Exploring job centers by accessibility using fuzzy set approach: the case study of the Columbus MSA

Abstract

When comparing accessibility, the interpretation of results is complex because of lack of standard or universal norm. This uncertainty issue of the distinction from the lack of standard can be solved using the multi-level approach of fuzzy set: universal, relative, and absolute index. Since a fuzzy set approach deals with the vagueness and indiscernibility of accessibility index, the proposed approach suggests a better solution to classify the index than a crisp set or even a single-level fuzzy set approach. In this study, we evaluate job accessibility of locations in the Columbus MSA in Ohio, USA for 18 worker groups. The uncertain distinction between strong/weak, rich/poor, and higher/lower accessibility is improved by the multi-level approach. Moreover, this study attempts to enhance our understanding of spatial structure of job accessibility disaggregated by occupation type and gender.

Appendices

Appendix 1: Crossover profiles for 18 groups illustrated with their fuzzy set MFs

Appendix 2: Uncertainty among the fuzzy sets by gender based on universal index

Appendix 3: Disaggregate doubly constrained spatial interaction model

$$T_{ij}^{kg} = A_{i}^{kg} O_{i}^{kg} B_{j}^{kg} D_{j}^{kg} \exp ( - \beta^{kg} c_{ij} )$$

(12)

$$A_{i}^{kg} = \frac{1}{{\sum\nolimits_{j} {B_{j}^{kg} D_{j}^{kg} \exp ( - \beta^{kg} c_{ij} )} }}$$

(13)

$$B_{j}^{kg} = \frac{1}{{\sum\nolimits_{i} {A_{i}^{kg} } O_{i}^{kg} \exp ( - \beta^{kg} c_{ij} )}}$$

(14)

$$\sum\limits_{j}^{{}} {T_{ij}^{kg} } = O_{i}^{kg} \quad \forall i$$

(15)

$$\sum\limits_{i}^{{}} {T_{ij}^{kg} } = D_{j}^{kg} \quad \forall j$$

(16)

where kg occupation (k) and gender (g) combination which ensures ($\sum\nolimits_{kg} {T_{ij}^{kg} } = T_{ij}$) for all i and j.

$$ACC_{j}^{kg} = (B_{j}^{kg} )^{ - 1} = \left[ {\sum\limits_{i} {A_{i}^{kg} O_{i}^{kg} \exp ( - \beta^{kg} c_{ij} )} } \right]$$

(17)

Spatial interactions by worker’ occupation and gender can be modeled by the Eq. (12). Equations (13) and (14) ensure (15) and (16), respectively. Notice that the O ^kg _i (15) and D ^kg _j (16) ensure the row sum and column sum in the SI model job accessibility (ACC ^kg _j ). The Eq. (17) representing job accessibility at destinations is disaggregated by worker’ occupation and gender using a doubly constrained spatial interaction model. Values for O ^kg _i and D ^kg _j for each gender (g) and occupational category (k) are obtained from the CTPP Part 1 (P1) and Part 2 (P2).