A Guide to Monte Carlo Simulations in Statistical Physics: Some necessary background

Multiple-criteria decision-making (MCDM) is an important branch of operations research which judges multiple criteria under decision-making environments. In the process of handling MCDM problems, because of the subjective judgment of human beings, it unavoidably involves a variety of uncertainties, like imprecision, fuzziness and incompleteness. The D numbers, as a reliable and effective expression of uncertain information, has a good performance to handle these types of uncertainties. However, there still are some spaces to be further researched. Therefore, a novel belief entropy-based method with regard to D numbers is proposed for MCDM problems. Finally, an application in the MCDM problem is illustrated to reveal the efficiency of the proposed method.

A Multiple-Criteria Decision-Making Method Based on D Numbers and Belief Entropy

As a generalization of Dempster-Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that theory. In this paper, inspired by distance based uncertainty measures for Dempster-Shafer theory, a total uncertainty measure for a D number is proposed based on its belief intervals. The proposed total uncertainty measure can simultaneously capture the discord, and non-specificity, and non-exclusiveness involved in D numbers. And some basic properties of this total uncertainty measure, including range, monotonicity, generalized set consistency, are also presented.

pdf/a-total-uncertainty-measure-for-d-numbers-based-on-belief-24o70dla59.pdf

A total uncertainty measure for D numbers based on belief intervals

A well-managed time-constrained workflow scheduling is needed for improving system performance and end user satisfaction. Meanwhile, the intrinsic uncertainty in dynamic systems increases the difficulties of scheduling problem. Therefore, it is a great challenge to improve performance and optimize several objectives simultaneously. To address these issues, a novel workflow scheduling method for distributed systems based on TOPSIS method with fuzzy set is proposed in this paper. The new method can minimize the makespan of the workflow application under uncertain environment. Finally, a numerical example is provided to demonstrate the efficiency of the proposed method.

Workflow scheduling in distributed systems under fuzzy environment

Information volume fractal dimension

For multiple attributes decision making, D numbers theory has been widely used to deal with uncertain and incomplete information. However, the incomplete information is abandoned in the D numbers’ integration representation. This results in unreasonable conclusions in some real-world applications. To overcome this drawback, this paper proposes an improved D numbers’ integration representation method, by effectively allocating the incomplete information into decision making according to the original value of D numbers. The proposed method is applied to assess the performance of different types of motorcycles. The results show that the proposed method can effectively increase both the accuracy and efficiency of assessment when compared with the original D numbers theory.

/pdf/a-modified-d-numbers-integration-for-multiple-attributes-1hmlxfriqr.pdf

A Modified D Numbers’ Integration for Multiple Attributes Decision Making

Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.

/pdf/a-modified-d-numbers-methodology-for-environmental-impact-4xci0yi0er.pdf

A modified D numbers methodology for environmental impact assessment

numbers theory is an appropriate method to deal with the information of uncertainty and incompleteness when making a reasonable decision. Previous numbers theory provides a rule to combine multiple numbers. However, the commutative law is not satisfied in the rule of combining multiple numbers. In this paper, a modified method for multiple numbers combination is proposed. The proposed method defines a new function for multiple numbers combination which is mainly determined by the original value of numbers. Then the proposed combination rule is applied to environmental impact assessment (EIA); our results show that the proposed method is efficient for multiple numbers combination and it is useful when dealing with uncertainty and incompleteness.

https://downloads.hindawi.com/journals/mpe/2016/3596517.pdf

A Modified Combination Rule for Numbers Theory

In complex networks, how to identify influential nodes in complex networks is a hot topic. Recently, weights of nodes and degree of nodes are combined for identifying influential nodes in the weighted networks. Degree centrality, closeness centrality and betweenness centrality are the most basic measures for describing the influence of nodes. In this paper, degree centrality, closeness centrality and betweenness centrality are considered. The three measures are built three basic probability assignment (BPAs) based on evidence theory, respectively. Then, a final measure, which is used to identify influence of nodes, is obtained by combining the three BPAs. Numerical examples are used to illustrate the effectiveness of the proposed method.

A new method for identifying influential nodes based on D-S evidence theory

Multiagent systems (MASs) have a wide range of industrial applications due to agents’ advantages. However, because of the agents’ dynamic behaviors, it is a challenge to ensure the quality of service they present. In this paper, to address this problem, we propose an adaptive agent trust estimation model where agents may decide to go from genuine to malicious or the other way around. In the proposed trust model, both direct trust and indirect reputation are used. However, the indirect reputation derived from the direct experience of third-party agents must have reasonable confidence to be useful. The proposed model introduces a near-perfect measure that utilizes consistency, credibility, and certainty to capture confidence. Moreover, agents are incentivized to contribute correct information (to be honest) through a credit mechanism in the proposed model. Simulation experiments are conducted to evaluate the proposed model’s performance against some of the previous trust models reported in the literature.

/pdf/an-adaptive-dempster-shafer-theory-of-evidence-based-trust-2ka0wee9.pdf

An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems

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