Fuzzy Set Theory

Instructor: Enrica Chiappero-Martinetti, Associate Professor of Economics, Faculty of Political Science, University of Pavia and Director of the Human Development, Capability and Poverty – International Research Centre at the Institute of Advanced Study (IUSS) at Pavia.

Class Objectives:

An overview of fuzzy methodologies and some conceptual issues
Membership functions and membership degrees
Aggregation operators
Potentiality and limits of FST vis-à-vis with other tools

Presentation

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Fuzzy Set Theory Part 1 [To save file, right click to "Save Target As" (Windows) or control + click (Mac)]
Fuzzy Set Theory Part 2

Problem Set on Fuzzy Set Theory

Answer Key 1
Answer Key 2

Reading List
Basic Textbook Readings:
SMITHSON, M. and J. VERKUILEN (2006) Fuzzy Set Theory: Applications in the Social Sciences, Thousand Oaks, London, New Delhi, SAGE Publications.

Suggestions on publications that relate or apply this topic to the capability approach:
ADDABBO, T., DI TOMMASO, M.L. and G. FACCHINETTI. (2004): “To What Extent Fuzzy Set Theory and Structural Equation Modelling Can Measure Functionings? An Application to Child Well Being”, ChilD Working Paper. 30/2004.
BALIAMOUNE, M. (2004): “On the Measurement of Human Well-Being: Fuzzy Set Theory and Sen’s Capability Approach”, Research paper 2004/16, WIDER. Helsinki.
CHAKRAVARTY, S. R. (2006): “An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets” in A Lemmi and G. Betti (eds.) Fuzzy Set Approach to Multidimensional Poverty Measurement. New York: Springer.
CHIAPPERO MARTINETTI, E. (2000): “A Multidimensional Assessment of Well-Being Based on Sen’s Functioning Approach”, Rivista Internazionale di Scienze Sociali.
CHIAPPERO MARTINETTI, E. (2006): “Capability Approach and Fuzzy Set Theory: Description, Aggregation and Inference Issues”, in A. Lemmi and G. Betti (eds.) Fuzzy Set Approach to Multidimensional Poverty Measurement. New York: Springer.
LELLI, S. (2001): “Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen’s Functioning Approach”. Centre of Economic Studies Discussion Paper, KU Leuven.
QIZILBASH, M. and D. CLARK. (2005): ‘The Capability Approach and Fuzzy Poverty Measures: An Application to the South African Context”, Journal of Social Indicators Research. 74: 103-129.
ROCHE, J. M. (2007): Monitoring Inequality between Social Groups: A Methodology Combining Fuzzy Set Theory and Principal Component Analysis”. Paper presented at the 4th HDCA conference, 18 – 20 September, New York City.