Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory

Zhou, Qianli; Deng, Yong

doi:10.1016/j.chaos.2022.112962

Cited by 11 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The peculiar properties of Sierpiński gaskets remain an active topic of research up to now (see, for instance, Refs. [102][103][104][105][106][107][108][109][110] and references therein). Another family of nested PCF fractals is represented by the loopless Vicsek fractals.…”

Section: Sierpi ńSki Gasket Shape (Network Versus Self-avoiding Curve...mentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

show abstract

Section: Sierpi ńSki Gasket Shape (Network Versus Self-avoiding Curve...mentioning

confidence: 99%

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

Evidence generalization-based discounting method: assigning unreliable information to partial ignorance

Hu,

Zhou,

et al. 2024

Artif Intell Rev

View full text Add to dashboard Cite

Conflict management is an important topic when dealing with unreliable sources information fusion in Dempster–Shafer theory. Discounting unreliable bodies of evidence has proven to be effective to decrease conflict. Based on the generalization of belief functions, a new generalization-based discounting method is proposed. When resolving conflicts with the same degree, our method can realize less information loss in comparison with other discounting methods. By simulating the process of resolving conflicts of randomly generated bodies of evidence, using entropy measurements and binary conflict as evaluation index, we show our method’s rationality and superiority. Finally, the hyperparameters of the conflict metrics are generated and generalization-based discounting is applied to classify real-world datasets. The improved classification performance further illustrates the usefulness of the method.

show abstract