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1. chinaXiv:202203.00069 [pdf]

最大邓熵三角中的白银比

Deng, Jixiang; Deng, Yong
Subjects: Mathematics >> Discrete Mathematics and Combinatorics

帕斯卡三角是二项式系数的三角形式,由它可以得到斐波那契数列和黄金比(约等于1.618)。一个问题是:帕斯卡三角中是否能得到白银比(约等于2.414)?本文首先基于最大邓熵的质量函数分布,建立了一个最大邓熵三角(MDET),这是一个类帕斯卡三角(Pascal-like triangle)。推导了MDET数列的通项公式,并分析了MDET数列中的极限比。经典的帕斯卡三角左右对称,通过对角加(Diagonal sum)只能得到一种数列——斐波那契数列,其极限比为黄金比。与帕斯卡三角不同,本文所提出的MDET是非对称结构,通过右对角加与左对角加可以生成两种数列——右MDET数列和左MDET数列。本文证明了右MDET数列中的极限比收敛于白银比,而左MDET数列中的极限比收敛于数值2。本文通过数值算例说明了所提出的MDET及其数列的性质。

submitted time 2022-03-18 Hits2797Downloads346 Comment 0

2. chinaXiv:202112.00085 [pdf]

随机排列集的最大熵

Deng, Jixiang; Deng, Yong
Subjects: Computer Science >> Integration Theory of Computer Science

最近,一种名为随机排列集(Random Permutation Set RPS)的集合被提出,它考虑了一个集合中所有元素的排列。 为了度量随机排列集的不确定度,随机排列集的熵被提出。 然而,随机排列集的最大熵原理却没有详细地论证。为了解决这一问题,本文提出了随机排列集的最大熵。随机排列集的最大熵的解析解及其对应的PMF条件得到了证明与讨论。我们用数值例子说明了随机排列集的最大熵的性质。实验结果表明,随机排列集的最大熵和最大邓熵、最大香农熵相互兼容。 当忽略排列事件(Permutation Event)中元素的顺序时,随机排列集的最大熵将退化为最大邓熵。当每个排列事件只包含一个元素时,随机排列集的最大熵将退化为最大香农熵。

submitted time 2021-12-14 Hits7148Downloads568 Comment 0

3. chinaXiv:202104.00004 [pdf]

QZNs: Quantum Z-numbers

Deng, Jixiang; Deng, Yong
Subjects: Computer Science >> Integration Theory of Computer Science

Because of the efficiency of modeling fuzziness and vagueness, Z-number plays an important role in real practice. However, Z-numbers, defined in the real number field, lack the ability to process the quantum information in quantum environment. It is reasonable to generalize Z-number into its quantum counterpart. In this paper, we propose quantum Z-numbers (QZNs), which are the quantum generalization of Z-numbers. In addition, seven basic quantum fuzzy operations of QZNs and their corresponding quantum circuits are presented and illustrated by numerical examples. Moreover, based on QZNs, a novel quantum multi-attributes decision making (MADM) algorithm is proposed and applied in medical diagnosis. The results show that, with the help of quantum computation, the proposed algorithm can make diagnoses correctly and efficiently.

submitted time 2021-04-12 Hits9142Downloads950 Comment 0

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