${\cal C}$ is nowhere dense, that is if and only if for each integer p there is $N\left( p \right)$ such that no graph in ${\cal C}$ contains the pth subdivision of a complete graph on $N\left( p \right)$ vertices as a subgraph.In this article we prove both conjectures. This solves some of the main problems in the area and among others provides an analytic characterization of the nowhere dense–somewhere dense dichotomy.

scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis

2022 ◽  
Vol 27 (3) ◽  
pp. 1-19
Author(s):  
Si Chen ◽  
Guoqi Xie ◽  
Renfa Li ◽  
Keqin Li
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Uncertainty Theory ◽  
Critical Issue ◽  
Cyber Physical System ◽  
Physical Systems ◽  
Uncertain Variables ◽  
Uncertainty Model ◽  
First Time ◽  
Enhancement Algorithm

Reasonable partitioning is a critical issue for cyber-physical system (CPS) design. Traditional CPS partitioning methods run in a determined context and depend on the parameter pre-estimations, but they ignore the uncertainty of parameters and hardly consider reliability. The state-of-the-art work proposed an uncertainty theory based CPS partitioning method, which includes parameter uncertainty and reliability analysis, but it only considers linear uncertainty distributions for variables and ignores the uncertainty of reliability. In this paper, we propose an uncertainty theory based CPS partitioning method with uncertain reliability analysis. We convert the uncertain objective and constraint into determined forms; such conversion methods can be applied to all forms of uncertain variables, not just for linear. By applying uncertain reliability analysis in the uncertainty model, we for the first time include the uncertainty of reliability into the CPS partitioning, where the reliability enhancement algorithm is proposed. We study the performance of the reliability obtained through uncertain reliability analysis, and experimental results show that the system reliability with uncertainty does not change significantly with the growth of task module numbers.

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