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