Uncertainty Theory

By Baoding Liu. Studies in Fuzziness and Soft Computing, 2004

2,535 citations recorded by the source corpus.

Subfields: Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/12c6129cf299f37fd13e09d4de3da2d00b4842b9

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In Management Science and Operations Research

1. Kai Yao
2. Xiaowei Chen
3. Yuanguo Zhu
4. Jin Peng
5. Baoding Liu
6. Yongchao Hou
7. Xiangfeng Yang
8. Wei Dai

Citations in the corpus

• Least-squares estimation for uncertain moving average model (2020, background): “1t iða, bÞ a from the operation laws of uncertain variables to calculate inverse uncertainty distribution (Liu 2015, 56).”
• A sufficient and necessary condition of uncertainty distribution (2010, background): “An uncertain variable is a measurable function ξ10 from an uncertainty space (Γ ,L,M) to the set of real numbers, i.e., for any Barrel set B of real numbers, the set12 {ξ ∈ B} = {γ ∈ Γ |ξ(γ) ∈ B} is an event.14 Definition 2.3 (Liu [6]).”
• A type of uncertain differential equations with analytic solution (2013, background): “Introduction Uncertainty theory, as a branch of axiomatic mathematics dealing with human’s belief degree, was founded by Liu [1] in 2007 and refined by Liu [2] in 2010.”
• Subadditivity of chance measure (2014, methodology): “After proposing the concept of independence [4], Liu [3] presented the operational law of uncertain variables.”
• Method of moments for estimating uncertainty distributions (2014, background): “Although probability measure satisfies the above three axioms, probability theory is not a special case of uncertainty theory because product probability measure does not satisfy the following product axiom (Liu [3]):”
• A survey of variants and extensions of the location-routing problem (2015, positive): “The problem is modeled according to the credibility theory of Liu (2004), and the authors present an SA algorithm.”
• A numerical method for solving uncertain differential equations (2013, methodology): “(Liu [8]) Let ξ be an uncertain variable with an uncertainty distribution .”
• Asian Option Pricing Formula for Uncertain Financial Market (2015, neutral): “As a branch of axiomatic mathematics, uncertainty theory was founded by Liu [11] in 2007 and perfected by Liu [14] in 2009.”
• Why is There a Need for Uncertainty Theory (2012, background): “How do we understand uncertainty? How do we model uncertainty? In order to answer those questions, an uncertainty theory was founded by Liu [6] in 2007 and refined by Liu [10] in 2010.”
• Mean-variance-skewness model for portfolio selection with fuzzy returns (2010, neutral): “Credibility theory Credibility theory was founded by Liu in 2004 and refined by Liu [13] as a branch of mathematics for studying fuzzy phenomena.”
• Existence and Uniqueness Theorem on Uncertain Dierential Equations with Local Lipschitz Condition (2012, positive): “In order to ensure that the number M{Λ} has certain mathematical properties, Liu [7, 10] presented the four following axioms: (1) normality, (2) self-duality, (3) countable subadditivity, and (4) product measure axioms.”