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Book ChapterDOI

Application of Functional Approach to Lists for Development of Relational Model Databases and Petri Net Analysis

01 Jan 2014-pp 407-444
TL;DR: In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations.
Abstract: The concept of list is very important in functional programming and data structures in computer science. The classical definition of lists was redefined by Jena, Tripathy, and Ghosh (2001) by using the notion of position functions, which is an extension of the concept of count function of multisets and of characteristic function of sets. Several concepts related to lists have been defined from this new angle and properties are proved further in subsequent articles. In this chapter, the authors focus on crisp lists and present all the concepts and properties developed so far. Recently, the functional approach to realization of relational databases and realization of operations on them has been proposed. In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations. The authors also develop a list theoretic relational algebra (LRA) and realize analysis of Petri nets using this LRA.
Citations
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Journal ArticleDOI
TL;DR: A novel defect prediction approach named GUHA based Classification Association Rule Mining algorithm G-CARM where "GUHA" stands for General Unary Hypothesis Automaton is proposed, and the experimental results indicate that the prediction performance of G- CARM approach is better than other prediction approaches.
Abstract: Software defect prediction, if is effective, enables the developers to distribute their testing efforts efficiently and let them focus on defect prone modules. It would be very resource consuming to test all the modules while the defect lies in fraction of modules. Information about fault-proneness of classes and methods can be used to develop new strategies which can help mitigate the overall development cost and increase the customer satisfaction. Several machine learning strategies have been used in recent past to identify defective modules. These models are built using publicly available historical software defect data sets. Most of the proposed techniques are not able to deal with the class imbalance problem efficiently. Therefore, it is necessary to develop a prediction model which consists of small simple and comprehensible rules. Considering these facts, in this paper, the authors propose a novel defect prediction approach named GUHA based Classification Association Rule Mining algorithm G-CARM where "GUHA" stands for General Unary Hypothesis Automaton. G-CARM approach is primarily based on Classification Association Rule Mining, and deploys a two stage process involving attribute discretization, and rule generation using GUHA. GUHA is oldest yet very powerful method of pattern mining. The basic idea of GUHA procedure is to mine the interesting attribute patterns that indicate defect proneness. The new method has been compared against five other models reported in recent literature viz. Naive Bayes, Support Vector Machine, RIPPER, J48 and Nearest Neighbour classifier by using several measures, including AUC and probability of detection. The experimental results indicate that the prediction performance of G-CARM approach is better than other prediction approaches. The authors' approach achieved 76% mean recall and 83% mean precision for defective modules and 93% mean recall and 83% mean precision for non-defective modules on CM1, KC1, KC2 and Eclipse data sets. Further defect rule generation process often generates a large number of rules which require considerable efforts while using these rules as a defect predictor, hence, a rule sub-set selection process is also proposed to select best set of rules according to the requirements. Evolution criteria for defect prediction like sensitivity, specificity, precision often compete against each other. It is therefore, important to use multi-objective optimization algorithms for selecting prediction rules. In this paper the authors report prediction rules that are Pareto efficient in the sense that no further improvements in the rule set is possible without sacrificing some performance criteria. Non-Dominated Sorting Genetic Algorithm has been used to find Pareto front and defect prediction rules.

5 citations

References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal ArticleDOI
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

Journal ArticleDOI
E. F. Codd1
TL;DR: In this article, a model based on n-ary relations, a normal form for data base relations, and the concept of a universal data sublanguage are introduced, and certain operations on relations are discussed and applied to the problems of redundancy and consistency in the user's model.
Abstract: Future users of large data banks must be protected from having to know how the data is organized in the machine (the internal representation). A prompting service which supplies such information is not a satisfactory solution. Activities of users at terminals and most application programs should remain unaffected when the internal representation of data is changed and even when some aspects of the external representation are changed. Changes in data representation will often be needed as a result of changes in query, update, and report traffic and natural growth in the types of stored information.Existing noninferential, formatted data systems provide users with tree-structured files or slightly more general network models of the data. In Section 1, inadequacies of these models are discussed. A model based on n-ary relations, a normal form for data base relations, and the concept of a universal data sublanguage are introduced. In Section 2, certain operations on relations (other than logical inference) are discussed and applied to the problems of redundancy and consistency in the user's model.

4,990 citations

Book
01 Jan 1989
TL;DR: Fundamentals of Database Systems combines clear explanations of theory and design, broad coverage of models and real systems, and excellent examples with up-to-date introductions to modern database technologies.
Abstract: From the Publisher: Fundamentals of Database Systems combines clear explanations of theory and design, broad coverage of models and real systems, and excellent examples with up-to-date introductions to modern database technologies. This edition is completely revised and updated, and reflects the latest trends in technological and application development. Professors Elmasri and Navathe focus on the relational model and include coverage of recent object-oriented developments. They also address advanced modeling and system enhancements in the areas of active databases, temporal and spatial databases, and multimedia information systems. This edition also surveys the latest application areas of data warehousing, data mining, web databases, digital libraries, GIS, and genome databases. New to the Third Edition Reorganized material on data modeling to clearly separate entity relationship modeling, extended entity relationship modeling, and object-oriented modeling Expanded coverage of the object-oriented and object/relational approach to data management, including ODMG and SQL3 Uses examples from real database systems including OracleTM and Microsoft AccessAE Includes discussion of decision support applications of data warehousing and data mining, as well as emerging technologies of web databases, multimedia, and mobile databases Covers advanced modeling in the areas of active, temporal, and spatial databases Provides coverage of issues of physical database tuning Discusses current database application areas of GIS, genome, and digital libraries

4,242 citations

Book
01 Jan 1981

3,509 citations