<p>The theory of cognitive maps was developed in 1976. Its main aim was the representation of (causal) relationships among “concepts” also known as “factors” or “nodes”. Concepts could be assigned values. Causal relationships between two concepts could be of three types: positive, negative or neutra
Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Tools and Applications
✍ Scribed by Michael Glykas
- Publisher
- Springer Science & Business Media
- Year
- 2010
- Tongue
- English
- Leaves
- 380
- Category
- Library
No coin nor oath required. For personal study only.
✦ Synopsis
This important edited volume is the first such book ever published on fuzzy cognitive maps (FCMs). Professor Michael Glykas has done an exceptional job in bringing together and editing its seventeen chapters. The volume appears nearly a quarter century after my original article “Fuzzy Cognitive Maps” appeared in the International Journal of Man-Machine Studies in 1986. The volume accordingly reflects many years of research effort in the development of FCM theory and applications—and portends many more decades of FCM research and applications to come. FCMs are fuzzy feedback models of causality. They combine aspects of fuzzy logic, neural networks, semantic networks, expert systems, and nonlinear dynamical systems. That rich structure endows FCMs with their own complexity and lets them apply to a wide range of problems in engineering and in the soft and hard sciences. Their partial edge connections allow a user to directly represent causality as a matter of degree and to learn new edge strengths from training data. Their directed graph structure allows forward or what-if inferencing. FCM cycles or feedback paths allow for complex nonlinear dynamics. Control of FCM nonlinear dynamics can in many cases let the user encode and decode concept patterns as fixed-point attractors or limit cycles or perhaps as more exotic dynamical equilibria. These global equilibrium patterns are often “hidden” in the nonlinear dynamics. The user will not likely see these global patterns by simply inspecting the local causal edges or nodes of large FCMs.
✦ Table of Contents
Title
Contents
List of Authors
Introduction: Uncertainty Issues in Spatial Information
The Nature of Spatial Information
Research Areas in Spatial Information
Overview
References
Part 1 Describing Spatial Configurations
Spatial Vagueness
Introduction
The Nature of Vagueness
Distinguishing Vagueness from Generality and Uncertainty
Vagueness in Different Linguistic Categories
Is Vagueness Intrinsic or Linguistic?
Vagueness and Spatiality
The ‘Sorites’ Paradox
The Problem of Individuation
Consequences of Indeterminate Spatial Extension
A Theory of Crisp and Blurred Regions
An Axiomatic Theory of the ‘Crisping’ Relation
The ‘Egg-Yolk’ Model
Fuzzy Logic Approaches
Spatial Interpretation of Fuzzy Sets
Fuzzy Region Connection Calculus
Supervaluationist Approaches
Origins and Motivations of Supervaluation Semantics
Admissible Precisifications and ‘Supertruth’
Computational Applications of Supervaluationism
Standpoint Semantics
What Is a Standpoint?
Parameterised Precisification Spaces
Defining and Interpreting Vague Concepts Using Parameters
Comparison between Approaches
Some Significant Vague Spatial Predicates
Vague Distance Relations: Near and Far
Elongation vs. Expansiveness
Geographic Feature Types and Terminology
Conclusion
References
A General Approach to the Fuzzy Modeling of Spatial Relationships
Introduction
An Important Distinction
Relative Position vs. Relationship---Example
Relationship vs. Relationship to a Reference Object----Example
$F$-Histograms
$F$-Templates
Definition
An Important Example: Basic Directional Templates
$F$-Histograms from Spatial Correlation
Interest in Force Histograms
Spatial Correlation
$F$-Templates from Force Field
On the Design of Efficient algorithms
Illustrative Example
Typical Steps
Set of Reference Directions
Applications and Related Literature
Directions for Future Work
References
Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning
Introduction
Background
Some Basic Geometrical Measures
Cardinality
Center of Gravity
Mathematical Morphology
Erosion
Morphological Dilation of Bipolar Fuzzy Sets
Properties
Interpretations
Ilustrative Example
Derived Operators
Distance from a Point to a Bipolar Fuzzy Set
Definition of Bipolar Fuzzy Spatial Relations
Application to Spatial Reasoning
Conclusion
References
Fuzzy and Rough Set Approaches for Uncertainty in Spatial Data
Introduction
Background
Overview
Fuzzy Set Basics
Rough Set Basics
Rough Set Modeling of Spatial Data
Applications
Fuzzy Set Terrain Modeling
Rough Sets for Gridded Data
Fuzzy Triangulated Irregular Networks
Fuzzy Spatial Interpolation
Representation of Spatial Relations
Spatial Relations
Topological Spatial Relationships for Vague Regions
Mining Spatial Information
Spatial Data Mining
Fuzzy Minimum Bounding Rectangles
Rough Object Oriented Spatial Database
Conclusions and Future Directions
References
Part 2 Symbolic Reasoning and Information Merging
An Exploratory Survey of Logic-Based Formalisms for Spatial Information
Introduction
Spatial Relations between Regions
Classical Logic for Topology
Modal Logic for Topology
Fuzzy and Rough Sets-Based Mereotopologies
Mereogeometries
Modal Logic of Geometry
Handling Properties Associated to Regions
Modal Logics of Localization
Handling Spatial Information by Means of Attributive Formulas
Concluding Discussion
References
Revising Geographical Knowledge: A Model for Local Belief Change
Introduction
Local Revision of Geographical Information
The G-Structure Model in a Geographic Framework
Maximal Spatial Extent of the Minimal Inconsistent Subsets
Local Revision Based on the G-Structure Model
Processing the Minimal Inconsistent Sets of One Structure
Processing Dependent MIS
An Algorithm for Local Revision
The G-Structurerevision Algorithm, and Its Complexity
Experimentation
The Flooding Problem
Experimental Results
Conclusion
References
Merging Expressive Spatial Ontologies Using Formal Concept Analysis with Uncertainty Considerations
Introduction
Background
Formal Concept Analysis and Galois Connection
The Description Logic $ALC$
Possibilistic Logic
Ontology Merging Using FCA
Source TBoxes
Source ABoxes
Generation of the Galois Connection Lattice
Dealing with Emerging Concepts
Dealing with Uncertainty
Related Work
Conclusion
References
Generating Fuzzy Regions from Conflicting Spatial Information
Introduction
Spatial Inconsistency
A Genetic Algorithm for Crisp Regions
Discretizing Space
Spatial Reasoning
Generating Polygons
A Genetic Algorithm
A Genetic Algorithm for Fuzzy Regions
Fuzzy Topological Relations
Modifications to the GA
Experimental Results
Concluding Remarks
References
Part 3 Prediction and Interpolation
Fuzzy Methods in Image Mining
Introduction
A Short Introductory Example
Fuzzy Theory
Image Mining
Object Identification
Extracting Objects from Images
Modelling
Tracking in Time
Prediction
Stakeholders
Spatial Data Quality
Positional Accuracy
Attribute Accuracy
Logical Consistency
Completeness
Lineage
Semantic Accuracy
Temporal Quality
Other Issue of Spatial Data Quality
From Point to Area - Scale
A Statistical Model for Scaling
Mathematical Modeling
Concluding Remarks
References
Kriging and Epistemic Uncertainty: A Critical Discussion
Introduction
Some Basic Concepts in Probabilistic Geostatistics
Structuring Assumptions
Simple Kriging
Variogram or Covariance Function Estimation
Theoretical Models of Variogram or Covariance Functions
Definiteness Properties of Covariance and Variogram Functions
Why Not Use the Sample Variogram ?
Sensitivity of Kriging to Variogram Parameters
Epistemic Uncertainty in Kriging
Imprecision in the Variogram
Kriging in the Bayesian Framework
Imprecision in the Data
Intervallist Kriging Approaches
The Quadratic Programming Approach
The Soft Kriging Approach
Fuzzy Kriging
Diamond’s Fuzzy Kriging
Bardossy’s Fuzzy Kriging
Uncertainty in Kriging: A Prospective Discussion
Spatial vs. Fictitious Variability
A Deterministic Justification of Simple Kriging
Towards Integrating Epistemic Uncertainty in Spatial Interpolative Prediction
Conclusion
References
Scaling Cautious Selection in Spatial Probabilistic Temporal Databases
Introduction
SPOT Databases: Background
SPOT Syntax
SPOT Semantics
Linear Programming and SPOT DBs
Interior and Containing Regions in the Space of Interpretations
Cautious Semantics
Multiple Interior Regions
Computing Interior Regions
Bounding via Composite Atoms
Experiments
Algorithms Used
Real World Ship Data
Artificial Data Queries
Related Work
Conclusion
References
Imperfect Spatiotemporal Information Analysis in a GIS: Application to Archæological Information Completion Hypothesis
Introduction
TheSIGRem Project
Introduction to the SIGRem Project
Description of BDRues
BDRues and Imperfection: Construction of BDFRues
Pattern Recognition in Images Using the Hough Transform
Hough Transform
Fuzzy Hough Transform
On the Valued Hypothesis Building
Accumulators’ Building
Accumulator Aggregation
Visualization
Application to BDRues Data
Discussion on Results
On the Influence of Weight on Results
Valued Hypothesis
Conclusion
References
Uncertainty in Interaction Modelling: Prospecting the Evolution of Urban Networks in South-Eastern France
Introduction
Methodological Choices
Modelling Regional Urban Networks from Spatial Interaction Data
Modelling the Development of Urban Networks through Bayesian Networks
Integrating Spatial Models and GIS Tools
The Case Study of Urban Networks in the PACA Region
The Urban Networks Defined by Commuter Trips in 1990 and 1999
Modelling the Evolution of the Network between 1990 and 1999
Proposing a Trend Scenario for 2008
Conclusions and Future Developments
References
Author Index
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