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Multi-tier sustainable supply chain relationships (MSSCR) are complex with involvement of multiple organisations, practices, objectives, and interconnectivities. These complexities make it difficult to effectively study MSSCR using traditional empirical statistical correlative research. In MSSCR the relationship between the focal firm and sub-supplier may be affected by the relationship between the focal firm and direct-supplier, and the relationship between the direct-supplier and the sub-supplier. This paper introduces a research methodology, based on K-Means clustering, rough set theory, and cluster membership to investigate complex relationships across multi-tier sustainable supply chain triads. Collaborative advantage variables including knowledge-sharing routines, relation-specific investments, complementary capabilities, effective governance mechanisms, and long-term commitment are conceptually presented to evaluate relationships among MSSCR practices and sustainability performance. Insights for practitioners and researchers are provided. Research insights can be gained by analytically providing alternative explanatory and equifinality relationships amongst variables and multi-pair organisations. The methodology can mitigate the endogeneity problem, such as omitted factors (variables), measurement error, even in small sample data situations. Directions for future research are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a new uncertainty modelling concept called strait fuzzy set is introduced, which brings new perspectives to both theoretical and practical advances in fuzzy mathematics. This set type allows objects/points to be graded with fuzzy membership intervals that are partitions of [0,1] (so that the union of these partitions is [0,1] and their intersection is empty) instead of fuzzy membership degrees represented as exact values in [0,1]. Moreover, some basic operations and properties of strait fuzzy sets are studied in detail. The concept of strait fuzzy rough set is put forward and its theoretical aspects are discussed. In addition, two different similarity approaches are proposed for strait fuzzy sets and strait fuzzy rough sets, and applied to measure the similarity rates of vaccines against influenza viruses. [ABSTRACT FROM AUTHOR]

Lean manufacturing practices (LMPs) and corporate environmental sustainability are becoming inextricably linked. Throughout the lean and green debate, many organisations have recognised that LMPs have implications for their sustainable development and competitive positioning. Not only LMPs are complex on their own, but when perceived from an environmental sustainability perspective, the decision to implement an LMP can become even more intricate. Although general tools exist, the lack of effective decision-making tools to help in the implementation of LMPs with an environmental sustainability dimension is palpable. Thus, this study tackles the aforementioned decision problem by incorporating environmental and operational performance outcome expectations as these expectations are viewed in light of the ease of implementation of various LMPs. A novel multi-criteria decision-making (MCDM) model for evaluation of LMPs is developed in this respect. The model integrates a three-parameter interval grey number with rough set theory and the TODIM method. The model is run using empirical data from six manufacturing organisations. The findings facilitate the identification of a 'locus of investments' for a better selection of LMPs. The robustness of the decision support model developed is assessed through sensitivity analysis. [ABSTRACT FROM AUTHOR]

Being an agro-based natural product, cotton always poses vagueness in the parameters. Hence, formulation of decision rules for prediction of cotton yarn quality from the imprecise cotton fiber properties is an intricate problem. Yarn tenacity is considered an imperative quality parameter in the cotton textile industry. Modelling of yarn tenacity has remained as the cynosure of research for textile engineers. In recent years, rough set theory has evolved as one of the most important techniques used for handling imprecise data. One of the cardinal uses of rough set theory is its application to rule generation. Our approach focuses on the elimination of the redundant data set in order to generate effective decision rules which retain the accuracy of the original data set. In this work rough set theory is employed to generate decision rules to predict yarn tenacity from six input parameters. The validation results prove that the generated 45 decision rules accurately predicted 14 out of 16 unknown test data. Thus, in the present competitive market, this model is potent for getting recognition from the textile industry. [ABSTRACT FROM AUTHOR]

Being an agro based natural product, silk always poses vagueness in the parameters. Hence, formulation of decision rules for prediction of raw silk quality from the imprecise cocoon parameters is an intricate problem. Rough set theory has evolved as one of the most important technique used for handling imprecise data. One of the cardinal uses of rough set theory is its application for rule generation. More often attribute reduction poses a major challenge for the applications of rough set theory. Our approach focuses on the elimination of the redundant data set in order to generate the effective decision rule which retain the accuracy of the original data set. In this work rough set theory is employed to generate decision rules to predict renditta from five cocoon parameters such as shell ratio, defective cocoon percentage, cocoon volume, cocoon weight and filament length. [ABSTRACT FROM AUTHOR]

In this study, a computerized diagnosis system is developed using Rough set classifier from multi-lead ECG signal for detection as well as the classification of five different types of myocardial infarction (MI) disease. The pathological features of ECG such as Inverted T-wave, ST segment deviation, or pathological Q wave, which are seen during MI, are extracted. An Information table and the knowledgebase are expanded from these pathological features after getting feedback from the cardiologist as well as consulting different medical books. The Information table contains 36 features and 341objects which include normal and five types of MI such as Anterior (AN), Inferior (IN), Antero lateral (ANLA), Inferior lateral (INLA), and Antero septal (ANSE) are used for assessment. The proposed system determines the degree of attributes dependency and their significance to find a smaller set of attributes, called reduct, alike the original set to predict the appropriate decision rules for MI classification. The robustness is justified by the "five-fold cross" validation technique using RSES tools. Finally, the proposed classifier illustrates its outperformance over the existing approaches in terms of sensitivity (99.75%), and accuracy (99.8%) for MI detection and 99.8% accuracy for MI classification. [ABSTRACT FROM AUTHOR]

At present, manufacturers tend to bundle a product with its related services as a product service system, to meet customer needs and achieve competitive advantage. Configuring a product service system involves selecting and combining appropriate product and service components, to satisfy individual customer needs. One crucial step to rapidly configure a product service system is to develop formalised configuration rules, which show the relationships between product service components and customer needs, including those expressed as perception needs. In this study, a rough set-based approach is proposed to acquire configuration rules. First, an information table is built by combining the results of factor analysis and questionnaire survey. Then, customer segmentation is accomplished by clustering. Based on the information table and customer segmentation, a dominance-based rough set approach is used to extract the configuration rules. Finally, a weighbridge is selected for the case study to validate the proposed approach. [ABSTRACT FROM PUBLISHER]

Safety is of paramount importance in high-risk systems. Safe and reliable operation of a system depends mainly on its key component, 'the human'. Human error is pivotal in an accident sequence and the rate of error is instrumental in the analysis of accidents which focuses on the development of interventions. However, assessing the rate of human error is a big challenge. Human performance and the rate of error are governed by the context of work. This study discusses a fuzzy rule-based causal relational mapping approach to investigate the variability of the human error rate with context. Different contexts are mapped onto the human error rate estimated from the reported accident cases. This mapping develops a causal relational diagram which can be used for predicting the human error rate in any context. Such information is useful to identify problems of areas and to develop safety countermeasures. [ABSTRACT FROM AUTHOR]

By introducing the concepts of intuitionistic L-fuzzy β-covering and intuitionistic L-fuzzy β-neighborhood, we define three kinds of intuitionistic L-fuzzy β-covering rough set models. The basic properties of those intuitionistic L-fuzzy β-covering rough set models are investigated. Moreover, we define the other three kinds of intuitionistic L-fuzzy β-covering rough set models by using the former three models. Finally, we present the matrix representations of the newly defined lower and upper approximation operators so that the calculation of lower and upper approximations of subsets can be converted into operations on matrices. [ABSTRACT FROM AUTHOR]

This paper aims to originate two new notions that are soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set, and investigate some important properties of soft rough Pythagorean fuzzy set and Pythagorean fuzzy soft rough set in detail. Furthermore, classical representations of Pythagorean fuzzy soft rough approximation operators are presented. Then the proposed operators are applied on decision-making problem in which the experts provide their preferences in Pythagorean fuzzy soft rough environment. Finally through an illustrative example, it is shown that how the proposed operators work in decision-making problems. [ABSTRACT FROM AUTHOR]

The overlying rock thickness of a subsea tunnel controls its vertical line. It not only ensures the safety and stability of tunnel construction period and operation period, but also ensures the economy of subsea tunnel. In the current research, few papers give full consideration to the complex indicators of prediction the overlying rock thickness. However, in this study, a hybrid intelligent system was established to predict the overlying rock thickness of a subsea tunnel based on Qingdao Kiaochow Bay Subsea Tunnel, China. The sea depth, basic quality index of rock mass, soft soil layer thickness, permeability coefficient, and construction management level were selected as the main factors influencing the overlying rock thickness. Using the data obtained from project site exploration, objective weight factors were calculated using rough set theory, and subjective weight factors were calculated using the analytic hierarchy process. Furthermore, the combination of weights was obtained for each factor. Finally, the weight of influencing factors was incorporated into the extension model, and the overlying rock thickness of pending section was calculated. The results of overlying rock thickness prediction model are consistent with the actual value, indicating that the model has good engineering applicability and application value. [ABSTRACT FROM AUTHOR]

Configuration performance prediction (CPP) is critical in the whole process of configuration design for a modular product family. Its aim is to estimate the key performance parameter values in advance, thus evaluating if the product variant can satisfy the customers' personalised requirements or not. In this paper, we propose a novel prediction approach based on the integration of rough set and neural network ensemble through discovering the knowledge from the historical configuration information table. The minimal hitting set is introduced and its equivalence relationship with the minimal attribute reduction is proven. A genetic algorithm is designed to perform the approximate reduction of the condition attributes. A neural network ensemble model used for regression prediction is constituted by means of the variant bagging method based on error clustering. This methodology can reuse the discovered configuration rules and knowledge efficiently, as well as reduce the effort of experimental measurement to some extent. Finally, the applicability of this prediction method is verified on a newly developed refrigerator family. [ABSTRACT FROM AUTHOR]

As the first phase of quality function deployment (QFD) and the only interface between the customers and product development team, house of quality (HOQ) plays the most important role in developing quality products that are able to satisfy customer needs. No matter in what shape or form HOQ can be built, the key to this process is to find out the hidden relationship between customers' requirements and product design specifications. This paper presents a general rough set based data mining approach for HOQ analysis. It utilises the historical information of customer needs and the design specifications of the product that was purchased, employs the basic rough set notions to reveal the interrelationships between customer needs and design specifications automatically. Due to the data reduction nature of the approach, a minimal set of customer needs that are crucial for the decision on the correlated design specifications is derived. The end result of the approach is in the form of a minimal rule set, which not only fulfils the goal of HOQ, but can be used as supporting data for marketing purposes. A case study on the product of electrically powered bicycles is included to illustrate the approach and its efficiency. [ABSTRACT FROM AUTHOR]

Product configuration design is of critical importance in design for mass customization. This paper will investigate two important issues in configuration design. The first issue is requirement configuration and a dependency analysis approach is proposed and implemented to link customer groups with clusters of product specifications. The second issue concerns the engineering configuration and it is modelled as an association relation between clusters of product specifications and configuration alternatives. A novel methodology and architecture are proposed for accomplishing the two configuration tasks and bridging the gap between them. This methodology is based on integration of popular data mining approaches (such as fuzzy clustering and association rule mining) and variable precision rough set. It focuses on the discovery of configuration rules from the purchased products according to customer groups. The proposed methodology is illustrated with a case study of an electrical bicycle. [ABSTRACT FROM AUTHOR]

This paper introduces an algorithm for researching the achievement stability set for parametric rough linear goal programming (PRLGP) issues with parameters in the achievement function and roughness in goal and system constraints. The proposed goal programing model has two types of uncertainty. We transform the PRLGP into an upper approximation model and a lower approximation model. Then, the Lexicographical goal programing method is utilized to solve such upper and lower approximation models iteratively to avoid the complexity of the attainment issue. This model has been applied as it enables the decision-maker to articulate the weights for goals however, for the sub-goals it shall be complicated as they possess the same measure. Finally, to clarify how to investigate the achievement stability set for the PRLGP, an algorithm and a numerical illustration was given. [ABSTRACT FROM AUTHOR]

Agriculture plays a vital role in Indian economy. On considering the overall geographical space verses population in India, 7% of population is chronicled in Tamilnadu, with 3% of water and 4% of land resources. Thus an automated prediction system becomes essential for predicting the crop based on the nutritional security of the country. In this paper, effort has been made to process the uncertainties by hybridizing rough set on intuitionistic fuzzy approximation space (RSIFAS) [Acharjya DP, Tripathy BK. Rough sets on intuitionistic fuzzy approximation spaces and knowledge representation. Int J Artif Int Comput Res. 2009;1 (1):29–36.] and neural network [Hecht NR. Theory of the backpropagation neural network. Proceedings of the international Joint Conference on neural networks, 1 (1989), 593–605.]. RSIFAS identifies the almost indiscernibility among the natural resources, and helps in reducing the computational procedure on employing data reduction techniques whereas neural network helps in prediction process. It helps to find the crops that may be cultivated based on the available natural resources. The proposed model is analyzed on data accumulated from Vellore district of Tamilnadu, India and achieved 93.7% of average classification accuracy. The model is compared with earlier models and found 6.9% better accuracy while prediction. [ABSTRACT FROM AUTHOR]

To extend the utilisation and flexibility of rough set extension on universes, we modify rough set over dual-universes model by comparing rough set extension on universes based on compatibility relation and rough set over dual-universes in the aspect of theories and applications. Instance in daily life is advanced to indicate shortcomings of rough set extension on universes based on compatibility relation and rough set over dual-universes. The similarities and differences between rough set over dual-universes and rough set extension models on universes based on compatibility relation are analysed from the view of approximation operators. New lower and upper approximations of rough set over dual-universes are designed by introducing setvalued map. An improved rough set model is constructed. The conclusion is that rough set over dual-universes in this article has a standard description and could solve practical problems well compared with rough set extension models on universes based on compatibility relation. [ABSTRACT FROM AUTHOR]

Nowadays, supplier selection process, a multicriteria decisionmaking problem, has become one of the most indispensable parts for every purchasing sector for the improvement of performances of business operations. Most of the literatures in this field have considered only the opinion of decision-makers. But in fact, each company has its own opinion about the suppliers. The purpose of this paper is to select the best supplier by integrating the opinions of both decision- makers and company's stake holders. In this literature, these opinions are taken as fuzzy soft sets. These two fuzzy soft sets are then integrated by the rough approximation theory. The attributes in this literature are taken in the form of linguistic variable. At the end of this paper, a case study is given to illustrate the proposed method for selecting the best supplier. [ABSTRACT FROM AUTHOR]

The rough sets based onL-fuzzy relations andL-fuzzy coverings are the two most well-knownL-fuzzy rough sets. Quite recently, we prove that some of these rough sets can be unified into one framework—rough sets based onL-generalized fuzzy neighborhood systems. So, the study on the rough sets based onL-generalized fuzzy neighborhood system has more general significance. Axiomatic characterization is the foundation ofL-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence ofL-fuzzy relations,L-fuzzy coverings that reproduce the approximation operators. In this paper, we shall give an axiomatic study onL-generalized fuzzy neighborhood system-based approximation operators. In particular, we will seek the axiomatic sets to characterize the approximation operators generated by serial, reflexive, unary and transitiveL-generalized fuzzy neighborhood systems, respectively. [ABSTRACT FROM PUBLISHER]

Various scientific studies have explored the causes of violent behaviour from different perspectives, with psychological tests, in particular, applied to the analysis of crime factors. The relationship between bi-factors has also been extensively studied including the link between age and crime. In reality, many factors interact to contribute to criminal behaviour and as such there is a need to have a greater level of insight into its complex nature. In this article we analyse violent crime information systems containing data on psychological, environmental and genetic factors. Our approach combines elements of rough set theory with fuzzy logic and particle swarm optimisation to yield an algorithm and methodology that can effectively extract multi-knowledge from information systems. The experimental results show that our approach outperforms alternative genetic algorithm and dynamic reduct-based techniques for reduct identification and has the added advantage of identifying multiple reducts and hence multi-knowledge (rules). Identified rules are consistent with classical statistical analysis of violent crime data and also reveal new insights into the interaction between several factors. As such, the results are helpful in improving our understanding of the factors contributing to violent crime and in highlighting the existence of hidden and intangible relationships between crime factors. [ABSTRACT FROM PUBLISHER]

To build a traffic safety feature model and to quantify accident influences caused by some traffic violation behaviors of drivers, an accident diagnostic decision-making model is established. For the purpose of diagnosing accident morphologies, rough set theory is applied and the influence of traffic factors of different accident morphologies is quantified through calculating the degree of attribute importance, selecting core traffic factors and adopting a C4.5 decision tree algorithm. In the paper, road traffic accident data from 2008 to 2013 in Anhui Province are used. Typical rules are selected, targeted strategy proposals are put forward, and then, a scientific and reasonable diagnostic basis is provided for the diagnosis of traffic safety risks and the prediction of potential traffic accidents. [ABSTRACT FROM AUTHOR]

This study differs from previous studies by applying multivariate statistical analysis and multi-criterion decision-making methods to the improvement of service quality. We use the rough set theory (RST) with a flow graph approach to determine customer attitudes regarding service quality, which can assist managers in developing strategies to improve service quality and thus satisfy the needs of customers. A set of rules is derived from a large sample of airline customers, and its predictive ability is evaluated. The flow graph and the cause-and-effect relationship of the decision rules are heavily exploited in service quality characteristics. As compared with the results of other data-mining analyses, our results are encouraging. This study demonstrates that the combination of the RST model and flow graphs assists in identifying the needs of customers, determining their characteristics, and facilitating the development of an improvement strategy. [ABSTRACT FROM PUBLISHER]

Information system homomorphisms have made a substantial contribution to attribute reduction of covering information systems. However, the efforts made on homomorphisms are far from sufficient. This paper further studies homomorphisms for attribute reduction of dynamic fuzzy covering information systems. First, the concepts of neighbourhood and induced fuzzy covering are proposed and their properties are discussed in detail. Then, we introduce the concepts of consistent functions and fuzzy covering mappings providing a basic theoretical foundation for compressing fuzzy covering information systems. Afterwards, the notion of homomorphisms is presented to reveal the relationship between fuzzy covering information systems. We show how large-scale fuzzy covering information systems and dynamic fuzzy covering information systems can be compressed into smaller ones by means of homomorphisms. Finally, illustrative examples are employed to show that attribute reduction can be simplified significantly by our proposed approach. [ABSTRACT FROM PUBLISHER]

The basic motivation of the theory of textures is to find a convenient point-set based setting for fuzzy sets. Recent works on textures show that they also provide a useful model for rough set theory. In this paper, we show that i-c spaces (interior-closure texture spaces) can be regarded as a textural rough set systems on a single universe. Then we consider the approaches containing direlations and dicovers for textural rough sets and we give some basic results related to direlations and dicovers. Considering the discrete textures we discuss on these results for rough sets based on relations and coverings. Finally, we prove that the category of topological spaces and continuous functions is isomorphic to the category of (covering) approximation spaces and continuous functions. [ABSTRACT FROM PUBLISHER]

This paper proposes an algorithm based on rough set (RS) framework for automated discovery of censored production rules with provided operator. These censored production rules are created by augmenting ordinary production rules with rare or particular conditions employing unless operator or provided operator, respectively. Systems which use censored production rules are free to ignore the censor conditions when the resources are limited. Censor conditions can be examined later leading to more specific and accurate rules if the time permits or resources are at hand. Integration of the RS theory with censored production rules allows for handling of vague and imprecise information in a limited resource environment. The proposed algorithm generates a separate list of rules for the lower and upper approximation of the concept. The rule belonging to lower approximation is a certain rule, and the rule belonging to upper approximation is a possible rule, which can be further investigated using the censor conditions. We extend the basic notion of production rules using thecensor conditionwithprovidedoperator to find out the certain rules in the given data-set. We have investigated our algorithm on the benchmark data-sets from the UCI machine learning repository, which have shown promising results. [ABSTRACT FROM PUBLISHER]

The classical rough set theory has been extended to fuzzy data environments by many authors, resulting in the development of the fuzzy rough set. Recently, vague set is treated as an extension of fuzzy set, but the existing theories and approaches of fuzzy rough set could not be applied directly to data set represented by vague set. In this article, we attempt to establish a theoretical model for vague data by combing both rough set and vague set. We first introduced the basic notions of vaguet-norms andt-conorms. Next, we developed a general vague rough approximation set for generalizing to fuzzy rough set. Then, to overcome the inconvenience of dealing vague data, we also introduced a model for transforming a vague set into a fuzzy set to take the place of an interval vague set. Moreover, we also give some perspectives for future research. [ABSTRACT FROM PUBLISHER]

Training data play an important role in the supervised classification process of remotely sensed images. Its quality is an important factor affecting the accuracy of image classification. Therefore, measuring the quality of training data is essential for classification procedures and subsequent operations. This paper discusses a new method for the quality assessment of training data before the classification procedure and investigates the correlation between measures for training data and measures for classified images at category and image level, respectively. Five groups of sample data collected from a Landsat TM image were used in correlation analyses. The results demonstrate that the proposed method is valid for measuring the quality of training data and can, to some extent, reflect the quality of classified images which are obtained through supervised classification with the corresponding training dataset. [ABSTRACT FROM AUTHOR]

Rule based reasoning (RBR) embodied in cam grinding will extend the application of knowledge-based system by utilizing previous knowledge and experience. However, it is very difficult to make rules without exact exceptions. Knowledge acquisition also is a bottleneck problem. Additionally, traditional methods of induction learning from previous experiences limit the development of RBR methodology. This article presents a novel methodology to apply Rough Set (RS) algorithm in rule induction and rule base establishing for RBR system. The RS-RBR system is used in cubic boron nitride (CBN) grinding wheel dressing for cam numerical control (NC) grinding. In the system, the RS is used to process the rule extraction; the RBR is used to assess the dressing parameters. A series of experiments have been accomplished by CNC8312A NC camshaft grinder. Finally, a case study is also implemented to prove the proposed method. [ABSTRACT FROM AUTHOR]

With granular computing point of view, the classical dominance-based rough set model is based on a single granulation. For an ordered information system, this paper proposes two new types of multiple granulation rough set (MGRS) models, where a target concept is approximated from different kinds of views by using dominant classes induced by multiple granulations. And a number of important properties of the two types of MGRS are investigated in an ordered information system. From the properties, it can be found that Greco's rough set model is a special instance compared to our MGRS model. Moreover, the relationships and differences are discussed carefully among Greco's rough set and two new types of MGRS. Furthermore, several important measures are presented in two types of MGRS models, such as rough measure, quality of approximation in an ordered information system. In order to illustrate our MGRS models in an ordered information system, a real life example is considered, which is helpful for applying this theory in practical issues. One can see get that the research is meaningful in applications for the issue of knowledge reduction in complex ordered information systems. [ABSTRACT FROM PUBLISHER]

In order to study the communication between information systems, Gong and Xiao (2010, International journal of general systems, 39, 189–206) proposed the concept of general relation mappings based on including degrees. Some properties and the extension for fuzzy information systems of the general relation mappings have been investigated there. In this paper, we point out by counterexamples that several assertions (Lemmas 3.1 and 3.2, Theorems 4.1 and 4.3) in the aforementioned work are not true in general. [ABSTRACT FROM AUTHOR]

In recent years, the rough set (RS) method has been in common use for remote-sensing classification, which provides one of the techniques of information extraction for Digital Earth. The discretization of remotely sensed data is an important data preprocessing approach in classical RS-based remote-sensing classification. Appropriate discretization methods can improve the adaptability of the classification rules and increase the accuracy of the remote-sensing classification. To assess the performance of discretization methods this article adopts three indicators, which are the compression capability indicator (CCI), consistency indicator (CI), and number of the cut points (NCP). An appropriate discretization method for the RS-based classification of a given remotely sensed image can be found by comparing the values of the three indicators and the classification accuracies of the discretized remotely sensed images obtained with the different discretization methods. To investigate the effectiveness of our method, this article applies three discretization methods of the Entropy/MDL, Naive, and SemiNaive to a TM image and three indicators for these discretization methods are then calculated. After comparing the three indicators and the classification accuracies of the discretized remotely sensed images, it has been found that the SemiNaive method significantly reduces large quantities of data and also keeps satisfactory classification accuracy. [ABSTRACT FROM AUTHOR]

The study of intrusion detection techniques has been one of the hot spot topics in the field of network security in recent years. For high-dimensional intrusion detection data sets and a single classifier's weak classification ability for data sets with many classes, a novel intrusion detection approach, termed intrusion detection based on multiple rough classifiers integration, is proposed. First, some training data sets are generated from intrusion detection data by random sampling. By combing rough sets and quantum genetic algorithm, a subset of attributes is selected. Then, each simplified data set is trained, which establishes a group of rough classifiers. Finally, the intrusion data classification result is obtained according to the absolute majority voting strategy. The experimental results illustrate the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341-356.) to a basic area of decision theory, namely 'mathematical programming'. This new framework concerns mathematical programming in a rough environment and is called 'rough programming' (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019-1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts. [ABSTRACT FROM AUTHOR]

Since the definition of attribute reduction based on classic discernibility matrix differs from that of it based on positive region, a new simplified discernibility matrix and the corresponding definition of attribute reduction were proposed. At the same time, it proves that the proposed definition is identical to its definition based on positive region. For computing simplified discernibility matrix, the indiscernibility relation, which is also called equivalence relation, should usually be calculated at first, so a new algorithm for computing equivalence relation was designed with radix sorting, whose temporal complexity is O(| C|| U|). Furthermore, an efficient attribute reduction algorithm is proposed, whose temporal complexity and spatial complexity are cut down to max( O(| C|| U′|| U′|, O(| U|| C|)) and max( O(| C|| U′|| U′|, O(| U|)) respectively. At last, an example is used to illustrate efficiency of the new algorithms. [ABSTRACT FROM AUTHOR]

This article uses rough set theory to explore spatial decision rules in neural-tube birth defects and searches for novel spatial factors related to the disease. The whole rule induction process includes data transformation, searching for attribute reducts, rule generation, prediction or classification, and accuracy assessment. We use Heshun as an example, where neural-tube birth defects are prevalent, to validate the approach. About 50% of the villages in Heshun are used as the sample data, from which all of the rules are extracted. Meanwhile, the other villages are used as reference data. The rules extracted from the training data are then applied to the reference data. The result shows that the rules' generalization is reasonably good. Moreover, a novel relationship between the spatial attributes and the neural-tube birth defects was discovered. That is, the villages that lie in Watershed 9 of this district and that are also associated with a gradient of between 16° and 25° are vulnerable to neural-tube birth defects. This result paves the road for predicting where high rates of neural-tube birth defects will occur and can be used as a preliminary step in finding a direct cause for the disease. [ABSTRACT FROM AUTHOR]

Communication between information systems is a basic problem in granular computing. In current research, a homomorphism mapping between information systems is required. In this paper, the concept of the general relation mapping between two universes is proposed in order to construct the equivalence relation on one universe according to the given equivalence relation on the other universe based on the including degrees. The main properties of the mapping are studied, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the given conditions. Finally, we also define the concept of fuzzy general relation mapping between two fuzzy information systems and give some properties. [ABSTRACT FROM AUTHOR]

An intelligent fault diagnostic method was presented to satisfy the development requirements of next-generation intelligent NC machine tools. The framework of fault diagnosis unit was established first, which consisted of signal acquisition, diagnosis rule extraction and fault identification mechanism. The technique of diagnosis rule extraction was then studied and an algorithm for acquisition of decision rules was proposed. The algorithm simplified the analysis of core properties and unnecessary properties, and calculated reduction set by the backwards tracking approach. This algorithm reduced complexity in reductions calculation and improved the efficiency of rule extraction. Finally, to process failure data collected by various sensors, a fault identification mechanism using evidence theory was presented. Feasibility and practicability of the proposed method has been verified by the development and the preliminary application of a prototype system. [ABSTRACT FROM AUTHOR]

A rough posynomial geometric programming is put forward by the author. This model is advantageous for us to consider questions not only from the quantity of aspect, but from the quality because it contains more information than a traditional geometric programming one. Here, a rough convex function concept is advanced in rough value sets on foundation of rough sets and rough convex sets. Besides, a knowledge expression model in rough posynomial geometric programming is established and so is a mathematical one. Thirdly, solution properties are studied in mathematical model of rough posynomial geometric programming, and antinomy of the more-for-less paradox is solved with an arithmetic in rough posynomial geometric programming given, which can be changed into a rough linear programming after monomial rough posynomial geometric programming is solved. Finally, validity in model and algorithm is verified by examples. [ABSTRACT FROM AUTHOR]

This article proposes a rough-set-based approach to early analysis of design concepts. The approach aims at providing a metrics to facilitate the evaluation of design concepts and enable early detection of inadequacy in design. Based on the rough set theory, an information system can be constructed using information such as design concepts and product capabilities gleaned from past designs. This information is then used to derive a set of design rules for the analysis of new design concepts. The proposed approach embodies a novel technique for the handling of unavailable information, which is a frequent occurrence in product design. It is augmented with a mechanism for incremental updating of design rules. The details of the approach, the mechanism for incremental updating of design rules and two case studies are presented in this article. [ABSTRACT FROM AUTHOR]

Transformation Induced Plasticity (TRIP) gives birth to new generation steels with high strength and good ductility. Both these properties of steel depend on a number of compositional and processing parameters, but till date there exist certain gaps in the understanding of the complex role of each parameters on the microstructure and thus the properties of the steel. Rough Set Theory is employed to derive decision rules that attempt to explain this complex behavior. Applying efficient heuristics, the number of attributes are reduced to form a minimal reduct, and their values are at the same time discretized into linguistic intervals. The derived rules could clearly indicate on the relative importance of the compositional and processing variables. [ABSTRACT FROM AUTHOR]

This paper presents a framework for the study of generalizing the standard notion of rough set approximation space. We propose new definitions of lower and upper approximations, which are basic concepts of the rough set theory. These definitions follow naturally from a particular property on the universe and are called general lower and upper approximations. Properties of general approximations are investigated, and their connections are examined. [ABSTRACT FROM AUTHOR]

In the supervised classification process of remotely sensed imagery, the quantity of samples is one of the important factors affecting the accuracy of the image classification as well as the keys used to evaluate the image classification. In general, the samples are acquired on the basis of prior knowledge, experience and higher resolution images. With the same size of samples and the same sampling model, several sets of training sample data can be obtained. In such sets, which set reflects perfect spectral characteristics and ensure the accuracy of the classification can be known only after the accuracy of the classification has been assessed. So, before classification, it would be a meaningful research to measure and assess the quality of samples for guiding and optimizing the consequent classification process. Then, based on the rough set, a new measuring index for the sample quality is proposed. The experiment data is the Landsat TM imagery of the Chinese Yellow River Delta on August 8th, 1999. The experiment compares the Bhattacharrya distance matrices and purity index Δ and Δ X based on rough set theory of 5 sample data and also analyzes its effect on sample quality. [ABSTRACT FROM AUTHOR]

Applying competency models to identify and develop capabilities of civil servants is now a leading strategy for every government. However, an ideal competency model usually contains too many intended competencies, impeding implementation. Recently, some scholars and experts argued that there is a maximum of eight competencies for effective assessment. Hence, how to simplify a set of competencies becomes an important issue. This study is presented as a test case to extend practical applications of rough set theory (RST) in the human resource field of Government. A well-known data mining technique, RST is a relatively new approach to this problem and is good at data reduction in qualitative analysis. Hence, the rough set approach is suitable for dealing with the qualitative problem in simplifying a set of competencies. This paper slimmed a set of competencies using RST, thus helping the Taiwan Government to better understand the perceived competency levels of its civil servants. Using the rough set analysis, this paper successfully reduced the numerous essential competencies into a more compact set, by omitting low-consensus competencies. [ABSTRACT FROM AUTHOR]

In this paper a segmentation algorithm for cucumber images is presented to solve the problems of target identification and position for a greenhouse cucumber-harvesting robot. A method of combining the three basic colours, branch-quantity and threshold processing is used to enhance the target images, increasing the contrast between background and target and reducing the information content of the colour image. The strengthened image is considered as a knowledge system. The cucumber images are then segmented by a classification decision table which is based on a knowledge-reduction algorithm from rough set theory, choosing the image colour attribute as a condition attribute and standard colour as a decision attribute. The image noise is removed using an expansion algorithm of mathematical morphology. The experimental results show that the proposed algorithm can enhance the image of greenhouse cucumbers and segment the profile of the cucumber image effectively. There is less noise in the image after segmentation. [ABSTRACT FROM AUTHOR]

This paper extends Pawlak's rough set onto the basis of a fuzzy partition of the universe of discourse. Some basic properties of partition-based fuzzy approximation operators are examined. To measure uncertainty in generalized fuzzy rough sets, a new notion of entropy of a fuzzy set is introduced. The notion is demonstrated to be adequate for measuring the fuzziness of a fuzzy event. The entropy of a fuzzy partition and conditional entropy are also proposed. These kinds of entropy satisfy some basic properties similar to those of Shannon's entropy. It is proved that the measure of fuzziness of a partition-based fuzzy rough set, FR( A ), is equal to zero if and only if the set A is crisp and definable. [ABSTRACT FROM AUTHOR]

This paper focuses on rough set models on two universes and reveals some new properties. A revised rough set model is proposed which provides a new selection of interval structures for uncertain reasoning using rough set theory and methods. [ABSTRACT FROM AUTHOR]

Rough set is a new approach to uncertainties in spatial analysis. In this paper, rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication. Rough spatial entities and their topological relationships are also proposed in rough space, thus a universal intersected equation is developed, and rough membership function is further extended with the gray scale in our case study. We complete three works. First, a set of simplified rough symbols is advanced on the basis of existing rough symbols. Second, rough spatial entity is put forward to study the real world as it is, without forcing uncertainties into crisp set. Third, rough spatial topological relationships are studied by using rough matrix and their figures. The relationships are divided into three types, crisp entity and crisp entity (CC), rough entity and crisp entity (RC), and rough entity and rough entity (RR). A universal intersected equation is further proposed. Finally, the maximum and minimum maps of river thematic classification are generated via rough membership function and rough relationships in our case study. [ABSTRACT FROM AUTHOR]

Rough set theory (RS), introduced by Zdzislaw Pawlak in the early 1980s, is a methodology that concerned with the classificatory analysis of imprecise, uncertain or incomplete information or knowledge expressed in terms of data acquired from experiences or observations. It has the ability to distinguish between object and reason about the objects in the universe in which objects are perceived through the information that is available about them through the values for a predetermined set of attribute. The main advantage of RS is that it requires no additional information to the data represented in table. On the other hand, Supervised Neural Network learns by abstracting a mapping function from the training data for classification purposes. However the drawback of using a supervised neural network is that a large amount of training data must be provided for it to obtain an accurate mapping function. The problem is further aggravated if the data are in the continuous form (real values). Thus, in this paper we overcome the problem by transforming the training data in the continuous form into discrete values using Rough Sets theory and Boolean Reasoning technique. Here, global shape features are chosen to represent the logo images. The invariant features representing logo images are obtained by using the Geometric Invariant Moment Technique (Hu, 1962). The classification results prove that discretization using Rough Sets and Boolean Reasoning can reduce the training cycle and significantly increase the accuracy of the classification of logo images. [ABSTRACT FROM AUTHOR]

A fundamental problem in data mining is whether the whole information available is always necessary to represent the information system (IS). Reduct is a rough set approach in data mining that determines the set of important attributes to represent the IS. The search for minimal reduct is based on the assumption that within the dataset in an IS, there are attributes that are more important than the rest. An algorithm in finding minimal reducts based on Propositional Satisfiability (SAT) algorithm is proposed. A branch and bound algorithm is presented to solve the proposed SAT problem. The experimental result shows that the proposed algorithm has significantly reduced the number of rules generated from the obtained reducts with high percentage of classification accuracy. [ABSTRACT FROM AUTHOR]

Land resources are facing crises of being misused, especially for an intersection area between town and country, and land control has to be enforced. This paper presents a development of data mining method for land control. A vector-match method for the prerequisite of data mining i. e., data cleaning is proposed, which deals with both character and numeric data via vectorizing character-string and matching number. A minimal decision algorithm of rough set is used to discover the knowledge hidden in the data warehouse. In order to monitor land use dynamically and accurately, it is suggested to set up a real-time land control system based on GPS, digital photogrammetry and online data mining. Finally, the means is applied in the intersection area between town and country of Wuhan city, and a set of knowledge about land control is discovered. [ABSTRACT FROM AUTHOR]