JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Optimization of class-attribute block in multi-granularity formal concept analysis

LI Jin-hai, HE Jian-jun, WU Wei-zhi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 1-12. doi:10.6040/j.issn.1671-9352.c.2020.002

Abstract ( 1131 )

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The existing meso-granularity labeled method in the multi-granularity formal concept analysis is not able to realize the cross-granularity combination for the internal information of class-attribute blocks. Motivated by this problem, this paper divides the internal information of a class-attribute block into sub-classes based on the requirements of practical applications, and puts forward multi-granularity class-attribute blocks by means of combining the obtained sub-classes in a cross-granularity way. Then it analyzes the internal structure of multi-granularity class-attribute blocks, and reveals the mechanism of how to update decision implications when the multi-granularity class-attribute block becomes from coarse to fine or fine to coarse. The obtained results in this paper can further improve the theory and method of multi-level knowledge discovery with multi-granularity formal concept analysis.

Approximate concept and rule acquisition based on attribute granularity

HE Xiao-li, SHE Yan-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 13-21. doi:10.6040/j.issn.1671-9352.c.2020.005

Abstract ( 967 )

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This paper introduces the idea of attribute granularity into the study of incomplete context. Firstly, by means of granularity trees and cuts, the relationship between approximate concepts at different levels of granularities is investigated. Next, the relationship between approximate decision rules at different levels of granularities in incomplete context is examined. Lastly, three types of consistences are introduced into incomplete context, and the relationship between different types of consistencs at different levels of granularities is also studied.

Rough approximation in multi-scale formal context

CHEN Dong-xiao, LI Jin-jin, LIN Rong-de, CHEN Ying-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 22-31. doi:10.6040/j.issn.1671-9352.c.2020.001

Abstract ( 874 )

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Firstly, a kind of multi-scale formal context is proposed in this paper. In this context, with the change of scale, the objects owned by each attribute change monotonously. Furthermore, the concept of rough approximation in multi-scale formal context is introduced, and the relationship between approximation sets in different scales is discussed. Finally, the belief and plausibility functions from the evidence theory are employed to introduce the definitions of upper and lower approximate consistent sets in multi-scale formal context and multi-scale formal decision context.

Concept reduction of preserving binary relations based on Boolean matrix

XIE Xiao-xian, LI Jin-jin, CHEN Dong-xiao, LIN Rong-de

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 32-45. doi:10.6040/j.issn.1671-9352.c.2020.004

Abstract ( 1162 )

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The problems of concept characteristics and concept reduction preserving binary relations are studied by Boolean matrix operation. Firstly, formal context is described as a Boolean matrix, the relation matrices of object\attribute are generated by using the binary relation matrix, and their related properties are studied. Further, concept characteristics of three different types of concepts in the processing of concept reduction are obtained by using Boolean matrix operation. Finally, the minimum operation of concept interval sets is done with Boolean matrix operation, the discernibility matrix is simplified, and a method of calculating concept reduction is given. Compared with the existed methods of concept reduction in formal context, the proposed matrix algorithm is simple and its time complexity is lower.

Granular structure in multi-source formal contexts

LI Shuang-ling, YUE Xiao-wei, QIN Ke-yun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 46-54. doi:10.6040/j.issn.1671-9352.c.2020.003

Abstract ( 905 )

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Knowledge discovery of multi-source data is an important problem that needs to be solved urgently in the field of big data analysis. Based on the theory of residuated lattices, the granular structure of concepts in fusion L fuzzy formal context of multi-source formal contexts is investigated. The relationships between the variable threshold concepts in the fusion L fuzzy formal context and the concepts in the single source formal contexts are surveyed. The granular reduction method for the fusion L fuzzy formal context is presented and the relationship between the granular reduction of this fuzzy formal context and that of single-source formal contexts are investigated.

Modularity equations between a class of S-uninorms and several commonly-used aggregation operators

ZHAO Wei-li, ZHOU Hong-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 55-70. doi:10.6040/j.issn.1671-9352.0.2019.460

Abstract ( 892 )

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Based on the fuzzy logic theory and fuzzy decision, the present paper focuses on the modularity equations between one class of S-uninorms and several aggregation operators such as uninorms, t-operators, S-uninorms and T-uninorms, and gives structural characterizations of these aggregation operators satisfying modularity equations. Moreover, the structural characterizations between T-uninorms and S-uninorms satisfying the modularity equations partially generalize the structural characterizations of 2-uninorms.

Boolean atoms of Heyting algebras and their application

ZHAO Ma-pan, FAN Feng-li, XIE Yong-jian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 71-80. doi:10.6040/j.issn.1671-9352.0.2020.031

Abstract ( 1165 )

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A kind of direct product decomposition of Heyting algebras is obtained using the Boolean elements of Heyting algebras. Based on this decomposition of Heyting algebras, it is proved that a finite Heyting algebra can be obtained by substituting the atoms of a Boolean algebra with Heyting algebras. This conclusion reveals a kind of new relationship between Heyting algebras and Boolean algebras.

A not-same frequency remote data possession checking method

MA Hai-feng, YANG Jia-hai, XUE Qing-shui, JU Xing-zhong, ZHU Hao-zhi, LIN Tao, YUAN Xin-xin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 81-87. doi:10.6040/j.issn.1671-9352.2.2019.146

Abstract ( 924 )

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The proposed not-same frequency verification mode can significantly reduce the detection delay after the occurrence of file corruption. Furthermore, the proposed not-same frequency enhanced remote data possession checking method can reduce the delay of corrupt data detection and prevent replace attack and so on. Security proof and experiments show that the proposed method is secure. And under the experimental samples, NE-RDPC has 19.3% performance improvement in average than E-RDPC.

Importance evaluation algorithm of dynamic nodes in social networks based on time series and TOPSIS

JIA Han, HAN Yi-liang, WU Xu-guang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 88-94. doi:10.6040/j.issn.1671-9352.2.2019.156

Abstract ( 1230 )

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Aiming at the fact that social networks are constantly changing with time, the consideration factor of time is introduced, based on the TOPSIS algorithm, and a comprehensive evaluation algorithm for node, node properties and time series is designed. Using Facebooks 28-month data set, it is divided into four time periods with 7 months as a stage, and the algorithm is verified in order of change time, and compared with the results of TOPSIS algorithm. The experimental results show that the proposed algorithm takes the importance of the nodes in each period of time into account, and the evaluation results are more in line with the actual dynamics of the nodes and have higher accuracy.

Security detection of CAN bus protocol for electric vehicle and charging pile

XU Jiang-pei, WANG Jin, LIU Chang, ZHOU Liang, LONG Feng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 95-104. doi:10.6040/j.issn.1671-9352.2.2019.144

Abstract ( 2144 )

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With the extensive deployment of intelligent charging piles, the related information security issues are gradually becoming serious. Through the external access interface, an attacker can penetrate to the CAN bus network which connects to the key control unit of charging pile. By sending malicious attack messages, an attacker can interfere with charging pile operating and seriously endanger the safety of charging infrastructure. In order to solve the problem of CAN bus information security of electric vehicle charging pile, a fuzzing test method of CAN bus based on maximum and minimum ant colony algorithm(MMAS)is proposed. This method improves the fuzzing test efficiency of CAN protocol by improving the maximum and minimum ant colony algorithm. It uses a specific mutation strategy to change the corresponding fields of the message packet,sending the fuzzing test message to CAN node of the charging pile through the CAN protocol analyzer. Based on the above testing method, it is found that the attack on charging piles by utilizing the current security vulnerabilities of charging protocol can lead to shutdown, denial of service and other security problems of charging piles.

Asset pricing and simulation under the environment of jumping and mixed Gaussian process

PENG Bo, GUO Jing-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 105-113. doi:10.6040/j.issn.1671-9352.0.2019.666

Abstract ( 1096 )

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The European option pricing model is established by based on mixed sub-fractional Brownian motion in jump environment. Firstly, the partial differential equation satisfying European option can be obtained through the Delta hedging principle. Secondly, the call option, the put option pricing formula and the call-put parity formula are respectively obtained by using the quasi-conditional expectation. Then, the asset risk is further quantified by Greeks Δ, Δ, ρ, Θ, Γ, ν and the partial derivative formula forthe Hurst index H. Finally, numerical simulation show that the Hurst index H and jump intensity λ in pricing parameters have a significant impact on the value of option.

Equilibrium of a closed-loop supply chain network considering manufacturers fairness concern

QU Peng-peng, ZHOU Yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5): 114-126. doi:10.6040/j.issn.1671-9352.0.2019.204

Abstract ( 921 )

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In order to analyze the impact of manufacturers fairness concern behavior on the equilibrium strategy and utilities of decision makers, a closed-loop supply chain network equilibrium model considering manufacturers fairness concern is constructed. The results show that, compared with the results of the fairness neutrality, the advantageous or disadvantageous unfairness concern of the manufacturers will reduce their utilities, and the advantageous unfairness concern will increase the quantity of the production and the recovery with the increase of unfairness concern degree, which is conducive to improving the reuse of resources, while the profits of themselves and retailers will decrease; the disadvantageous unfairness concern will decrease the quantity of the production and the recovery with the increase of unfairness concern degree, which is not benefit to the reusing of the resources, while it will increase the profits of themselves and retailers. The results will guide manufacturers to select appropriate fairness concern strategies and improve their competitiveness and the resource utilization.

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