Modelling and Reasoning with Vague Concepts

List of FiguresPreface AcknowledgmentsForeword1: Introduction2: Vague Concepts And Fuzzy Sets 2.1 Fuzzy Set Theory2.2 Functionality and Truth-Functionality2.3 Operational Semantics for Membership Functions 3: Label Semantics3.1 Introduction and Motivation3.2 Appropriateness Measures and Mass Assignments on Labels3.3 Label Expressions and lambda-Sets3.4 A Voting Model for Label Semantics 3.5 Properties of Appropriateness Measures 3.6 Functional Label Semantics 3.7 Relating Appropriateness Measures to Dempster-Shafer Theory 3.8 Mass Selection Functions based on t-norms 3.9 Alternative Mass Selection Functions 3.10 An Axiomatic Approach to Appropriateness Measures 3.11 Label Semantics as a Model of Assertions 3.12 Relating Label Semantics to Existing Theories of Vagueness 4: Multi-Dimensional And Multi-Instance Label Semantics 4.1 Descriptions Based on Many Attributes 4.2 Multi-dimensional Label Expressions and A-Sets 4.3 Properties of Multi-dimensional Appropriateness Measures 4.4 Describing Multiple Objects 5: Information From Vague Concepts 5.1 Possibility Theory 5.2 The Probability of Fuzzy Sets 5.3 Bayesian Conditioning in Label Semantics 5.4 Possibilistic Conditioning in Label Semantics 5.5 Matching Concepts 5.6 Conditioning From Mass Assignments in Label Semantics6: Learning Linguistic Models From Data 6.1 Defining Labels for Data Modelling 6.2 Bayesian Classification using Mass Relations 6.3 Prediction using Mass Relations 6.4 Qualitative Information from Mass Relations 6.5 Learning Linguistic Decision Trees 6.6 Prediction using Decision Trees 6.7 Query evaluation and Inference from Linguistic Decision Trees7: Fusing Knowledge And Data7.1 From Label Expressions to Informative Priors7.2 Combining Label Expressions with Data8: Non-Additive Appropriateness Measures8.1 Properties of Generalised Appropriateness Measures8.2 Possibilstic Appropriateness Measures8.3 An Axiomatic Approach to Generalised Appropriateness Measures8.4 The Law of Excluded MiddleReferencesIndex