Fuzzy Set Approach to Multidimensional Poverty Measurement (eBook)

Achille Lemmi is Professor of Economic Statistics at the University of Siena. His areas of interest and research include personal income distribution models, poverty and living conditions estimation and analysis, and poverty dynamics. Gianni Betti is Associate Professor of Economic Statistics at the University of Siena. His areas of interest and research include poverty and living conditions analysis, equivalence scales, small area estimation and poverty mapping.

List of contributing authors 11
Introduction 16
1 Philosophical Accounts of Vagueness, Fuzzy Poverty Measures and Multidimensionality 23
1.1 Introduction 23
2 The Mathematical Framework of Fuzzy Logic 43
2.1 Introduction 43
2.2.1 Fuzzy propositions 44
2.2.2 Fuzzy subsets, fuzzy numbers 45
2.3 The connectors of fuzzy logic 47
2.3.1 Zadeh's operators 47
2.3.2 Other fuzzy logical connectives 52
2.4 Decision-making and evaluation in a fuzzy context 55
2.4.1 Optimal fuzzy decision: the Bellman and Zadeh's model 55
2.4.2 "Fuzzy" aggregation in evaluation problems. 56
References 60
3 An Axiomatic Approach to IVIultidimensional Poverty IVIeasurement via Fuzzy Sets 62
3.1 Introduction 62
3.2 Fuzzy Membership Function 65
3.3 Properties for a Fuzzy Multidimensional Poverty Index 69
3.4 The Subgroup Decomposable Fuzzy Multidimensional Poverty 74
3.5 Conclusions 80
References 82
4 On the Convergence of Various Unidimensional Approaches 86
4.1 Introduction 86
4.2 Basic components of the unidimensional approach 87
4.3 The choice of definition and the scope of poverty 91
4.3.1 Impact of the weighting procedures 91
4.3.2 Impact of the economic well-being variables 92
4.4 Choice of definition and identification of the poor 95
4.4.1 Looking at the poorest quintile 95
4.4.2 The population defined as poor 98
4.4.3 Identifying the poor according to more than two distributions 100
4.5 Concluding comments 101
5 Capability Approach and Fuzzy Set Theory: Description, Aggregation and Inference Issues 105
5.1 Introduction 105
5.2 Brief remarks on distinctive features of the capability approach 107
5.3 Describing multidimensional poverty and well-being through fuzzy membership functions 110
5.4 Aggregating well-being dimensions through fuzzy operators 117
5.5 Assessing multidimensional well-being through fuzzy inference systems 120
5.6 Conclusion 123
References 124
6 Multidimensional and Longitudinal Poverty: an Integrated Fuzzy Approach 126
6.1 Introduction 126
6.2 Income poverty 128
6.3 Non-monetary deprivation ("Fuzzy Supplementary") 131
6.4 Fuzzy set operations appropriate for the analysis of poverty and deprivation 133
6.4.1 Multidimensional measures 133
6.4.2 Definition of poverty measures according to both monetary and non-monetary dimensions 134
6.4.3 Income poverty and non-monetary deprivation in combination: IVIanifest and Latent deprivation 138
6.5 On longitudinal analysis of poverty conceptualized as a fuzzy state 139
6.5.1 Longitudinal application of the Composite fuzzy operation 139
6.5.2 The general procedure 140
6.6 Application to specific situations 143
6.6.1 Persistence of poverty 143
6.6.2 Rates of exit and re-entry 145
6.7 Concluding remarks 146
References 146
7 French Poverty Measures using Fuzzy Set Approaches 149
7.1 Introduction 149
7.2 Application of tiie TFR approach using data from the French Surveys on Living Conditions for the years 1986 and 1993 150
7.3 Statistical sensitivity analysis of the TFR poverty index on the number of attributes 154
7.4 Extracting a law from multidimensional poverty scores analogous to the Pareto Law for income distribution: a method based on the TFR approach 155
7.5 Concluding comments 161
References 162
Appendix: List of deprivation indicators selected from the INSEE-French Surveys of Living Conditions 1986 and 1993 163
8 The "Fuzzy Set" Approach to Multidimensional Poverty Analysis: Using the Shapley Decomposition to Analyze the Determinants of Poverty in Israel 165
8.1 Introduction 165
8.2 Theoretical Background 166
8.3 The Case of Israel in 1995 167
8.3.1 Selecting the Indicators 167
8.3.2 The Data Sources 168
8.3.3 Computing the percentage of poor according to the various approaches 168
8.3.4 The Determinants of multi-dimensional poverty 169
8.3.5 The Shapley Approach to Index Decomposition and its Implications for Multidimensional Poverty Analysis 178
8.4 Concluding Comments 180
Bibliography 181
Appendix: List of Variables available in the 1995 Israeli Census 182
9 Multidimensional Fuzzy Set Approach Poverty Estimates in Romania 185
9.1 Introduction 185
9.2 Socio-economic and demographic context 186
9.3 Monetary dimension of poverty 189
9.3.1 National method 189
9.3.2 Relative method 192
9.4 Multidimensional estimation of poverty 193
9.4.1 Poverty and occupationat status 194
9.4.2 Poverty and education 196
9.4.3 Poverty and demographic characteristics of households 196
9.4.4 Territorial distribution of poverty 198
9.5 Conclusions 199
References 204
10 Multidimensional and Fuzzy Poverty in Switzerland 205
10.1 Introduction 205
10.2 Poverty in Switzerland 206
10.3 Decompositions of poverty 211
10.3.1 Poverty by employment status 212
10.3.2 Poverty by household composition 215
10.4 Concluding remarks 217
References 218
11 A Comparison of Poverty According to Primary Goods, Capabilities and Outcomes. Evidence from Frencli School Leavers' Surveys 220
11.1 Introduction 220
11.2 Three concepts of poverty 221
11.2.1 Clarifying basic features 221
11.2.1 Describing connections between tlie three concepts 224
11.3 A multidimensional measure of poverty: the fuzzy logic 225
11.3.1 Data processing: income, qualitative and continuous indicators 227
11.3.2 The proposed membership function 229
11.3.3 Example: calculation of a composite membership function 230
11.4 Empirical comparison on French Youth Panel Survey from 1996 to 1999 231
11.4.1 Preliminaries 231
11.4.2 The informational basis of primary goods 232
11.4.3 The informational basis of primary social outcomes 234
11.4.4 The informational basis of refined functionings 235
11.4.5 Analyse recovery of the three populations 236
11.5 Conclusion 238
Appendix 1 - The CEREQ Panel Data Surveys 238
Appendix 2 - French Educational Level 239
References 239
12 Multidimensional Fuzzy Relative Poverty Dynamic Measures in Poland 241
12.1 Introduction 241
12.2 Sources of Data 242
12.3 Methods of Analysis 243
12.3.1 Multidimensional Analysis of Poverty 243
12.3.2 Evaluation of the Poverty Nature 247
12.3.3 Poverty Determinants 249
12.4 Changes in the Poverty Sphere in Poland from 1996 to 1999 250
12.4.1 Degree of the Poverty Threat 250
12.4.2 Poverty Nature 253
12.4.3 Poverty Determinants 256
12.5 Summary 261
References 262
13 Modelling Fuzzy and Multidimensional Poverty Measures in the United Kingdom with Variance Components Panel Regression 264
13.1 Introduction 264
13.2 Fuzzy and multidimensional poverty definitions 266
13.3 Panel regression models with variance components 267
13.4 Cross-sectional empirical analysis 269
13.5 Longitudinal empirical analysis 271
13.5.1 Trend estimation 273
13.5.2 The effect of covariates 276
13.6 Concluding remarks 280
References 280
Index 283

Reading rehearsal currently not available.