A Novel Evidence Conflict Measurement for Multi-Sensor Data Fusion Based on the Evidence Distance and Evidence Angle

Multifractal analysis of mass function

In order to explore the fractal characteristic in Dempster-Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with α = 1 , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters α represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter α to generalize the existing dimension. Due to the diversity of the value of α , we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method.

Multisensor Data Fusion in IoT Environments in Dempster-Shafer Theory Setting: An Improved Evidence Distance-Based Approach

In IoT environments, voluminous amounts of data are produced every single second. Due to multiple factors, these data are prone to various imperfections, they could be uncertain, conflicting, or even incorrect leading to wrong decisions. Multisensor data fusion has proved to be powerful for managing data coming from heterogeneous sources and moving towards effective decision-making. Dempster-Shafer (D-S) theory is a robust and flexible mathematical tool for modeling and merging uncertain, imprecise, and incomplete data, and is widely used in multisensor data fusion applications such as decision-making, fault diagnosis, pattern recognition, etc. However, the combination of contradictory data has always been challenging in D-S theory, unreasonable results may arise when dealing with highly conflicting sources. In this paper, an improved evidence combination approach is proposed to represent and manage both conflict and uncertainty in IoT environments in order to improve decision-making accuracy. It mainly relies on an improved evidence distance based on Hellinger distance and Deng entropy. To demonstrate the effectiveness of the proposed method, a benchmark example for target recognition and two real application cases in fault diagnosis and IoT decision-making have been provided. Fusion results were compared with several similar methods, and simulation analyses have shown the superiority of the proposed method in terms of conflict management, convergence speed, fusion results reliability, and decision accuracy. In fact, our approach achieved remarkable accuracy rates of 99.32% in target recognition example, 96.14% in fault diagnosis problem, and 99.54% in IoT decision-making application.

Vague multi-attribute group decision-making method based on evidence theory with a new aspect to solve weights

In order to solve the problems of weight solving and information aggregation in the Vague multi-attribute group decision-making, this paper first solves the weight of Vague evaluation value, and then fuses the information of Vague sets through evidence theory, and obtains an information aggregation algorithm for Vague multi-attribute group decision-making. Firstly, The algorithm draws on the idea of solving the weight of evidence in the improved evidence theory algorithm, and calculates the weight of Vague evaluation value, and revises the original evaluation information after obtaining the weight of each Vague evaluation value. Secondly, this algorithm analyzes the mathematical relationship between the Vague sets and the evidence theory, and uses the evidence theory to fuse the evaluation information to obtain the final Vague evaluation value of each alternative. Finally, this algorithm uses a score function to calculate the score of each alternative to determine the best alternative. The algorithm given in the paper enables decision-makers to make rational decisions in uncertain environments, and then select the best alternative.

Conflict Management for Target Recognition Based on PPT Entropy and Entropy Distance

Conflicting evidence affects the final target recognition results. Thus, managing conflicting evidence efficiently can help to improve the belief degree of the true target. In current research, the existing approaches based on belief entropy use belief entropy itself to measure evidence conflict. However, it is not convincing to characterize the evidence conflict only through belief entropy itself. To solve this problem, we comprehensively consider the influences of the belief entropy itself and mutual belief entropy on conflict measurement, and propose a novel approach based on an improved belief entropy and entropy distance. The improved belief entropy based on pignistic probability transformation function is named pignistic probability transformation (PPT) entropy that measures the conflict between evidences from the perspective of self-belief entropy. Compared with the state-of-the-art belief entropy, it can measure the uncertainty of evidence more accurately, and make full use of the intersection information of evidence to estimate the degree of evidence conflict more reasonably. Entropy distance is a new distance measurement method and is used to measure the conflict between evidences from the perspective of mutual belief entropy. Two measures are mutually complementary in a sense. The results of numerical examples and target recognition applications demonstrate that our proposed approach has a faster convergence speed, and a higher belief degree of the true target compared with the existing methods.

A Membership-Fusing Model for Characterizing the Shift of Methanogen Community in a Three-Stage Sludge-Treatment Process

Anaerobic digestion (AD) is an economical and effective method to treat sludge. AD with several pretreatments is the prior process to treat surplus sludge for a wastewater treatment plant. During a sludge-treatment process, various methanogens play their specific role in each sludge-processing stage where different methanogens predominate. Therefore, an expert in the shift of methanogen community could facilitate the workers in a plant to understand the efficiency of the sludge-treatment process. In this paper, a membership-fusing model is established to characterize the shift of methanogen community in a three-stage sludge-treatment process. The introduction of fuzzy sets clarifies the vagueness of the methanogen community structure between two processing stages. Dempster–Shafer (DS) evidence theory effectively alleviates the data error generated among paralleling samples. The accuracy of the model was verified, and the result shows the model could clearly distinguish the methanogen community structure of the three stages and make accurate judgment on the processing stage affiliation. The reliability of the model in dealing with different numbers of conflict data was proved and the experiment indicates the model could make a reliable judgment on the processing stage affiliation by reasonably fusing the interference data.