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1.
Uncertainty casts a shadow over all facets of software engineering. This negative meta-property is found in every aspect of software including requirement specifications, design, and code. It can also manifest itself in the tools and engineering practices employed, and in the off-the-shelf software incorporated into the final product. Unfortunately, it is often the case that software engineers ignore these sources of uncertainty or abstract them away. Perhaps this is because there is insufficient understanding of this uncertainty, and no universal techniques for handling its many forms. This paper focuses on the issues of uncertainty in software engineering. It further describes a rough set framework for making decisions in the face of such uncertainty and inconsistency. In particular, we show how to induce rule-based decision making from uncertain information in software engineering applications. Moreover, a freely available tool, Rosetta, is employed to automate the decision-making process. NASA has mandated the use of commercial off-the-shelf (COTS) solutions where possible. But in commercial real-time operating systems certain attributes are uncertain, even where published information is available. Therefore, the selection of a commercial real-time operating system for an embedded system is the software engineering problem with which we explain the rough set decision-making process. 相似文献
2.
This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided. 相似文献
3.
Generalized fuzzy rough sets determined by a triangular norm 总被引:4,自引:0,他引:4
The theory of rough sets has become well established as an approach for uncertainty management in a wide variety of applications. Various fuzzy generalizations of rough approximations have been made over the years. This paper presents a general framework for the study of T-fuzzy rough approximation operators in which both the constructive and axiomatic approaches are used. By using a pair of dual triangular norms in the constructive approach, some definitions of the upper and lower approximation operators of fuzzy sets are proposed and analyzed by means of arbitrary fuzzy relations. The connections between special fuzzy relations and the T-upper and T-lower approximation operators of fuzzy sets are also examined. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, T-fuzzy approximation operators are defined by axioms. Different axiom sets of T-upper and T-lower fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations producing the same operators. The independence of axioms characterizing the T-fuzzy rough approximation operators is examined. Then the minimal sets of axioms for the characterization of the T-fuzzy approximation operators are presented. Based on information theory, the entropy of the generalized fuzzy approximation space, which is similar to Shannon’s entropy, is formulated. To measure uncertainty in T-generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T = min, it is proved that the measure of fuzziness of the generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable. 相似文献
4.
Neil Mac Parthaláin Author Vitae Author Vitae 《Pattern recognition》2009,42(5):655-667
Of all of the challenges which face the effective application of computational intelligence technologies for pattern recognition, dataset dimensionality is undoubtedly one of the primary impediments. In order for pattern classifiers to be efficient, a dimensionality reduction stage is usually performed prior to classification. Much use has been made of rough set theory for this purpose as it is completely data-driven and no other information is required; most other methods require some additional knowledge. However, traditional rough set-based methods in the literature are restricted to the requirement that all data must be discrete. It is therefore not possible to consider real-valued or noisy data. This is usually addressed by employing a discretisation method, which can result in information loss. This paper proposes a new approach based on the tolerance rough set model, which has the ability to deal with real-valued data whilst simultaneously retaining dataset semantics. More significantly, this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty. The use of this information can result in the discovery of more compact feature subsets and improved classification accuracy. These results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques. 相似文献
5.
Soft sets and soft rough sets 总被引:4,自引:0,他引:4
In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak’s rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak’s rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given. 相似文献
6.
Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria. Fuzzy preference relations are incorporated into a fuzzy rough set model, which leads to a fuzzy preference based rough set model. The measure of attribute dependency of the Pawlak’s rough set model is generalized to compute the relevance between criteria and decisions. The definitions of upward dependency, downward dependency and global dependency are introduced. Algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets. 相似文献
7.
Three-way decisions with probabilistic rough sets 总被引:3,自引:0,他引:3
Yiyu Yao 《Information Sciences》2010,180(3):341-353
The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes a decision of abstaining. This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model. The results enrich the rough set theory by ideas from Bayesian decision theory and hypothesis testing in statistics. The connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications. 相似文献
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Generalized rough sets over fuzzy lattices 总被引:2,自引:0,他引:2
Guilong Liu 《Information Sciences》2008,178(6):1651-1662
This paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches. From the viewpoint of the constructive approach, the basic properties of generalized rough sets over fuzzy lattices are obtained. The matrix representation of the lower and upper approximations is given. According to this matrix view, a simple algorithm is obtained for computing the lower and upper approximations. As for the axiomatic approach, a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices. 相似文献
10.
Eric C.C. Tsang Chen Degang Daniel S. Yeung 《Computers & Mathematics with Applications》2008,56(1):279-289
The covering generalized rough sets are an improvement of traditional rough set model to deal with more complex practical problems which the traditional one cannot handle. It is well known that any generalization of traditional rough set theory should first have practical applied background and two important theoretical issues must be addressed. The first one is to present reasonable definitions of set approximations, and the second one is to develop reasonable algorithms for attributes reduct. The existing covering generalized rough sets, however, mainly pay attention to constructing approximation operators. The ideas of constructing lower approximations are similar but the ideas of constructing upper approximations are different and they all seem to be unreasonable. Furthermore, less effort has been put on the discussion of the applied background and the attributes reduct of covering generalized rough sets. In this paper we concentrate our discussion on the above two issues. We first discuss the applied background of covering generalized rough sets by proposing three kinds of datasets which the traditional rough sets cannot handle and improve the definition of upper approximation for covering generalized rough sets to make it more reasonable than the existing ones. Then we study the attributes reduct with covering generalized rough sets and present an algorithm by using discernibility matrix to compute all the attributes reducts with covering generalized rough sets. With these discussions we can set up a basic foundation of the covering generalized rough set theory and broaden its applications. 相似文献
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12.
Dubois and Prade (1990) [1] introduced the notion of fuzzy rough sets as a fuzzy generalization of rough sets, which was originally proposed by Pawlak (1982) [8]. Later, Radzikowska and Kerre introduced the so-called (I,T)-fuzzy rough sets, where I is an implication and T is a triangular norm. In the present paper, by using a pair of implications (I,J), we define the so-called (I,J)-fuzzy rough sets, which generalize the concept of fuzzy rough sets in the sense of Radzikowska and Kerre, and that of Mi and Zhang. Basic properties of (I,J)-fuzzy rough sets are investigated in detail. 相似文献
13.
基于蕴涵的区间值直觉模糊粗糙集 总被引:3,自引:0,他引:3
提出一种基于区间值直觉模糊蕴涵的区间值直觉模糊粗糙集模型.首先,介绍了区间值直觉模糊集、区间值直觉模糊关系和区间值直觉模糊逻辑算子的概念;然后,利用区间值直觉模糊三角模和区间值直觉模糊蕴涵,在区间值直觉模糊近似空间中定义了区间值直觉模糊集的上近似和下近似;最后,给出并证明了这些近似算子的一些性质. 相似文献
14.
Discovering intelligent technical trading rules from nonlinear and complex stock market data, and then developing decision support trading systems, is an important challenge. The objective of this study is to develop an intelligent hybrid trading system for discovering technical trading rules using rough set analysis and a genetic algorithm (GA). In order to obtain better trading decisions, a novel rule discovery mechanism using a GA approach is proposed for solving optimization problems (i.e., data discretization and reducts) of rough set analysis when discovering technical trading rules for the futures market. Experiments are designed to test the proposed model against comparable approaches (i.e., random, correlation, and GA approaches). In addition, these comprehensive experiments cover most of the current trading system topics, including the use of a sliding window method (with or without validation dataset), the number of trading rules, and the size of training period. To evaluate an intelligent hybrid trading system, experiments were carried out on the historical data of the Korea Composite Stock Price Index 200 (KOSPI 200) futures market. In particular, trading performance is analyzed according to the number of sets of decision rules and the size of the training period for discovering trading rules for the testing period. The results show that the proposed model significantly outperforms the benchmark model in terms of the average return and as a risk-adjusted measure. 相似文献
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Rudiments of rough sets 总被引:17,自引:0,他引:17
Zdzis?aw Pawlak 《Information Sciences》2007,177(1):3-27
Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, knowledge discovery, decision analysis, and expert systems. In the article, we present the basic concepts of rough set theory and point out some rough set-based research directions and applications. 相似文献
17.
对目前常见的粗糙集属性约简算法进行了研究和总结,在此基础上,针对差别矩阵以及启发式约简算法提出了改进算法,减少算法在计算时所需的时间和空间复杂度,求取最小约简。将改进后的约简算法系统地应用到学生考试成绩分析中,对得到的规则进行科学地评价,找出影响学生成绩的潜在因素,并提出学习建议。通过实际应用表明了改进算法的有效性和可行性。 相似文献
18.
This paper presents a general framework for the study of relation-based (I,T)-intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. In the constructive approach, by employing an intuitionistic fuzzy implicator I and an intuitionistic fuzzy triangle norm T, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of (I,T)-intuitionistic fuzzy rough approximation operators are examined. The connections between special types of intuitionistic fuzzy relations and properties of intuitionistic fuzzy approximation operators are established. In the axiomatic approach, an operator-oriented characterization of (I,T)-intuitionistic fuzzy rough sets is proposed. Different axiom sets characterizing the essential properties of intuitionistic fuzzy approximation operators associated with various intuitionistic fuzzy relations are explored. 相似文献
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The further investigation of covering-based rough sets: Uncertainty characterization, similarity measure and generalized models 总被引:1,自引:0,他引:1
Zhanhong Shi 《Information Sciences》2010,180(19):3745-3763
The notion of rough sets was originally proposed by Pawlak. In Pawlak’s rough set theory, the equivalence relation or partition plays an important role. However, the equivalence relation or partition is restrictive for many applications because it can only deal with complete information systems. This limits the theory’s application to a certain extent. Therefore covering-based rough sets are derived by replacing the partitions of a universe with its coverings. This paper focuses on the further investigation of covering-based rough sets. Firstly, we discuss the uncertainty of covering in the covering approximation space, and show that it can be characterized by rough entropy and the granulation of covering. Secondly, since it is necessary to measure the similarity between covering rough sets in practical applications such as pattern recognition, image processing and fuzzy reasoning, we present an approach which measures these similarities using a triangular norm. We show that in a covering approximation space, a triangular norm can induce an inclusion degree, and that the similarity measure between covering rough sets can be given according to this triangular norm and inclusion degree. Thirdly, two generalized covering-based rough set models are proposed, and we employ practical examples to illustrate their applications. Finally, relationships between the proposed covering-based rough set models and the existing rough set models are also made. 相似文献