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    20 August 2014
    Volume 49 Issue 08
    New research of functional dependency and multi-valued dependency
    AN Qiu-sheng, KONG Xiang-yu
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  1-5.  doi:10.6040/j.issn.1671-9352.1.2014.081
    Abstract ( 538 )   PDF (753KB) ( 459 )   Save
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    Functional dependency and multi-Valued dependency and their relationships are studied from different angles in this paper. And their research view of classic database theory, rough set theory and formal concept analysis (FCA) to functional dependency and multi-Valued dependency are discussed. Finally, some important conclusions are obtained.
    Cover rough sets on a semi-monolayer cover
    WU Zheng-jiang, LIU Yong-li, GAO Yan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  6-14.  doi:10.6040/j.issn.1671-9352.1.2014.170
    Abstract ( 569 )   PDF (996KB) ( 452 )   Save
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    Semi-monolayer cover is an efficient way to formalize the missing value in information table with discrete values. When system discrete the continuous attribute-values, it is a perfect mathematic model to content the misclassification object. Because a semi-monolayer cover is the minimal and precise cover, and the approximation operator on the cover is more special than the standard cover rough approximation operator. In this paper, four pairs of approximation operators are defined from two ways. One way starts with the subset of U, other way bases on the set of dot in U. Based on the discussion of their properties, the relations of the four pairs of approximation operators are discussed.
    Dynamic reduction theory for interval concept lattice based on covering and its realization
    ZHANG Chun-ying, WANG Li-ya, LIU Bao-xiang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  15-21.  doi:10.6040/j.issn.1671-9352.1.2014.207
    Abstract ( 479 )   PDF (2035KB) ( 353 )   Save
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    The structure of interval concept lattice is complex and the lattice built by the existing construction algorithm has the problem of concept redundancy. To reduce the redundancy of interval concepts, a dynamic reduction method for interval concept lattice is put forward which starts from a formal context directly. Firstly, the similarity degree of the binary relations and covering-neighborhood-space are defined which could ensure that the compressed lattice still can reflect the relationship between concepts. Secondly, according to the reduction operators, the compressed concept is acquired. Thirdly, it is proved that the reduced interval concept set is a subset of the original. Then, it built the dynamic reduction model for interval concept lattice based on the covering-neighborhood-space and reduction operators. The number of concepts in lattice is controlled by the threshold value of similarity class which can realize the dynamic of reduction. Finally, the correctness of model and the high efficiency of reduction are shown by a case study.
    FMT-universal triple Ⅰ* method for R-implication operators
    TANG Yi-ming, LI Xiao-mei, WU Xi
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  22-27.  doi:10.6040/j.issn.1671-9352.1.2014.200
    Abstract ( 411 )   PDF (694KB) ( 292 )   Save
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    Focusing on the FMT(fuzzy modus tollens)problem of fuzzy reasoning, as a generalization and improvement of triple Ⅰ* method, the FMT-universal triple Ⅰ* method is put forward and thoroughly investigated. First of all, the attributes of the FMT-universal triple Ⅰ* method are analyzed, and its basic principle is proposed, which improves the one of triple Ⅰ* method. Furthermore, the unified form of FMT-universal triple Ⅰ* method is established, meanwhile some optimal solutions are obtained for several classical R-implication operators. Finally, the contrapositive reversibility property of FMT-universal triple Ⅰ* method is proved with excellent results.
    Heterogeneous formal contexts for uncertainty reasoning
    LING Mi-ran, MI Ju-sheng, MA Li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  28-32.  doi:10.6040/j.issn.1671-9352.1.2014.113
    Abstract ( 420 )   PDF (672KB) ( 312 )   Save
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    Heterogeneous formal context is a new type of fuzzification for formal concept analysis that works with heterogeneous values. The evidence theory is introduced for reasoning on heterogeneous formal contexts. The thought of D-S combination formula is applied to heterogeneous formal contexts for reasoning. Then, the synthesis steps is proposed, according to the steps, and the heterogeneous formal contexts is demonstrated by an example in practice.
    The inconsistent degree of an inconsistent decision table
    YAO Xiao-lin, MI Ju-sheng, LING Mi-ran
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  33-39.  doi:10.6040/j.issn.1671-9352.1.2014.115
    Abstract ( 430 )   PDF (682KB) ( 356 )   Save
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    The definition of inconsistent decision rule pairs is proposed in an inconsistent decision information system with inconsistent decision rules. It is relatively complicated by using discernibility matrix to extract inconsistent decision rule pairs from inconsistent decision table with many objects or attributes. Inclusion degree is used to screen the equivalence classes which can produce inconsistent decision rule pairs, then discernibility matrix is employed to extract inconsistent decision rule pairs, thus calculating the number. The number can be also calculated by the component of generalized decision function directly. And then the inconsistent degree of an inconsistent decision table is computed. Finally, the relationship of inconsistent degree between original inconsistent decision table and reduced inconsistent decision table is studied.
    An incremental three-way decisions soft clustering algorithm
    ZHANG Cong, YU Hong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  40-47.  doi:10.6040/j.issn.1671-9352.1.2014.114
    Abstract ( 430 )   PDF (1033KB) ( 1211 )   Save
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    Most of the clustering algorithms reported assume a data set always does not change. However, it is often observed that the analyzed data set changes over time in many applications. To combat changes, we introduce a new incremental soft clustering approach based on three-way decisions theory. Firstly, the interval sets are used to represent a cluster, wherein the upper bound, the border, the lower bound of interval sets corresponding to positive region, boundary region, negative region generated by the three-way decisions respectively, and an initial clustering algorithm is proposed by using representative points. Secondly, to eliminate the influence of the processing order on final incremental clustering results, the incremental data is pre-clustered used the same way. To quickly search similar areas for incremental data, a searching tree based on the representative points is constructed, and the strategies of searching and updating are presented. Finally, the three-way decisions strategy is used to incremental clustering. The results of the experiments show the approach is effective to incremental clustering.
    Multi-granularity cost-sensitive three-way decision for face recognition
    ZHANG Li-bo, LI Hua-xiong, ZHOU Xian-zhong, HUANG Bing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  48-57.  doi:10.6040/j.issn.1671-9352.1.2014.195
    Abstract ( 587 )   PDF (4129KB) ( 522 )   Save
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    The application of multi-granularity three-way decision method in face recognition are explored. Firstly, two representations of the image's granularity to simulate the visual effects of different granularities are presented, and acquire face images of different granularities accordingly. Then the cost-sensitive three-way decision model is introduced to decision-making to get the decision with the minimum cost. Finally, the experiment on the PIE and ORL data prove that multi-granularity cost-sensitive three-way decision is effective to simulate the decison process of human beings.
    Research on identificating Chinese micro-blog opinion sentence based on three-way decisions
    TIAN Hai-long, ZHU Yan-hui, LIANG Tao, MA Jin, LIU Jing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  58-65.  doi:10.6040/j.issn.1671-9352.1.2014.199
    Abstract ( 585 )   PDF (1472KB) ( 512 )   Save
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    Micro-blog opinion sentence identification is the foundation for opinion mining and public opinion analysis.Therefore, the accuracy of identification of critical opinion sentences is very important for the follow-up research work. A Chinese micro-blog perspective sentence identification method based on three-way decisions.using support vector machine classifiers and sigmoid function to caculate the probability of a micro-blog belonging to perspective sentence,and conducting a contrast experiment between Chinese microblog perspective sentence identificaition method based on three-way decisions and traditional support vector machine,it shows that three-way decisions has accepted a good identification effect.
    Research on the evaluation of venture investment based on the risk minimization of three-way decision
    DU Li-na, XU Jiu-cheng, LIU Yang-yang, SUN Lin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  66-72.  doi:10.6040/j.issn.1671-9352.1.2014.155
    Abstract ( 454 )   PDF (1082KB) ( 862 )   Save
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    Aiming to deal with those problems that the fuzzy membership degree which acts as the state function dose not satisfy the normalization and additivity, and the max-min operation of fuzzy sets will lose a lot of useful information in the evaluation of the venture investment, in this paper, the Bayesian theory and the three-way decisions was introduced into the fuzzy comprehensive evaluation model. A risk factor was defined with the risk function and a new risk evaluation matrix was constructed, then a new evaluation model of venture investment was proposed based on the risk minimization of three-way decisions. After that, the minimum loss decision is taken according to the risk minimization principle, thus the problems existing in the fuzzy comprehensive evaluation method are solved and the evaluation results are more reasonable and more accurate.
    Tolerance rough fuzzy set model
    ZHAI Jun-hai, ZHANG Yao, WANG Xi-zhao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  73-79.  doi:10.6040/j.issn.1671-9352.1.2014.089
    Abstract ( 486 )   PDF (1151KB) ( 520 )   Save
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    In rough fuzzy set model, the approached target concept is a fuzzy set, the knowledge used for approaching the target concept is equivalence relation, in other words, the attributes used for representing the object is of discrete value. However, in many practical applications, the attributes used for representing the object is of real value. In order to deal with this problem, the equivalence relation in rough fuzzy set model is extended to tolerance relation; the tolerance rough fuzzy set model is proposed. When the tolerance relation is degenerated into equivalence relation, the tolerance rough fuzzy set model becomes the rough fuzzy set model; tolerance rough fuzzy set model extends the application of rough fuzzy set.
    Matroidal structure of the upper approximation of covering-based rough set defined by the neighborhood
    LI Qing-yin, ZHU William
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  80-85.  doi:10.6040/j.issn.1671-9352.1.2014.009
    Abstract ( 464 )   PDF (695KB) ( 278 )   Save
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    By neighborhoods, a matroidal structure of the upper approximation of covering-based rough sets is constructed. Through transversal theory and base axioms, the matroidal structure is established. By the lower approximations of the complementary neighborhood, a family related to neighborhoods is equivalent represented. Finally, a sufficient and necessary condition for the family to be the set of all hyperplanes of the matroid is studied from the viewpoint of cardinality.
    Fuzzy roughness and rough entropy of covering based generalized rough intuitionistic fuzzy set model
    SHI Su-wei, LI Jin-jin, TAN An-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  86-91.  doi:10.6040/j.issn.1671-9352.1.2014.061
    Abstract ( 407 )   PDF (692KB) ( 269 )   Save
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    On the basis of the covering rough intuitionistisc fuzzy set model, this paper introduces the notions of roughness and rough entropy, by which the uncertainty measure of intuitionistisc fuzzy set is investigated and their properties are discussed. It is proved that the fuzzy roughness and rough entropy of intuitionistisc fuzzy sets are monotonously decreasing with the subdivision of covering sets by examples.
    On invariance properties of covering-based rough sets under consistent function
    ZHANG Yan-lan, LI Chang-qing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  92-96.  doi:10.6040/j.issn.1671-9352.1.2014.151
    Abstract ( 406 )   PDF (678KB) ( 250 )   Save
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    Invariance properties of covering-based rough sets under consistent function are discussed. It is proved that there exist one-to-one correspondences between covering upper approximations of original approximation space and covering upper approximations of image approximation space under consistent function. Furthermore, the image of reduction of original approximation space is the reduction of image approximation space.
    Computing minimal description and maximal description in covering-based rough sets through matrices
    LIN Zi-qiong, WANG Jing-qian, ZHU William
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  97-101.  doi:10.6040/j.issn.1671-9352.1.2014.034
    Abstract ( 596 )   PDF (675KB) ( 361 )   Save
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    The minimal description and maximal description in covering-based rough sets are computed through matrices. Firstly, some significant matrices about coverings are presented through the matrix representation of a covering. Secondly, according to these proposed matrices and a new matrix operation, the minimal description and maximal description in covering-based rough sets are computed from the viewpoint of matrices.
    Cognitive system model and approach to transformation of information granules under triadic formal concept analysis
    TANG Ya-qiang, FAN Min, LI Jin-hai
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  102-106.  doi:10.6040/j.issn.1671-9352.1.2014.217
    Abstract ( 510 )   PDF (668KB) ( 498 )   Save
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    This study mainly focuses on cognitive system model in the framework of triadic formal concept analysis. More precisely, the notions of sufficient information granule, necessary information granule, and sufficient and necessary information granule are proposed. Also, methods of transforming arbitrary information granule into sufficient, necessary, and sufficient and necessary information granules are presented under the background of fixing the third dimension.
    Normal distribution of lattice close-degree based on granular computing
    MA Yuan-yuan, MENG Hui-li, XU Jiu-cheng, ZHU Ma
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  107-110.  doi:10.6040/j.issn.1671-9352.1.2014.064
    Abstract ( 488 )   PDF (736KB) ( 267 )   Save
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    Through the traditional fuzzy close-degree's axiomatic definition is transformed, it makes the close-degree based on the granular computing. The close-degree can reflect the similarity between the two grain sets. By the analysis of practical problems, it is given based on granular computing satisfy normal distribution of a lattice close-degree function and its related theorems and proofs. It convenient practical problem analysis and processing.
    Enterprises trust comprehensive evaluation based on fussy rough AHP in cloud computing
    LUO hai-yan, LÜ Ping, LIU Lin-zhong, YANG Xun
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  111-117.  doi:10.6040/j.issn.1671-9352.0.2014.274
    Abstract ( 537 )   PDF (887KB) ( 335 )   Save
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    Aiming at the shortcomings of the traditional trust evaluation model among supply chain adjoint enterprises, it establishes fussy rough AHP trust evaluation model in cloud computing and improves the flow that the former trust evaluation model can't well reflect the comprehensive weights. It builds AHP model to calculate the combination of subjective weight of trust evidence and applies the fuzzy rough set theory in defining the index objective weight, therefore calculates the comprehensive weight.Finally trust fuzzy model is established to work out enterprise comprehensive trust evaluation value. It is proved by examples that this model can be well applied in the node enterprises trust evaluation in cloud computing and it's an effective comprehensive evaluation method.
    A study of adaptive Memetic algorithm based on particle swarm optimization
    QU Bin-peng, WANG Zhi-hao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(08):  118-124.  doi:10.6040/j.issn.1671-9352.7.2014.002
    Abstract ( 273 )   PDF (1094KB) ( 350 )   Save
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    According to the analyzing of the proposed adaptive Memetic algorithm,the Particle Swarm Optimization is used as Memetic algorithm's GS. An Adaptive Memetic Algorithm Based on Particle Swarm Optimization is constituted according to different types of Adaptive Memetic. The experimental results show that the PMemetic algorithm improves the global search capability, the convergence speed and the solution accuracy. Experimental results demonstrate that the algorithm can get the better optimal path.