32,074 research outputs found

### Identifying influential nodes based on fuzzy local dimension in complex networks

How to identify influential nodes in complex networks is an important aspect
in the study of complex network. In this paper, a novel fuzzy local dimension
(FLD) is proposed to rank the influential nodes in complex networks, where a
node with high fuzzy local dimension has high influential ability. This
proposed method focuses on the influence of the distance from the center node
on the local dimension of center node by fuzzy set, resulting in a change in
influential ability. In order to show this proposed method's effectiveness and
accuracy, four real-world networks are applied in this paper. Meanwhile,
Susceptible-Infected (SI) is used to simulate the spreading process by FLD and
other centrality measures, and Kendall's tau coefficient is used to describe
the correlation between the influential nodes obtained by centrality and the
results measured by SI model. Observing from the ranking lists and simulated
results, this method is effective and accurate to rank the influential nodes.Comment: 38 pages, 6 figure

### A quantum dynamic belief decision making model

The sure thing principle and the law of total probability are basic laws in
classic probability theory. A disjunction fallacy leads to the violation of
these two classical probability laws. In this paper, a new quantum dynamic
belief decision making model based on quantum dynamic modelling and
Dempster-Shafer (D-S) evidence theory is proposed to address this issue and
model the real human decision-making process. Some mathematical techniques are
borrowed from quantum mathematics. Generally, belief and action are two parts
in a decision making process. The uncertainty in belief part is represented by
a superposition of certain states. The uncertainty in actions is represented as
an extra uncertainty state. The interference effect is produced due to the
entanglement between beliefs and actions. Basic probability assignment (BPA) of
decisions is generated by quantum dynamic modelling. Then BPA of the extra
uncertain state and an entanglement degree defined by an entropy function named
Deng entropy are used to measure the interference effect. Compared the existing
model, the number of free parameters is less in our model. Finally, a classical
categorization decision-making experiment is illustrated to show the
effectiveness of our model.Comment: 37 page

### Exploring the Combination Rules of D Numbers From a Perspective of Conflict Redistribution

Dempster-Shafer theory of evidence is widely applied to uncertainty modelling
and knowledge reasoning because of its advantages in dealing with uncertain
information. But some conditions or requirements, such as exclusiveness
hypothesis and completeness constraint, limit the development and application
of that theory to a large extend. To overcome the shortcomings and enhance its
capability of representing the uncertainty, a novel model, called D numbers,
has been proposed recently. However, many key issues, for example how to
implement the combination of D numbers, remain unsolved. In the paper, we have
explored the combination of D Numbers from a perspective of conflict
redistribution, and proposed two combination rules being suitable for different
situations for the fusion of two D numbers. The proposed combination rules can
reduce to the classical Dempster's rule in Dempster-Shafer theory under a
certain conditions. Numerical examples and discussion about the proposed rules
are also given in the paper.Comment: 6 pages, 4 figure

### A quantum dynamic belief model to explain the interference effects of categorization on decision making

Categorization is necessary for many decision making tasks. However, the
categorization process may interfere the decision making result and the law of
total probability can be violated in some situations. To predict the
interference effect of categorization, some model based on quantum probability
has been proposed. In this paper, a new quantum dynamic belief (QDB) model is
proposed. Considering the precise decision may not be made during the process,
the concept of uncertainty is introduced in our model to simulate real human
thinking process. Then the interference effect categorization can be predicted
by handling the uncertain information. The proposed model is applied to a
categorization decision-making experiment to explain the interference effect of
categorization. Compared with other models, our model is relatively more
succinct and the result shows the correctness and effectiveness of our model.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1703.0238

### An evidential Markov decision making model

The sure thing principle and the law of total probability are basic laws in
classic probability theory. A disjunction fallacy leads to the violation of
these two classical laws. In this paper, an Evidential Markov (EM) decision
making model based on Dempster-Shafer (D-S) evidence theory and Markov
modelling is proposed to address this issue and model the real human
decision-making process. In an evidential framework, the states are extended by
introducing an uncertain state which represents the hesitance of a decision
maker. The classical Markov model can not produce the disjunction effect, which
assumes that a decision has to be certain at one time. However, the state is
allowed to be uncertain in the EM model before the final decision is made. An
extra uncertainty degree parameter is defined by a belief entropy, named Deng
entropy, to assignment the basic probability assignment of the uncertain state,
which is the key to predict the disjunction effect. A classical categorization
decision-making experiment is used to illustrate the effectiveness and validity
of EM model. The disjunction effect can be well predicted and the free
parameters are less compared with the existing models.Comment: 38 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1703.0238

### A Physarum-inspired model for the probit-based stochastic user equilibrium problem

Stochastic user equilibrium is an important issue in the traffic assignment
problems, tradition models for the stochastic user equilibrium problem are
designed as mathematical programming problems. In this article, a
Physarum-inspired model for the probit-based stochastic user equilibrium
problem is proposed. There are two main contributions of our work. On the one
hand, the origin Physarum model is modified to find the shortest path in
traffic direction networks with the properties of two-way traffic
characteristic. On the other hand, the modified Physarum-inspired model could
get the equilibrium flows when traveller's perceived transportation cost
complies with normal distribution. The proposed method is constituted with a
two-step procedure. First, the modified Physarum model is applied to get the
auxiliary flows. Second, the auxiliary flows are averaged to obtain the
equilibrium flows. Numerical examples are conducted to illustrate the
performance of the proposed method, which is compared with the Method of
Successive Average method.Comment: 24 pages,5 figure

### D numbers theory based game-theoretic framework in adversarial decision making under fuzzy environment

Adversarial decision making is a particular type of decision making problem
where the gain a decision maker obtains as a result of his decisions is
affected by the actions taken by others. Representation of alternatives'
evaluations and methods to find the optimal alternative are two important
aspects in the adversarial decision making. The aim of this study is to develop
a general framework for solving the adversarial decision making issue under
uncertain environment. By combining fuzzy set theory, game theory and D numbers
theory (DNT), a DNT based game-theoretic framework for adversarial decision
making under fuzzy environment is presented. Within the proposed framework or
model, fuzzy set theory is used to model the uncertain evaluations of decision
makers to alternatives, the non-exclusiveness among fuzzy evaluations are taken
into consideration by using DNT, and the conflict of interests among decision
makers is considered in a two-person non-constant sum game theory perspective.
An illustrative application is given to demonstrate the effectiveness of the
proposed model. This work, on one hand, has developed an effective framework
for adversarial decision making under fuzzy environment; One the other hand, it
has further improved the basis of DNT as a generalization of Dempster-Shafer
theory for uncertainty reasoning.Comment: 59 pages, 5 figure

### Evidential supplier selection based on interval data fusion

Supplier selection is a typical multi-criteria decision making (MCDM) problem
and lots of uncertain information exist inevitably. To address this issue, a
new method was proposed based on interval data fusion. Our method follows the
original way to generate classical basic probability assignment(BPA) determined
by the distance among the evidences. However, the weights of criteria are kept
as interval numbers to generate interval BPAs and do the fusion of interval
BPAs. Finally, the order is ranked and the decision is made according to the
obtained interval BPAs. In this paper, a numerical example of supplier
selection is applied to verify the feasibility and validity of our method. The
new method is presented aiming at solving multiple-criteria decision-making
problems in which the weights of criteria or experts are described in fuzzy
data like linguistic terms or interval data.Comment: 29 page

### Tunable mechanical properties of the graphene/MoS2 tubal van der Waals heterostructure

We propose a tubal van der Waals heterostructure by rolling up the graphene
and MoS2 atomic layers into a tubal form. We illustrate that the interlayer
space for the tubal van der Waals heterostructure can be varied in a specific
range, which is determined by the competition between the interlayer van der
Waals force and the mechanical properties of the atomic layers. The variability
of the interlayer space can be utilized to efficiently tune mechanical
properties of the tubal van der Waals heterostructure. More specifically, we
demonstrate that the Poisson's ratio of the tubal van der Waals heterostructure
can be manipulated by a factor of two by varying the interlayer space from 1.44
to 4.44. Our work promotes a new member with tunable Poisson's ratio to the van
der Waals heterostructure family

### Limit sets and commensurability of Kleinian groups

In this paper, we obtain several results on the commensurability of two
Kleinian groups and their limit sets. We prove that two finitely generated
subgroups $G_1$ and $G_2$ of an infinite co-volume Kleinian group G \subset
\Isom(\mathbf{H}^3) having $\Lambda(G_1) = \Lambda(G_2)$ are commensurable. In
particular, it is proved that any finitely generated subgroup $H$ of a Kleinian
group G \subset \Isom(\mathbf{H}^3) with $\Lambda(H) = \Lambda(G)$ is of
finite index if and only if $H$ is not a virtually fiber subgroup.Comment: 9 page

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