Automated analysis of the SCR-style requirements specifications

The SCR(Software Cost Reduction)requirements method is an effective method for specifying software system requirements.This paper presents a formal model analyzing SCR-style requirements.The analysis model mainly applies state translation rules,semantic computing rules and attributes to define formal semantics of a tabular notation in the SCR requirements method,and may be used to analyze requirements specifications to be specified by the SCR requirements method.Using a simple example,this paper introduces how to analyze consistency and completeness of requirements specifications.     

Reduction Algorithms Based on Discernibility Matrix：The Ordered Atributes Method

In this Paper,we present reduction algorithms based on the principle of Skowron‘s discernibility matrix-the ordered attributes method.The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved.Since a discernibility matrix requires the size of the memory of |U|^2,U is a universe of bojects,it would be impossible to apply these algorithms directly to a massive object set.In order to solve the problem,a so=called quasi-discernibility matrix and two reduction algorithms are prpopsed.Although the proposed algorithms are incomplete for Pawlak reduct,their optimal paradigms ensure the completeness as long as they satisfy some conditions.Finally,we consider the problem on the reduction of distributive object sets.     

Reduct and attribute order

Based on the principle of discernibility matrix, a kind of reduction algorithm with attribute order has been developed and its solution has been proved to be complete for reduct and unique for a given attribute order. Being called the reduct problem, this algorithm can be regarded as a mapping R = Reduct(S) from the attribute order space O to the reduct space R for an information system (U, C ∪ D）, where U is the universe and C and D are two sets of condition and decision attributes respectively. This paper focuses on the reverse problem of reduct problem S = Order(R), i.e., for a given reduct R of an information system, we determine the solution of S = Order(R) in the space θ. First, we need to prove that there is at least one attribute order S such that S = Order(R). Then, some decision rules are proposed, which can be used directly to decide whether the pair of attribute orders has the same reduct. The main method is based on the fact that an attribute order can be transformed into another one by moving the attribute for limited times. Thus, the decision of the pair of attribute orders can be altered to the decision of the sequence of neighboring pairs of attribute orders. Therefore,the basic theorem of neighboring pair of attribute orders is first proved, then, the decision theorem of attribute order is proved accordingly by the second attribute.     

Inductive Learning

Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasible way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Research on ML has concentrated in the main on inductive learning,a paradigm for inducing rules from unordered sets of exmaples.AQ11 and ID3,the two most widespred algorithms in ML,are both inductive.This paper first summarizes AQ11,ID3 and the newly-developed extension matrix approach based HCV algorithm;and then reviews the recent development of inductive learing and automatic knowledge acquisition from data bases.     

Second Attribute Algorithm Based on Tree Expression

One view of finding a personalized solution of reduct in an information system is grounded on the viewpoint that attribute order can serve as a kind of semantic representation of user requirements. Thus the problem of finding personalized solutions can be transformed into computing the reduct on an attribute order. The second attribute theorem describes the relationship between the set of attribute orders and the set of reducts, and can be used to transform the problem of searching solutions to meet user requirements into the problem of modifying reduct based on a given attribute order. An algorithm is implied based on the second attribute theorem, with computation on the discernibility matrix. Its time complexity is O（n^2 × m） （n is the number of the objects and m the number of the attributes of an information system）. This paper presents another effective second attribute algorithm for facilitating the use of the second attribute theorem, with computation on the tree expression of an information system. The time complexity of the new algorithm is linear in n. This algorithm is proved to be equivalent to the algorithm on the discernibility matrix.     

An Agent Based Framework for Internetware Computing

Internetware intends to be a paradigm of Web-based software development. At present, researches on Internetware have gained daily expanding attentions and interests. This paper proposes an agent based framework for Internetware computing. Four principles are presented that are followed by this framework. They are the autonomy principle, the abstract principle, the explicitness principle and the competence principle. Three types of agents with di?erent responsibilities are designed and specified. They are the capability providing agents, the capability planning agents and the capability consuming agents. In this sense, capability decomposition and satisfaction turns to be a key issue for this framework and becomes a communication protocol among these distributed and heterogenous agents. A capability conceptualization is proposed and based on the conceptualization, an agent coalition formation mechanism has been developed. This mechanism features that (1) all the participants make their one decisions on whether or not joining the coalition based on the capability realization pattern generated by the capability planning agents as well as the benefits they can obtain; and (2) the coalition selection is conducted by a negotiation process for satisfying the expectations of all the participants as the complexity of this problem has been proven to be NP-complete.     

A new approach on designing l1 optimal regulator with minimum order for SISO linear systems

For a SISO linear discrete-time system with a specified input signal, a novel method to realize optimal l1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l\ norm objective.     

Spectral clustering based on matrix perturbation theory

This paper exposes some intrinsic characteristics of the spectral clustering method by using the tools from the matrix perturbation theory. We construct a weight ma- trix of a graph and study its eigenvalues and eigenvectors. It shows that the num- ber of clusters is equal to the number of eigenvalues that are larger than 1, and the number of points in each of the clusters can be approximated by the associated eigenvalue. It also shows that the eigenvector of the weight matrix can be used directly to perform clustering; that is, the directional angle between the two-row vectors of the matrix derived from the eigenvectors is a suitable distance measure for clustering. As a result, an unsupervised spectral clustering algorithm based on weight matrix (USCAWM) is developed. The experimental results on a number of artificial and real-world data sets show the correctness of the theoretical analysis.     

Frequency-domain stability criteria for SISO and MIMO nonlinear feedback systems with constant and variable time-delays

New frequency-domain criteria are proposed for the $L_2$-stability of both nonlinear single-input-single-output (SISO) and nonlinear multiple-input-multiple-output (MIMO) feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities (FATQNs) with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i) zero, ii) a constant, iii) variable-time and iv) fixed-history (only for SISO systems). The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal+anticausal O''Shea-Zames-Falb multiplier function (scalar for SISO systems and matrix for MIMO systems). Its time-domain $L_1$-norm is constrained by the coefficients and characteristic parameters (CPs) of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria.     

Asymptotic stability of port‑hamiltonian systems with constant inputs

In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step signals. To achieve this goal, two methods based on integral action and comparison principle are presented in this paper. These methods change the convex Hamiltonian function and the restricted damping matrix of the previous results into a Hamiltonian function with a local minimum and a positive semidefinite matrix, respectively. Due to common conditions of Hamiltonian function and damping matrix, the proposed method asymptotically stabilizes more classes of PH systems with constant inputs than the existing methods. Finally, the validity and advantages of the presented methods are shown in an example.     

基于差别矩阵和mRMR的分步优化特征选择算法

分类问题普遍存在于现代工业生产中。在进行分类任务之前,利用特征选择筛选有用的信息,能够有效地提高分类效率和分类精度。最小冗余最大相关算法(mRMR)考虑最大化特征与类别的相关性和最小化特征之间的冗余性,能够有效地选择特征子集;但该算法存在中后期特征重要度偏差大以及无法直接给出特征子集的问题。针对该问题,文中提出了结合邻域粗糙集差别矩阵和mRMR原理的特征选择算法。根据最大相关性和最小冗余性原则,利用邻域熵和邻域互信息定义了特征的重要度,以更好地处理混合数据类型。基于差别矩阵定义了动态差别集,利用差别集的动态演化有效去除冗余属性,缩小搜索范围,优化特征子集,并根据差别矩阵判定迭代截止条件。实验选取SVM,J48,KNN和MLP作为分类器来评价该特征选择算法的性能。在公共数据集上的实验结果表明,与已有算法相比,所提算法的平均分类精度提升了2%左右,同时在特征较多的数据集上能够有效地缩短特征选择时间。所提算法继承了差别矩阵和mRMR的优点,能够有效地处理特征选择问题。     

不完备软区分矩阵及其在决策问题中的应用

基于软区分矩阵,首先提出了不完备软区分矩阵的概念,讨论了不完备软区分矩阵的相关性质;接着提出了基于不完备软区分矩阵的决策算法。该算法可以通过扫描一次不完备软区分矩阵就能得到所有对象的序关系,从而可得最优选择对象和次优对象。最后,通过实例来说明该方法在决策问题中的正确性和有效性。     

基于Rough Set理论的"数据浓缩"

本文了基于ＲｏｕｇｈＳｅｔ（ＲＳ）理论数据浓缩的几个问题。     

分辨矩阵法耗时推算

针对粗集理论的分辨矩阵方法求解知识约简过程中时空性能上存在的问题,提出分辨矩阵法耗时推算的原理和算法,包括2个耗时段的推算及推算结果的可靠性验证。推算可预知分辨矩阵法处理数据所消耗的时间,对数据挖掘实验的可行性进行预测。     

一个机器学习新算法——HP算法的实现及研究

在示例学习这一机器学习的分支领域中有两类非常重要的算法,其中一个以ID3为代表算法,其知识表示是决策树.另一类是AQ算法,其知识表示是产生式规则.ID3的优点是匹配速度快,但其规则数目太多.AQ虽然能生成数目相对ID3不十分多的产生式规则,但其匹配速度与ID3比较却慢的多.因此就示例学习这一领域提出了一个新算法--HP,这个算法是基于n维欧几里德空间中的超平面提出的,对一个正例集和一个反例集,这一算法的规则只有一个,其匹配速度比AQ要快得多.     

基于序关系的快速计算正区域核的算法

目前设计基于正区域的求核算法的主要方法是差别矩阵方法.该方法通过搜索差别矩阵的所有差别元素来得到核,故比较耗时.为此,在简化决策表和简化差别矩阵的基础上,若将其对象按条件属性值看成一个数,则对象是有序的.利用这个序,可将具有核属性的差别元素集映射到一个较小的搜索空间上,故只需判断简化差别矩阵的少量差别元素就可以找到核属性集.在此基础上,利用基数排序的思想,设计了一个高效求核算法,其时间复杂度为O(|C|2|U/C|)+O(|C||U|),空间复杂度为O(|U|).由于新算法只需判断简化差别矩阵的少量差别元素就可以找到核算属性集,故算法的效率得到了改善.     

一种否定高信度规则的属性查找算法

粗糙集理论中可辨识矩阵是在整个论域U上构造的。该文扩展了可辨识矩阵的应用,提出一种否定高信度决策规则的属性查找算法,求出条件属性和决策属性的不可分辨二元关系在等价类上进行运算。在论域U的子集上构造可辨识矩阵,根据分辨函数求解问题。将算法应用于医学数据。实验结果表明,该算法局部采用可辨识矩阵可以有效地减少存储空间,提高查找效率。     

利用序关系求差别矩阵的核的高效算法

目前设计基于差别矩阵的求核算法的主要方法是差别矩阵方法.在该种方法中,是通过搜索差别矩阵的所有差别元素得到核.由于是在所有的差别元素上搜索,故该方法比较耗时.本文在简化决策表和简化差别矩阵的基础上,将具有核属性的差别元素集归纳在某一相对较小的集合上,故新算法只需搜索和检查简化差别矩阵的少量差别元素就可以得到核算属性集.设计了一个高效求核算法,其时间复杂度为max{O(|C|2|U/C|),O(|C||U|)},其空间复杂度为O(|U|).由于新算法只判断简化差别矩阵的少量差别元素就可以找到核算属性集,故新算法的效率得到了有效地改善.     

Data analysis based on discernibility and indiscernibility

Rough set theory models similarities and differences of objects based on the notions of indiscernibility and discernibility. With respect to any subset of attributes, one can define two pairs of dual relations: the strong indiscernibility and weak discernibility relations, and the weak indiscernibility and strong discernibility relations. The similarities of objects are examined by the indiscernibility relations, and the differences by the discernibility relations, respectively. Alternatively, one can construct an indiscernibility matrix to represent the family of strong indiscernibility or weak discernibility relations. One also can construct a discernibility matrix to represent the family of strong discernibility or weak indiscernibility relations. The consideration of the matrix-counterpart of relations, and the relation-counterpart of matrices, brings more insights into rough set theory.Based on indiscernibility and discernibility, three different types of reducts can be constructed, keeping the indiscernibility, discernibility, and indiscernibility-and-discernibility relations, respectively. Although the indiscernibility reducts have been intensively studied in the literature, the other two types of reducts are relatively new and require more attention. The existing methods for constructing the indiscernibility reducts also can be applied to construct the other two types of reducts. An empirical experiment for letter recognition is reported for demonstrating the usefulness of the discussed relations and reducts.