Fuzzy Sets in Information Retrieval and Cluster Analysis

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 Fuzzy Relational 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.