Uncertainty Theory

Liu, Baoding

doi:10.1007/978-3-540-73165-8_5

Cited by 541 publications

(288 citation statements)

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“…Convergence is used as one measure of uncertainty in a sys-tem [Liu15]. However, convergence is usually considered as a collective behavior over function domains for numerical analysis applications.…”

Section: On Convergence and Uncertaintymentioning

confidence: 99%

Uncertainty Footprint: Visualization of Nonuniform Behavior of Iterative Algorithms Applied to 4D Cell Tracking

Wan

Hansen

2017

Computer Graphics Forum

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Research on microscopy data from developing biological samples usually requires tracking individual cells over time. When cells are three-dimensionally and densely packed in a time-dependent scan of volumes, tracking results can become unreliable and uncertain. Not only are cell segmentation results often inaccurate to start with, but it also lacks a simple method to evaluate the tracking outcome. Previous cell tracking methods have been validated against benchmark data from real scans or artificial data, whose ground truth results are established by manual work or simulation. However, the wide variety of real-world data makes an exhaustive validation impossible. Established cell tracking tools often fail on new data, whose issues are also difficult to diagnose with only manual examinations. Therefore, data-independent tracking evaluation methods are desired for an explosion of microscopy data with increasing scale and resolution. In this paper, we propose the uncertainty footprint, an uncertainty quantification and visualization technique that examines nonuniformity at local convergence for an iterative evaluation process on a spatial domain supported by partially overlapping bases. We demonstrate that the patterns revealed by the uncertainty footprint indicate data processing quality in two algorithms from a typical cell tracking workflow – cell identification and association. A detailed analysis of the patterns further allows us to diagnose issues and design methods for improvements. A 4D cell tracking workflow equipped with the uncertainty footprint is capable of self diagnosis and correction for a higher accuracy than previous methods whose evaluation is limited by manual examinations.

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Section: On Convergence and Uncertaintymentioning

confidence: 99%

Uncertainty Footprint: Visualization of Nonuniform Behavior of Iterative Algorithms Applied to 4D Cell Tracking

Wan

Hansen

2017

Computer Graphics Forum

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“…The uncertainty theory [1] has been developed and improved constantly for more than ten years, since Professor Liu Baoding, Tsinghua University and his team put forward it. Its theoretical system was recognized and accepted gradually by the majority of scholars and experts, and part of them have put themselves in studying this theory [2] [3].…”

Section: Introductionmentioning

confidence: 99%

Supply Chain Commitment Contract Model Based on Uncertainty Theory under Uncertain Market Information

Cui¹,

Xiaolin²,

Lu³

2015

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Based on the uncertainty theory, market demand information updating as the background, we study the coordination and optimization problem of three-stage supply chain in this paper. In half a asymmetric market information, participants are risk neutral; under the situation of the manufacturers and wholesalers having twice pre-season decision-making opportunity, wholesalers can be replenished in the season; manufacturers join the lowest supply contract of commitment: manufacturers for exchanging the information that they cannot get directly from the market will promise wholesalers to have a season lowest supply in pre-season. According to this contract, we establish optimization models of manufacturers and wholesalers respectively, and get the optimal strategy of supply chain members by analyzing the supply chain system. Finally, by giving a numerical example and comparing the results with that under random circumstances, the result is reasonable.

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“…In terms of fuzzy theory development, the possibility measure and necessity measure were proposed by Zadeh in 1978 [31]; afterwards, Liu et al proposed the credibility measure in 2002 [32], and an uncertainty theory with an axiomatic basis was established in 2004 [33].…”

Section: Parabolic Fuzzy Variablementioning

confidence: 99%

“…The function u(x) = Pos{θ ∈ Θ | ξ(θ) = x, x ∈ R} derived from the probability measure is known as the membership function of ξ [33].…”

Section: Parabolic Fuzzy Variablementioning

confidence: 99%

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Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

Zhang

Watada

2018

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium-and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach. key words: American option, fuzzy set theory, fuzzy simulation technology, Levy process, GJR-GARCH model, least squares Monte Carlo approach, binomial tree method, quasi-random number, Brownian Bridge approach

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Uncertainty Theory

Cited by 541 publications

References 0 publications

Uncertainty Footprint: Visualization of Nonuniform Behavior of Iterative Algorithms Applied to 4D Cell Tracking

Uncertainty Footprint: Visualization of Nonuniform Behavior of Iterative Algorithms Applied to 4D Cell Tracking

Supply Chain Commitment Contract Model Based on Uncertainty Theory under Uncertain Market Information

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

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