Comparison of Linguistic Summaries and Fuzzy Functional Dependencies Related to Data Mining

Abstract

Data mining methods based on fuzzy logic have been developed recently and have become an increasingly important research area. In this chapter, the authors examine possibilities for discovering potentially useful knowledge from relational database by integrating fuzzy functional dependencies and linguistic summaries. Both methods use fuzzy logic tools for data analysis, acquiring, and representation of expert knowledge. Fuzzy functional dependencies could detect whether dependency between two examined attributes in the whole database exists. If dependency exists only between parts of examined attributes' domains, fuzzy functional dependencies cannot detect its characters. Linguistic summaries are a convenient method for revealing this kind of dependency. Using fuzzy functional dependencies and linguistic summaries in a complementary way could mine valuable information from relational databases. Mining intensities of dependencies between database attributes could support decision making, reduce the number of attributes in databases, and estimate missing values. The proposed approach is evaluated with case studies using real data from the official statistics. Strengths and weaknesses of the described methods are discussed. At the end of the chapter, topics for further research activities are outlined.

Synergy of linguistic summaries and fuzzy functional dependencies for mining knowledge in the data

“…1a), or only in particular parts of their respective domains (Fig. 1b) [7]. If we detect an intensity of dependency which is not sufficiently strong (Fig.…”

“…In order to reveal relational knowledge by FFDs and LSs, the common preliminary step is the fuzzification of examined attributes' domains [7]. In order to obtain relevant results we should (i) create fuzzy sets by the uniform domain covering method [18]; (ii) apply the same fuzzy sets in FFDs and LSs.…”

“…for each pair of tuples t i and t j is calculated by [7]:  T r is a relation whose columns are conformances (1) and rows are couples of entitles t i and t j : …”

Linguistically summarizing hierarchical data: The case of statistical territorial data

“…where v is the validity of a summary (2), C is generality (coverage) measure (6), the operator and between a) and b) is expressed by the minimum t-norm. The closer O is to the value of 1, the more is LS judged as outlier.…”

“…Summarization can be realized on a whole database, on a part of database delimited by flexible boundaries, or on a hierarchical data [5,6]. A suitable example of hierarchical data is the structure of territorial units following the recommendation of Eurostat (Statistical Office of the European Communities) [14].…”