A New Entropy Measurement for the Analysis of Uncertain Data in MCDA Problems Using Intuitionistic Fuzzy Sets and COPRAS Method

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.

Information structures and entropy measurement for a fuzzy probabilistic information system

An information system (IS), an important model in the field of artificial intelligence, takes information structure as the basic structure. A fuzzy probabilistic information system (FPIS) is the combination of some fuzzy relations in the same universe that satisfy probability distribution. A FPIS as an IS with fuzzy relations includes three types of uncertainties (i.e., roughness, fuzziness and probability). This paper studies information structures in a FPIS from the perspective of granular computing (GrC). Firstly, two types of information structures in a FPIS are defined by set vectors. Then, equality, dependence and independence between information structures in a FPIS are proposed, and they are depicted by means of the inclusion degree. Next, information distance between information structures in a FPIS is presented. Finally, entropy measurement for a FPIS is investigated based on the proposed information structures. These results may be helpful for understanding the nature of structures and uncertainty in a FPIS.

Measures of uncertainty for a fuzzy probabilistic approximation space

An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

How to Measure a Two-Sided Market

Applying the theories of complex network and entropy measurement to the market, the two-sided market structure is analyzed in constructing the O2O platform transaction on the entropy measurement of the nodes and links. Market structure entropy (MSE) is initially introduced to measure the consistency degree of the individuals and the groups in the O2O market, according to the interaction in the profits, the time/space, and the information relationship. Considering that the market structure entropies are changing upward or downward, MSE is used to judge the consistency degree between the individuals and the groups. Respectively, considering the scale, the cost and the value dimensions, MSE is expanded to explain the market quality entropy, the market time-effect entropy, and the market capacity entropy.MSE provides a methodology in studying the O2O platform transaction and gives the quantitative index in the evaluation of the O2O market state.

Reduction in a fuzzy probabilistic information system

An information system (IS) is an important mathematical tool for artificial intelligence. A fuzzy probabilistic information system (FPIS), the combination of some fuzzy relations in the same universe which satisfies the probability distribution, can be seen as an IS with fuzzy relations. A FPIS overcomes the shortcoming that rough set theory assumes elements in the universe with equal probability and leads to lose some useful information. This paper integrates the probability distribution into the fuzzy relations in a FPIS and studies its reduction. Firstly, the concept of a FPIS is introduced and its reduction is proposed. Then, the fuzzy relations in a FPIS are divided into three categories (P-necessary, P-relatively necessary and P-unnecessary fuzzy relations) according to their importance. Next, entropy measurement for a FPIS is investigated. Moreover, some reduction algorithms are constructed. Finally, an example is given to verify the effectiveness of these proposed algorithms.

Entropy-based dynamic graph embedding for anomaly detection on multiple climate time series

Abnormal climate event is that some meteorological conditions are extreme in a certain time interval. The existing methods for detecting abnormal climate events utilize supervised learning models to learn the abnormal patterns, but they cannot detect the untrained patterns. To overcome this problem, we construct a dynamic graph by discovering the correlation among the climate time series and propose a novel dynamic graph embedding model based on graph entropy called EDynGE to discriminate anomalies. The graph entropy measurement quantifies the information of the graphs and constructs the embedding space. We conducted experiments on synthetic datasets and real-world meteorological datasets. The results showed that EdynGE model achieved a better F1-score than the baselines by 43.2%, and the number of days of abnormal climate events has increased by 304.5 days in the past 30 years.

A Thermodynamic Approach to Measuring Entropy in a Few-Electron Nanodevice

The entropy of a system gives a powerful insight into its microscopic degrees of freedom, however standard experimental ways of measuring entropy through heat capacity are hard to apply to nanoscale systems, as they require the measurement of increasingly small amounts of heat. Two alternative entropy measurement methods have been recently proposed for nanodevices: through charge balance measurements and transport properties. We describe a self-consistent thermodynamic framework for treating few-electron nanodevices which incorporates both existing entropy measurement methods, whilst highlighting several ongoing misconceptions. We show that both methods can be described as special cases of a more general relation and prove its applicability in systems with complex microscopic dynamics – those with many excited states of various degeneracies.

DDoS Detection Using a Cloud-Edge Collaboration Method Based on Entropy-Measuring SOM and KD-Tree in SDN

Software-defined networking (SDN) emerges as an innovative network paradigm, which separates the control plane from the data plane to improve the network programmability and flexibility. It is widely applied in the Internet of Things (IoT). However, SDN is vulnerable to DDoS attacks, which can cause network disasters. In order to protect SDN security, a DDoS detection method using cloud-edge collaboration based on Entropy-Measuring Self-organizing Maps and KD-tree (EMSOM-KD) is designed for SDN. Entropy measurement is utilized to select the ideal SOM map and classify SOM neurons considering the limitation of dead and suspicious neurons. EMSOM can detect most flows directly and filter out a few doubtable flows. Then these flows are fine-grained, identified by KD-tree. Due to the limited and precious resources of the controller, parameter computation is performed in the cloud. The edge controller implements DDoS detection by EMSOM-KD. The experiments are conducted to evaluate the performance of the proposed method. The results show that EMSOM-KD has better detection accuracy; moreover, it improves the KD-tree detection efficiency.