Combining fuzzy AHP with MDS in identifying the preference similarity of alternatives

Multidimensional scaling (MDS) analysis is a dimension-reduction technique that is used to estimate the coordinates of a set of objects. However, not every criterion used in multidimensional scaling is equally and precisely weighted in the real world. To address this issue, we use fuzzy analytic hierarchy process (FAHP) to determine the weighting of subjective/perceptive judgments for each criterion and to derive fuzzy synthetic utility values of alternatives in a fuzzy multi-criteria decision-making (FMCDM) environment. Furthermore, we combine FAHP with MDS to identify the similarities and preferences of alternatives in terms of the axes of the space, which represent the perceived attributes and characteristics of those alternatives. By doing so, the visual dimensionality and configuration or pattern of alternatives whose weighted distance structure best fits the input data can be obtained and explained easily. A real case of expatriate assignment decision-making was used to demonstrate that the combination of FAHP and MDS results in a meaningful visual map.