Skyline refinement exploiting fuzzy formal concept analysis

PurposeThe study of the skyline queries has received considerable attention from several database researchers since the end of 2000's. Skyline queries are an appropriate tool that can help users to make intelligent decisions in the presence of multidimensional data when different, and often contradictory criteria are to be taken into account. Based on the concept of Pareto dominance, the skyline process extracts the most interesting (not dominated in the sense of Pareto) objects from a set of data. Skyline computation methods often lead to a set with a large size which is less informative for the end users and not easy to be exploited. The purpose of this paper is to tackle this problem, known as the large size skyline problem, and propose a solution to deal with it by applying an appropriate refining process.Design/methodology/approachThe problem of the skyline refinement is formalized in the fuzzy formal concept analysis setting. Then, an ideal fuzzy formal concept is computed in the sense of some particular defined criteria. By leveraging the elements of this ideal concept, one can reduce the size of the computed Skyline.FindingsAn appropriate and rational solution is discussed for the problem of interest. Then, a tool, named SkyRef, is developed. Rich experiments are done using this tool on both synthetic and real datasets.Research limitations/implicationsThe authors have conducted experiments on synthetic and some real datasets to show the effectiveness of the proposed approaches. However, thorough experiments on large-scale real datasets are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.Practical implicationsThe tool developed SkyRef can have many domains applications that require decision-making, personalized recommendation and where the size of skyline has to be reduced. In particular, SkyRef can be used in several real-world applications such as economic, security, medicine and services.Social implicationsThis work can be expected in all domains that require decision-making like hotel finder, restaurant recommender, recruitment of candidates, etc.Originality/valueThis study mixes two research fields artificial intelligence (i.e. formal concept analysis) and databases (i.e. skyline queries). The key elements of the solution proposed for the skyline refinement problem are borrowed from the fuzzy formal concept analysis which makes it clearer and rational, semantically speaking. On the other hand, this study opens the door for using the formal concept analysis and its extensions in solving other issues related to skyline queries, such as relaxation.

Hesitant fuzzy graphs, hesitant fuzzy hypergraphs and fuzzy graph decisions1

Up to now, there have been a lot of research results about multi-attribute decision making problems by fuzzy graph theory. However, there are few investigations about multi-attribute decision making problems under the background of indecisiveness. The main reason is that the difference of cognition and the complexity of thinking by decision makers, for the same question have different opinions. In this paper, we proposed a hesitant fuzzy hypergraph model based on hesitant fuzzy sets and fuzzy hypergraphs. At the same time, some basic graph operations of hesitant fuzzy hypergraphs are investigated and several equivalence relationship between hesitant fuzzy hypergraphs, hesitant fuzzy formal concept analysis and hesitant fuzzy information systems are discussed. Since granular computing can deal with multi-attribute decision-making problems well, we considered the hesitant fuzzy hypergraph model of granular computing, and established an algorithm of multi-attribute decision-making problem based on hesitant fuzzy hypergraph model. Finally an example is given to illustrate the effectiveness of the algorithm.

Fuzzy Implication and Functional Dependency on Formal Context

Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.