Modelling and Reasoning with Vague Concepts / Edition 1

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Vagueness is central to the flexibility and robustness of natural language descriptions. Vague concepts are robust to the imprecision of our perceptions, while still allowing us to convey useful, and sometimes vital, information. The study of vagueness in Artificial Intelligence (AI) is therefore motivated by the desire to incorporate this robustness and flexibility into intelligent computer systems. Such a goal, however, requires a formal model of vague concepts that will allow us to quantify and manipulate the uncertainty resulting from their use as a means of passing information between autonomous agents. This volume outlines a formal representation framework for modelling and reasoning with vague concepts in Artificial Intelligence. The new calculus has many applications, especially in automated reasoning, learning, data analysis and information fusion. This book gives a rigorous introduction to label semantics theory, illustrated with many examples, and suggests clear operational interpretations of the proposed measures. It also provides a detailed description of how the theory can be applied in data analysis and information fusion based on a range of benchmark problems.

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Product Details

  • ISBN-13: 9780387290560
  • Publisher: Springer US
  • Publication date: 1/11/2006
  • Series: Studies in Computational Intelligence Series, #12
  • Edition description: 2006
  • Edition number: 1
  • Pages: 246
  • Product dimensions: 6.40 (w) x 9.30 (h) x 0.80 (d)

Table of Contents

List of Figures

1: Introduction

2: Vague Concepts And Fuzzy Sets
2.1 Fuzzy Set Theory
2.2 Functionality and Truth-Functionality
2.3 Operational Semantics for Membership Functions

3: Label Semantics
3.1 Introduction and Motivation
3.2 Appropriateness Measures and Mass Assignments on Labels
3.3 Label Expressions and lambda-Sets
3.4 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 Semantics

6: 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 Trees

7: Fusing Knowledge And Data
7.1 From Label Expressions to Informative Priors
7.2 Combining Label Expressions with Data

8: Non-Additive Appropriateness Measures
8.1 Properties of Generalised Appropriateness Measures
8.2 Possibilstic Appropriateness Measures
8.3 An Axiomatic Approach to Generalised Appropriateness Measures
8.4 The Law of Excluded Middle


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