Information Dimension of Galton Board

Zhou, Qianli; Deng, Yong; Pedrycz, Witold

doi:10.1142/s0218348x22500797

Cited by 11 publications

(3 citation statements)

References 41 publications

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“…The theory of belief function is an uncertain reasoning one initiated by Dempster [29] and inherited and developed by Shafer [30], therefore also known as Dempster-Shafer theory (DST). After half a century of development, the theory has been well developed and played an important role in a wide variety of fields, such as decision-making [40][41][42] and information fusion [43][44][45]. Suppose that the answer to the question of concern consists of a finite set of mutually exclusive elements, called frame of discernement (FoD), expressed as = {θ 1 , θ 2 , .…”

Section: Belief Function Theorymentioning

confidence: 99%

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Liu¹,

Fei²,

Mi³

2023

Computer Modeling in Engineering &Amp; Sciences

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Probabilistic linguistic term sets (PLTSs) are an effective tool for expressing subjective human cognition that offer advantages in the field of multi-attribute decision-making (MADM). However, studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers (DMs) in certain circumstances, such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete, thus affecting their role in the decision-making process. Belief function theory is a leading stream of thought in uncertainty processing that is suitable for dealing with the limitations of PLTS. Therefore, the purpose of this study is to extend PLTS to incorporate belief function theory. First, we provide the basic concepts of the extended PLTS (i.e., belief-based PLTS) through case analyses. Second, the aggregation operator of belief-based PLTS is defined with the ordered weighted average (OWA)-based soft likelihood function, which is improved by considering the reliability of the information source. Third, to measure the magnitude of different belief-based PLTSs, the belief interval of singleton is calculated, and the comparison method of belief-based PLTS is constructed based on probabilities. On the basis of the preceding discussion, we further develop an emergency decision framework that includes several novel techniques, such as attribute weight determination and decision information aggregation. Finally, the usefulness of the framework is demonstrated through a case study, and its effectiveness is illustrated through a series of comparisons.

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Section: Belief Function Theorymentioning

confidence: 99%

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Liu¹,

Fei²,

Mi³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…Recent research has indicated that D-S evidence theory can adhere to fractal laws [10] . Fractal entropy, proposed by Zhu and Deng, serves as a model for the transformation of signal probability [11] .…”

Section: Introductionmentioning

confidence: 99%

Cosine distance measure in Dempster-Shafer evidence theory based on fractal entropy

Wei,

Gao,

Shan

et al. 2024

Third International Conference on Electronic Information Engineering and Data Processing (EIEDP 2024)

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Multi-sensor data fusion technology plays a crucial role in practical applications. Dempster-Schafer's evidence theory is widely employed in the field of information fusion due to its flexibility and effectiveness in modeling and processing uncertain information. To better quantify the differences among different pieces of evidence, this white paper presents illustrative examples within the framework of Dempster-Shafer's proof theory, utilizing fractal entropy as an intuitive indicator of changes in information. We propose a technique for measuring sine distance that utilizes maximum belief entropy to partition the mass function, allowing for one-time preprocessing using fractal entropy division. Subsequently, we utilize the cosine function to analyze disparities in the mass function post-preprocessing. Furthermore, this paper elucidates several characteristics of our novel distance measurement method and analyzes its advantages through numerical examples. Finally, we apply the proposed measurement approach to information fusion and evaluate its efficacy.

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“…Recently, many attentions were paid to the fractal feature of evidence theory Zhou et al. ( 2022b ); Zhu et al. ( 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of mass function

Qiang

Deng

2023

Soft Comput

Self Cite

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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 , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters 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 to generalize the existing dimension. Due to the diversity of the value of , 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.

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Information Dimension of Galton Board

Cited by 11 publications

References 41 publications

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Cosine distance measure in Dempster-Shafer evidence theory based on fractal entropy

Multifractal analysis of mass function

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