Table of Content

  

20 August 2022
Volume 57 Issue 8

Cognition of network concepts based on variable precision possibility operator

FAN Min, LUO Shan, LI Jin-hai

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  1-12.  doi:10.6040/j.issn.1671-9352.0.2022.066

Abstract ( 792 )   PDF (650KB) ( 470 )   Save

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Concept cognition in a network is an important direction in the field of network data analysis. Starting from the necessity operator and possibility operator in formal concept analysis, this paper puts forward variable precision possibility operator, and illustrates that the classical possibility operators are special cases of the variable precision possibility operators. Furthermore, some properties of the possibility operators are studied, and their significances in the study of infectious disease networks are explained. Then, based on the variable precision possibility operators, two generalized network concepts and their upper approximations, lower approximations and boundary regions are proposed, and the upper and lower approximations and their boundary regions under variable precision possibility operators are illustrated to have much richer semantics through an example. After that, combined with the network eigenvalue method in complex network analysis, the network weak concepts are defined, and a network weak concept acquisition method based on variable precision possibility operator is presented. Finally, our algorithm is used to conduct some experiments on the UCI database, and the obtained results show that variable-precision possibility operators have advantages in network concept cognition.

Bernoulli shift of decision evolution set

HU Yu-wen, XU Jiu-cheng, XU Tian-he

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  13-20.  doi:10.6040/j.issn.1671-9352.7.2021.146

Abstract ( 709 )   PDF (1245KB) ( 479 )   Save

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Decision evolution set is a new method to deal with evolution problem of decision rules changing in time series. Decision evolution matrix is an important concepts of decision evolution set. Through the decision evolution matrix, we can intuitively understand the performance of each conditional attribute at a single time point and a continuous time series. However, the decision evolution matrix is defined in the current system, there is still a lack of numerical quantization. In this paper, Bernoulli shift is introduced to quantify the decision evolution matrix, and an example is given to demonstrate the role of these quantized values in prediction.

Robust clustering based on adaptive graph regularization and low-rank matrix decomposition

LI Xin-yu, FAN Hui, LIU Jing-lei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  21-38.  doi:10.6040/j.issn.1671-9352.7.2021.069

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Clustering is an important research content in the field of data mining and machine learning. Generally, similarity graphs are constructed based on data samples, and then the samples are divided into corresponding classes based on the similarity graphs. However, the real data is often damaged, resulting in inaccurate similarity graphs, which directly affects the clustering results. In order to solve these problems, a robust clustering-oriented adaptive graph adjustment and low-rank matrix decomposition method is proposed. The core idea of the method is to decompose the original data X into pure data D and noisy data S, then construct a Laplacian matrix based on pure data and perform adaptive graph adjustment. Subsequently, a joint learning framework is given, which integrates data separation, adaptive graph regularization, noise removal and low-rank matrix decomposition into an objective function. Use augmented Lagrangian multiplier method to update variables separately. Finally, the paper theoretically proves the convergence of the algorithm and conduct experiments. The experimental results show that the proposed method has certain advantages compared with some existing methods.

Multi-label feature selection with streaming and missing labels

ZHANG Zhi-hao, LIN Yao-jin, LU Shun, WU Yi-lin, WANG Chen-xi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  39-52.  doi:10.6040/j.issn.1671-9352.7.2021.141

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In the practical tasks of supervised learning, the high dimensionality of feature space, the dynamic and missing of labels bring severe challenges to supervised learning. To address these problems, a multi-label feature selection with streaming and missing labels algorithm is proposed. Firstly, to solve the impact of missing labels, the missing matrix is completed by learning label correlations. Secondly, sparse learning is utilized to select label-specific features for each newly arrived label. Then, a representative feature subset is selected by calculating the score of each label-specific features of label. Finally, a series of experiments on 11 benchmark data sets demonstrate that the proposed algorithm can effectively select a representative feature subset with better classification performance.

Numerical properties of Gödel semantics in fuzzy argumentation frameworks

ZHAO Shuang-yan, WU Jia-chao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  53-59.  doi:10.6040/j.issn.1671-9352.0.2021.803

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The Gödel semantics in fuzzy argumentation frameworks covers several basic extension semantics, but does not further study the properties of each extension semantics. This brings some difficulties to the calculation and quick recognition of the semantic system. Through the in-depth study of the numerical properties of each extension semantics, this paper provides some solutions to the above problems. With the help of the basic properties of the Gödel t-norm, the numerical properties of the conflict-free set, the admissible extension, the complete extension, the preferred extension(the stable extension), and the grounded extension in the Gödel semantics are deduced one by one, and the algorithms of the grounded extension are given in fuzzy AFs without cycles and fuzzy AFs consisting of odd cycles or even cycles. These conclusions are the theoretical generalization of the semantic system. At the same time, the method of bypassing the definition and directly judging the extension semantics based on numerical values, as well as the algorithm of calculating the grounded extension from empty sets, are the development of the semantics in terms of algorithm and quick identification.

Complementary concepts and their properties and generation in FCA

HAN Pei-lei, WEI Ling, WANG Zhen, ZHAO Si-yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  60-67.  doi:10.6040/j.issn.1671-9352.0.2022.055

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In formal concept analysis, partial order relation of concept lattice describes generalization and specialization between concepts. There also exists some specific semantic information that is worth studying between incomparable concepts. Inspired by this, complementary concepts are studied in this paper. Firstly, the complementary degree of two object subsets is described by considering a specific attribute subset in formal context, based on which the strong and weak complementary relations are defined according to different actual needs. Further, the complementary concepts and their related properties are studied, and the optimal strong complementary concept and optimal weak complementary concept are explored under different semantics, and the corresponding algorithms are also given. Finally, examples are presented given to illustrate the rationality and applicability of the content of this paper.

Semantics of the soft set induced by intuitionistic fuzzy set and its three-way decision

GONG Zeng-tai, TA Guang-peng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  68-76.  doi:10.6040/j.issn.1671-9352.0.2021.419

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In this paper, by means of the shadowed set, this paper transforms intuitionistic fuzzy set into pessimistic shadowed set and optimistic shadowed set by using intuitionistic fuzzy parameters, and proposes pessimistic three-way decision and optimistic three-way decision of intuitionistic fuzzy set. The method of inducting soft set by intuitionistic fuzzy set is given, and the qualitative model of three-way decision with soft set is proposed by using three-way decision theory. Combined with pessimistic three-way decision and optimistic three-way decision of intuitionistic fuzzy set, a quantitative model of three-way decision with soft sets is given by using intuitionistic fuzzy parameters.

Generalized interval-valued Pythagorean triangular fuzzy aggregation operator and application in decision making

SU Xiao-yan, CHEN Jing-rong, YIN Hui-ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  77-87.  doi:10.6040/j.issn.1671-9352.0.2021.448

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In this article, the interval-valued Pythagorean triangular fuzzy number is proposed for the decision making problems when the sum of membership degree and non-membership degree of decision variables exceeds 1 on continuous sets, and the decision application of its generalized aggregation operator is analyzed. Firstly, the concept of interval-valued Pythagorean triangular fuzzy numbers is given, and its algorithm is obtained. Secondly, the weighted average operator, weighted geometric operator, ordered weighted average operator, ordered weighted geometric operator, generalized ordered weighted average operator and generalized ordered weighted geometric operator of interval-valued Pythagorean triangular fuzzy numbers are defined, and their related properties are introduced. Finally, a multi-attribute decision making model based on generalized interval-valued Pythagorean triangular fuzzy aggregation operator is constructed, and the stability of generalized ordered weighted average operator and generalized ordered weighted geometric operator is analyzed according to an example. The figures are used to prove intuitively that the former is superior to the latter when dealing with decision making problems. The effectiveness and feasibility of the decision making model are illustrated.

Bifurcation phenomena and nonlinear wave solutions of BKK equation

HAN Qing-xiu, LIU Hong-xia, WU Yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  88-94.  doi:10.6040/j.issn.1671-9352.0.2021.615

Abstract ( 867 )   PDF (831KB) ( 444 )   Save

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The bifurcation phenomena and nonlinear wave solutions of Broer-Kaup-Kupershmidt(BKK)equation are studied. Firstly, the first integral and singularities of the BKK equation are obtained by travelling wave transformation. Then the bifurcation phase portraits of the BKK equation in each region are presented by using the bifurcation method and qualitative theory of dynamical systems, and some nonlinear wave solutions of the equation are obtained. Furthermore, three bifurcation phenomena of kink wave are revealed. Finally, Maple software is used to simulate these bifurcation phenomena.

Multiple solutions of fractional p-q-Laplacian system with sign-changing weight functions

LI Chun-ping, SANG Yan-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  95-102.  doi:10.6040/j.issn.1671-9352.0.2021.220

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The multiple solutions of fractional p-q-Laplacian system involving concave-convex nonlinearities and sign-changing weight functions is considered. The system has at least two nontrivial solutions when the pair of the parameters(λ, μ)belongs to a certain subset of Rⁿ are proved by making use of the Nehari manifold and Ekelands variational principle.

Stability of the bidirectional ring networks with multiple time delays and multiple parameters

PANG Yu-ting, ZHAO Dong-xia, BAO Fang-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(8):  103-110.  doi:10.6040/j.issn.1671-9352.0.2021.618

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The dynamic analysis of the four-neuron ring neural network with multiple time delays and multiple parameters is carried out. Firstly, the system is linearized near the trivial solution, and the characteristic equation of the system is obtained. Then the characteristic equation is factorized into four first-order exponential polynomials. Furthermore, by using the zero-point distribution property of exponential polynomial, sufficient conditions for the delay-dependent and delay-independent stability are established. Moreover, an exhaustive comparison analysis is made between the results obtained and those in the existing literature. Finally, some numerical simulations are presented to show the effectiveness and superiority of the results.