Fuzzy Cognitive Maps: Best Practices and Modern Methods

ISBN-13: 9783031489624 / Angielski

Philippe J. Giabbanelli; Gonzalo N?poles

Spis treści

Fuzzy Cognitive Maps: Best Practices and Modern Methods 

Philippe J. Giabbanelli and Gonzalo Nápoles

1 Defining and Using Fuzzy Cognitive Mapping 

Philippe J. Giabbanelli, C.B. Knox, Kelsi Furman, Antonie Jetter and

Steven Gray

1.1 Introduction

1.2 Three equivalent definitions 

1.2.1 FCMs as mental models 

1.2.2 FCMs as mathematical objects 

1.2.3 FCMs as simulation tools 

1.3 A typology of uses 

1.3.1 FCMs as Expert Systems 

1.3.2 FCMs in Collective Intelligence

1.3.3 FCMs as boundary objects to support learning 

1.3.4 FCMs as prediction models 

Exercises 

References 

2 Creating an FCM with participants in an interview or workshop setting 

C.B. Knox, Kelsi Furman, Antonie Jetter, Steven Gray and Philippe J.Giabbanelli

2.1 Decision Factors 

2.1.1 Individual vs Group Modeling 

2.1.2 Facilitator vs. Participant Mapping 

2.1.3 Hand-Drawn Models vs Modeling Software 

2.1.4 Pre-Defined, Open-Ended Concepts or Hybrid Approach

2.2 Data Collection 

2.2.1 Creating a Parsimonious Model and Weighting Connections 

2.2.2 Participant Recruitment 

2.2.3 Facilitation Considerations 

2.3 Conclusions 

Exercises 

References

3 Principles of simulations with FCMs 

Gonzalo Nápoles and Philippe J. Giabbanelli

3.1 Introduction: revisiting the reasoning mechanism 

3.2 Activation functions 

3.3 Convergence: a mathematical perspective 

3.4 Convergence: a simulation approach 

3.5 A detailed example in Python 

3.6 Exercises 

References 

4 Hybrid Simulations 

Philippe J. Giabbanelli

4.1 Introduction 

4.2 Rationale for a hybrid ABM/FCM simulation

4.3 Main steps to design a hybrid ABM/FCM simulation

4.4 Example of study design and Python implementation 

4.5 Scaling-up simulations using parallelism 

4.6 Exercises 

References

5 Analysis of Fuzzy Cognitive Maps 

Ryan Schuerkamp and Philippe J. Giabbanelli

5.1 Why Analyze Fuzzy Cognitive Maps? 

5.2 What Are the Important Concepts? 

5.2.1 Transmitter, Receiver, and Ordinary Concepts 

5.2.2 Centrality Measures 

5.3 Validating the Facilitation Process 

5.3.1 Number of Concepts and Relationships 

5.3.2 Receiver-Transmitter Ratio 

5.3.3 Metrics based on shortest paths 

5.3.4 Clustering Coefficient 

5.3.5 Density 

5.3.6 Feedback Loops 

5.4 Conclusion 

5.5 Exercises 

References 

6 Extensions of Fuzzy Cognitive Maps 

Ryan Schuerkamp and Philippe J. Giabbanelli

6.1 Why Do We Extend Fuzzy Cognitive Maps?

6.2 Interval-Valued Fuzzy Cognitive Maps 

6.2.1 Example Interval-Valued Fuzzy Cognitive Map Inference 

6.3 Time-Interval Fuzzy Cognitive Maps 

6.3.1 Example Time-Interval Fuzzy Cognitive Map Inference 

6.4 Extended-Fuzzy Cognitive Maps 

6.4.1 Example Extended-Fuzzy Cognitive Map Inference 

6.5 Trends and Future of Extensions of Fuzzy Cognitive Maps 

6.6 Exercises 

References

7 Creating FCM models from quantitative data with evolutionary algorithms 

David Bernard and Philippe J. Giabbanelli

7.1 Introduction 

7.2 Representing the genome . 

7.2.1 Transformations between vector and matrix 

7.2.2 Constraints 

7.3 Evaluation 

7.4 Genetic Algorithms 

7.5 Analysis 

7.6 CMA-ES 

Exercises 

References 

8 Advanced learning algorithm to create FCM models from quantitative data 

Agnieszka Jastrzębska and Gonzalo Nápoles

8.1 Introduction 

8.2 Hybrid Fuzzy Cognitive Map model 

8.3 Training the hybrid FCM model 

8.4 Optimizing the hybrid FCM model 

8.4.1 Detecting superfluous relationships 

8.4.2 Calibrating the sigmoid offset 

8.4.3 Calibrating the weights 

8.5 How to use these algorithms in practice? 

8.6 Applying the FCM model to real-world data 

8.6.1 Sensitivity to the sigmoid function parameters 

8.6.2 Comparison with other learning approaches 

8.7 Further readings 

8.8 Exercises 

References

9 Introduction to Fuzzy Cognitive Map-based classification 

Agnieszka Jastrzębska and Gonzalo Nápoles

9.1 Introduction 

9.2 Preliminaries 

9.2.1 Notions of classification and features 

9.2.2 Preliminary processing 

9.2.3 Performance metrics 

9.3 The FCM-based classification model 

9.3.1 Basic FCM architecture for data classification 

9.3.2 Genetic Algorithm-based optimization 

9.3.3 How does the model classify new instances? 

9.4 Classification toy case study 

9.4.1 Data description

9.4.2 Classifier implementation 

9.4.3 Classification – overall quality 

9.5 Further readings

9.6 Exercises 

References 

10 Addressing accuracy issues of Fuzzy Cognitive Map-based classifiers 

Gonzalo Nápoles and Agnieszka Jastrzębska

10.1 Introduction 

10.2 Long-term Cognitive Network-based classifier 

10.2.1 Generalizing the traditional FCM formalism 

10.2.2 Recurrence-aware decision model 

10.2.3 Learning algorithm for LTCN-based classifiers 

10.3 Model-dependent feature importance measure 

10.4 How to use the LTCN-based classifier in practice? 

10.5 Empirical evaluation of the LTCN classifier 

10.5.1 Pattern classification datasets 

10.5.2 Does the LTCN classifier outperform the FCM classifier? 

10.5.3 Hyperparameter sensitivity analysis 

10.5.4 Comparison of LTCN with state-of-the-art classifiers 

10.6 Illustrative case study: phishing dataset 

10.7 Further readings 

10.8 Exercises 

References 

Index 

O autorze

​Dr. Philippe J. Giabbanelli received his B.S. from Université Côte d'Azur (France) and his M.Sc. and Ph.D. from Simon Fraser University (Canada). He worked as a researcher at the University of Cambridge (UK) and as a tenure-track faculty at several nationally ranked American universities, where he developed a variety of courses on predictive modeling and artificial intelligence. He taught fuzzy cognitive maps (FCMs) from the perspective of AI, as an object of study for network science, or as a tool in modeling and simulation. His research focuses on developing and applying AI to support population health interventions. He has published about 130 articles (mostly with his students), covering multiple aspects of FCM research from the elicitation and aggregation of causal maps to their structural validation or their combination with other techniques such as agent-based modeling.

 

Dr. Gonzalo Nápoles received his B.S. and M.Sc. from the Central University of Las Villas (Cuba) and his Ph.D. from Hasselt University (Belgium) and Maastricht University (the Netherlands). Currently, he is a tenured assistant professor at the Department of Cognitive Science and Artificial Intelligence, Tilburg University (the Netherlands). He has taught fuzzy cognitive maps (FCMs) in several courses, including the First Summer School on Fuzzy Cognitive Mapping held in Volos (Greece). His research focuses on developing learning algorithms for FCM models, understanding their mathematical properties, and exploiting their potentialities in pattern classification and time series forecasting settings. He was a recipient of the Cuban Academy of Science Award for his contributions to the FCM field. More recently, his research efforts have shifted toward developing fair machine learning algorithms that can intrinsically be explained (to a large extent) and methods to mitigate implicit and explicit bias.

Blurb

This book starts with the rationale for creating an FCM by contrast to other techniques for participatory modeling, as this rationale is a key element to justify the adoption of techniques in a research paper. Fuzzy cognitive mapping is an active research field with over 20,000 publications devoted to externalizing the qualitative perspectives or “mental models” of individuals and groups. Since the emergence of fuzzy cognitive maps (FCMs) back in the 80s, new algorithms have been developed to reduce bias, facilitate the externalization process, or efficiently utilize quantitative data via machine learning. It covers the development of an FCM with participants through a traditional in-person setting, drawing from the experience of practitioners and highlighting solutions to commonly encountered challenges. The book continues with introducing principles of simulations with FCMs as a tool to perform what-if scenario analysis, while extending those principles to more elaborated simulation scenarios where FCMs and agent-based modeling are combined. Once an FCM model is obtained, the book then details the analytical tools available for practitioners (e.g., to identify the most important factors) and provides examples to aid in the interpretation of results. The discussion concerning relevant extensions is equally pertinent, which are devoted to increasing the expressiveness of the FCM formalism in problems involving uncertainty. The last four chapters focus on building FCM models from historical data. These models are typically needed when facing multi-output prediction or pattern classification problems. In that regard, the book smoothly guides the reader from simple approaches to more elaborated algorithms, symbolizing the noticeable progress of this field in the last 35 years. Problems, recent references, and functional codes are included in each chapter to provide practice and support further learning from practitioners and researchers.