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Full Description
The present monograph intends to establish a solid link among three fields: fuzzy set theory, information retrieval, and cluster analysis. Fuzzy set theory supplies new concepts and methods for the other two fields, and provides a common frame work within which they can be reorganized. Four principal groups of readers are assumed: researchers or students who are interested in (a) application of fuzzy sets, (b) theory of information retrieval or bibliographic databases, (c) hierarchical clustering, and (d) application of methods in systems science. Readers in group (a) may notice that the fuzzy set theory used here is very simple, since only finite sets are dealt with. This simplification enables the max min algebra to deal with fuzzy relations and matrices as equivalent entities. Fuzzy graphs are also used for describing theoretical properties of fuzzy relations. This assumption of finite sets is sufficient for applying fuzzy sets to information retrieval and cluster analysis. This means that little theory, beyond the basic theory of fuzzy sets, is required. Although readers in group (b) with little background in the theory of fuzzy sets may have difficulty with a few sections, they will also find enough in this monograph to support an intuitive grasp of this new concept of fuzzy information retrieval. Chapter 4 provides fuzzy retrieval without the use of mathematical symbols. Also, fuzzy graphs will serve as an aid to the intuitive understanding of fuzzy relations.
Contents
1 Introduction.- 1.1 The Subject.- 1.2 Information Retrieval.- 1.3 Hierarchical Cluster Analysis.- 1.4 A Pragmatic Approach.- 1.5 Principles of Mathematical Models.- 1.6 Outline of the Contents.- 2 Fuzzy Sets.- 2.1 Crisp Sets and Fuzzy Sets.- 2.2 Set Operations.- 2.3 Basic Properties of Fuzzy Sets.- 2.4 Image of a Fuzzy Set, Convexity.- 2.5 Measures on Fuzzy Sets.- 2.6 Fuzzy Relations.- 2.7 Crisp Graphs.- 2.8 Fuzzy Graphs.- 2.9 A Max-Min Algebra and Fuzzy Graphs.- 3 Review of Information Retrieval.- 3.1 Introduction.- 3.2 A Crisp System for Information Retrieval.- 3.3 Measures for Evaluation of Information Retrieval Effectiveness.- 3.4 Associative Indices for Information Retrieval.- 3.5 The Citation Index.- 3.6 Weighted Retrieval and a Diagram for Information Retrieval.- 4 Introduction to Fuzzy Information Retrieval.- 4.1 A Simple Type of Fuzzy Information Retrieval.- 4.2 A Typology of Fuzzy Retrieval.- 5 Information Retrieval through Fuzzy Associations.- 5.1 A Mathematical Model for Fuzzy Thesauri.- 5.2 Fuzzy Associations.- 5.3 Information Retrieval Through Fuzzy Associations.- 6 Hierarchical Cluster Analysis and Fuzzy Sets.- 6.1 Introduction to Cluster Analysis.- 6.2 Measures of Similarity and Distance.- 6.3 Algorithms for Hierarchical Clustering.- 6.4 Single Linkage and Fuzzy Graph.- 6.5 Dendrogram and Tree Traversal.- 6.6 Reversal in a Dendrogram.- 6.7 A Class of New Methods.- 6.8 Application to Document Clustering.- 7 Feedback in Information Retrieval and Search for Clusters.- 7.1 Retrieval Through Clusters.- 7.2 Block Diagrams and Max-Min Algebra.- 7.3 Feedback in Block Diagrams.- 8 Other Methods in Fuzzy Information Retrieval and Related Topics.- 8.1 Other Methods in Fuzzy Information Retrieval.- 8.2 Evaluation Measures in Fuzzy Information Retrieval.- 8.3 FuzzyRelational Database.- 8.4 A Brief Review for Studies in Fuzzy Information Retrieval.- 8.5 Development of a Fuzzy Retrieval System.- 8.6 Graphical Representations of Bibliographic Structure.- 9 Discussion and Suggestions for Further Studies.- References.
