Fundamenta Informaticae - Volume 157, issue 3

Authors: Grahne, Gösta | Onet, Adrian

Article Type: Research Article

Abstract: A lot of research activity has recently taken place around the chase procedure, due to its usefulness in data integration, data exchange, query optimization, peer data exchange and data correspondence, to mention a few. As the chase has been investigated and further developed by a number of research groups and authors, many variants of the chase have emerged and associated results obtained. Due to the heterogeneous nature of the area it is frequently difficult to verify the scope of each result. In this paper we take closer look at recent developments, and provide additional results. Our analysis allows us create …a taxonomy of the chase variations and the properties they satisfy. Two of the most central problems regarding the chase is termination, and discovery of restricted classes of sets of dependencies that guarantee termination of the chase. The search for the restricted classes has been motivated by a fairly recent result that shows that it is undecidable (RE-complete, to be more precise) to determine whether the chase with a given dependency set will terminate on a given instance. There is a small dissonance here, since the quest has been for classes of sets of dependencies guaranteeing termination of the chase on all instances, even though the latter problem was not known to be undecidable. We resolve the dissonance in this paper by showing that determining whether the chase with a given set of dependencies terminates on all instances is unsolvable, and on level ∏ 2 0 in the Arithmetical Hierarchy. For this we use a reduction from word rewriting systems, thereby also showing the close connection between the chase and word rewriting. The same reduction also gives us the aforementioned instance-dependent RE-completeness result as a byproduct. For one of the restricted classes guaranteeing termination on all instances, the stratified sets dependencies, we provide new complexity results for the problem of testing whether a given set of dependencies belongs to it. These results rectify some previous claims that have occurred in the literature. Show more

Keywords: Chase, Date Exchange, Data Repair, Incomplete databases, Undecidability Complexity

DOI: 10.3233/FI-2018-1627

Citation: Fundamenta Informaticae, vol. 157, no. 3, pp. 221-270, 2018

Authors: Wei, Guiwu

Article Type: Research Article

Abstract: In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic, geometric aggregation operators and Hamacher operations with picture fuzzy information. Then, motivated by the ideal of traditional arithmetic, geometric aggregation operators and Hamacher operations, we have developed some aggregation operators for aggregating picture fuzzy information: picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, picture fuzzy Hamacher correlated aggregation operators, induced picture fuzzy Hamacher aggregation operators, induced picture fuzzy Hamacher correlated aggregation operators, picture fuzzy Hamacher prioritized aggregation operators, picture fuzzy Hamacher power aggregation operators. Then, we have utilized these operators to …develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness. Show more

Keywords: multiple attribute decision making, picture fuzzy set, picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, prioritized aggregation, power aggregation

DOI: 10.3233/FI-2018-1628

Citation: Fundamenta Informaticae, vol. 157, no. 3, pp. 271-320, 2018