Abstract:
Recent trends in poverty analysis have focused more on multidimensional poverty measures such as the Fuzzy Set Schemes (FSSs) rather than the unidimensional approaches. A major criticism of the unidimensional approaches is its restrictive scope on the nature and cause of poverty. The FSSs have been restricted by their lack of computational uniqueness in the determination of the Membership Functions (MFs) with no assessment criteria. Therefore, this study was aimed at developing Fuzzy Set Membership Function Schemes (FSMFSs) with assessment criteria.
Fuzzy set membership function schemes were developed from the mean, geometric mean and modified harmonic mean of the levels of eight Deprivation Attributes (DAs). These DAs, namely source of water for drinking and cooking, energy source for cooking, energy source for lighting, toilet facilities by type, refuse disposal by method, material used for dwelling floor, type of housing unit, and distance to toilet were obtained from the 2010 Harmonised National Living Standard Survey of the National Bureau of Statistics. These were used in the determination of MFs of the FSMFSs. Assessment criteria, namely, Quasi Mean Absolute Deviation (QMAD), Quasi Mean Percentage Error (QMPE) and Quasi Mean Square Deviation (QMSD), of the form ((m_i (x_i ))/m_2 ), where m_i (x_i ) and m_2 are functions of the poverty ratio per household and attribute space, respectively were further developed to assess the performances of the schemes. These were then compared with the performances of two existing FSMFSs of Cerioli and Zani (CZ) as well as Cheli and Lemmi (CL). The estimates from the developed assessment criteria were ranked for the schemes considered and the scheme with the least rank was adjudged the best.
The developed FSMFSs were Varying Mean Fuzzy Set Membership Function Scheme (VMFSMFS), Varying Geometric Mean Fuzzy Set Membership Function Scheme (VGMFSMFS) and Varying Reciprocal Mean Fuzzy Set Membership Function Scheme (VRMFSMFS). The MFs of the developed FSMFSs ranged from 0 to 1 for all the eight DAs as expected for any multidimensional poverty fuzzy set scheme. The VMFSMFS, VGMFSMFS, VRMFSMFS and CL indicated least deprivation in type of housing with weights 1.32846, 1.32127, 1.26052 and 1.28632, respectively. The CZ indicated least deprivation in distance to toilet with weight 1.54860. The QMAD, QMPE and QMSD were 0.00952, 0.06980 and 0.03494 for VMFSMF; 0.00934, 0.00105 and 0.03159, for VGMFSMF; 0.00931, 0.06406 and 0.06680 for VRMFSMF; 0.01109, 0.00153 and 0.03302 for CZ; and 0.01195, 0.00714 and 0.07005 for CL, respectively. The estimates of the assessment criteria for the developed FSMFSs were lower than estimates from the two existing FSMFSs. The VGMFSMF performed best among the developed FSMFSs, while CZ performed better than CL.
This study has established that varying geometric mean fuzzy set membership function scheme gave wider inference on the nature and scope of poverty and the assessment criteria provided basis for the statistical evaluation of current and future membership function schemes in multidimensional poverty analysis.
