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

A Quantum Spin Hall Round Disk as a Spin Rotator and Filter

We study theoretically the spin transport of a Quantum Spin Hall round disk. When an electron traverses the disk in virtue of the edge states, its spin's in-plane component can be rotated by a magnetic flux through the disk. The spin rotation occurs due to the interference of two helical edge states with opposite spins, which is regarded as the Aharonov-Bohm effect in the spin space and a manifestation of the Berry phase. Besides, the disk has a spin filter effect on the tunneling current when we apply an appropriate magnetic field and gate voltage on it. The spin polarization ratio can reach 100% when the couplings between the disk and leads are weak.Comment: 6 pages, 4 figure