It is important to predict the hidden behavior of a complex system. In the existing models for predicting the hidden behavior, the hidden belief rule base (HBRB) is an effective model which can use ...qualitative knowledge and quantitative data. However, the frame of discernment (FoD) of HBRB which is composed of some states or propositions and the universal set including all states or propositions is not complete. The global ignorance and local ignorance cannot be considered at the same time, which may lead to the inaccurate forecasting results. To solve the problems, a new HBRB model named as PHBRB in which the hidden behavior is described on the FoD of the power set is proposed in this correspondence paper. Furthermore, by using the evidential reasoning rule as the inference tool of PHBRB, a new projection covariance matrix adaption evolution strategy is developed to optimize the parameters of PHBRB so that more accurate prediction results can be obtained. A case study of network security situation prediction is conducted to demonstrate the effectiveness of the newly proposed method.
For a quasinilpotent bounded linear operator
T
, we write
k
x
=
lim sup
z
→
0
log
‖
(
z
-
T
)
-
1
x
‖
log
‖
(
z
-
T
)
-
1
‖
for each nonzero vector
x
. Set
Λ
(
T
)
=
{
k
x
:
x
≠
0
}
, and call it the
...power set
Λ
(
T
)
of
T
. This notation was introduced by Douglas and Yang (see Hermitian geometry on resolvent set.
arXiv:1608.05990
, 2016; Oper Theory Adv Appl 267, Springer, Cham, 2018; Sci Cina Math.
https://doi.org/10.1007/s11425-000-0000-0
). They showed that for
τ
∈
Λ
(
T
)
,
M
τ
:
=
{
0
,
x
:
k
x
≤
τ
}
is a linear subspace invariant under each
A
commuting with
T
; hence, if there are two different points
τ
j
∈
Λ
(
T
)
such that
M
τ
j
’s are closed, then
T
has a nontrivial hyperinvariant subspace. In this paper, we show that if a quasinilpotent unilateral weighted shift
T
is strongly strictly cyclic, then
Λ
(
T
)
=
{
1
}
. Moreover, we construct a quasinilpotent operator
T
such that
Λ
(
T
)
=
0
,
1
and
M
τ
is not closed for all
τ
in 0, 1). Even so, we still find a subset
N
of
Lat
T
, the lattice of invariant subspaces of
T
, such that
N
is order isomorphic to
Λ
(
T
)
.
Purpose. The purpose of the study is to improve the methodological approach to modeling the power set of the environmental risk management system of enterprises that are part of agricultural holdings ...taking into account the sustainable development values. To achieve this goal, the components of the environmental risk management system of agroholdings are identified; the types and nature of connections between the components of the environmental risk management system and the sustainable development values are substantiated; the power set is built. Methodology / approach. Methods of systematization, induction and deduction, as well as structural-process scientific approach were used to identify components of environmental risk management systems of agroholdings. The rules of logic and the provisions of set theory were used to argue that the environmental risk management systems of agroholdings should be formed as a power set. The method of expert assessments was used to prove the fact that the recognition of the values of sustainable development in the practice of management of agroholdings leads to positive socio-economic effects (by surveying 34 managers at different levels of management). Results. The components of environmental risk management systems that should be in enterprises that are part of agroholdings are identified. It is argued that environmental risk management systems of agroholdings should be formed as a power set. Empirical data show that the recognition of the values of sustainable development in the practice of management of agroholdings leads to positive socio-economic effects. Originality / scientific novelty. The methodological approach to modeling the power set of the environmental risk management system of agroholdings in the system of sustainable development values has been improved. It is based on the use of tools for the provisions of set theory and makes it possible to causally provide functional interaction between all structural components of the environmental risk management system. The methodological approach allows optimizing of environmental risk management. As a result, the decisions will reduce conflicts of interest between agroholdings and society. Practical value / implications. The practical value of applying an improved methodological approach involves the possibility of its use by agroholdings to make decisions to reduce environmental risks. Adherence to the values of sustainable development in environmental risk management provides positive effects and reduces conflicts of interest between agroholdings and society. Therefore, the improved methodological approach has good prospects for practical application. This was practically proved on the basis of empirical data of A.G.R. Group, Agrotis, Agrotrade, AP Group, ASTARTA-Kyiv, Agroprodservice, Agroton, ATK, Western Bug, MPR, PAEK, Ristone Holding, SVAROG, Ukrprominvest AGRO, HARVEAST.
Ocean wave energy has been regarded as a promising and sustainable power source for offshore power system. In order to handle the uncertainty and fluctuation of the wave power, the power system is ...generally designed to be highly dependent on short-time energy storage facilities such as battery packs. This means the cost of energy storage facility tends to dramatically increase when a large wave farm is deployed. This paper proposes a model predictive control algorithm to realise the continuous power set-point tracking of a single six-of-freedom point absorber with multiple power take-off units, to mitigate the dependence of the energy storage in offshore power supply. The key controller settings that determine the power quality of the wave energy converter are analysed over various power set-points. Furthermore, the performance of power set-point tracking is assessed over significant wave heights and peak periods. It is found that although the power set-point tracking algorithm only achieves 10-27% of power generation capacity at the expense of reducing power fluctuation, the controlled point absorber is still capable to serve as a high-quality power source in some of offshore scenarios.
Wireless sensor network (WSN) is inevitably subject to node failures due to their harsh operating environments and extra-long working hours. In order to ensure reliable and correct data collection, ...WSN node fault diagnosis is necessary. Fault diagnosis of sensor nodes usually requires the extraction of data features from the original collected data. However, the data features of different types of faults sometimes have similarities, making it difficult to distinguish and represent the types of faults in the diagnosis results, these indistinguishable types of faults are called ambiguous information. Therefore, a belief rule base with power set (PBRB) fault diagnosis method is proposed. In this method, the power set identification framework is used to represent the fuzzy information, the evidential reasoning (ER) method is used as the reasoning process, and the projection covariance matrix adaptive evolution strategy (P-CMA-ES) is used as the parameter optimization algorithm. The results of the case study show that PBRB method has higher accuracy and better stability compared to other commonly used fault diagnosis methods. According to the research results, PBRB can not only represent the fault types that are difficult to distinguish, but also has the advantage of small sample training. This makes the model obtain high fault diagnosis accuracy and stability.
Fault diagnosis, Wireless sensor network, Belief rule base, Power set.
A permutation group
G
acting on a set
Ω
induces a permutation group on the power set
P
(
Ω
)
(the set of all subsets of
Ω
). Let
G
be a finite permutation group of degree
n
and
s
(
G
) denote the ...number of orbits of
G
on
P
(
Ω
)
. It is an interesting problem to determine the lower bound
inf
log
2
s
(
G
)
n
over all groups
G
that do not contain any alternating group
A
ℓ
(where
ℓ
>
t
for some fixed
t
⩾
4
)
as a composition factor. The second author obtained the answer for the case
t
=
4
in Yang (J Algebra Appl 19:2150005, 2020). In this paper, we continue this investigation and study the cases when
t
⩾
5
, and give the explicit lower bounds
inf
log
2
s
(
G
)
n
for each positive integer
5
⩽
t
⩽
166
.
We study power-set operations on classes of trees and tree algebras. Our main
result consists of a distributive law between the tree monad and the
upwards-closed power-set monad, in the case where ...all trees are assumed to be
linear. For non-linear ones, we prove that such a distributive law does not
exist.
Transfer learning is a great technology that can leverage knowledge from label-rich domains to address problems in similar domains that lack labeled data. Most previous works focus on single-source ...transfer, assuming the source domain contains sufficient labeled data and is close to the target domain. However, in practical applications, this assumption is hardly met, and labeled data exist in different domains. To improve the adaptability of transfer learning models for multi-source scenarios, many existing methods utilize the commonality and specificity across source domains. They either map all source domains with the target domain into a common feature space for knowledge transfer or combine multiple classifiers trained on pairs of each source and target to form a target classifier. However, the correlations across multiple source domains that can bring significant impacts on learning performance are ignored. In light of this, we propose a novel multi-source transfer learning method based on the power set framework (PSF-MSTL). First, PSF-MSTL constructs a power set framework that enables different source domains to be interrelated. Second, PSF-MSTL makes the source-domain framework integral and able to provide complementary knowledge using a dual-promotion strategy. Additionally, PSF-MSTL is formulated as an optimization problem, and an iterative algorithm is presented to address it. Finally, we conduct extensive experiments to show that PSF-MSTL can outperform many advanced multi-source transfer learning methods.
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