A grey approach to site selection for nursing homes: An extension of the fuzzy analytic hierarchy process

The construction of more nursing homes has become one of the most needed pension services in China, and the issue of site selection is one of the most important steps in their construction. The problem of site selection for nursing homes is a complex system engineering problem that involves not only economic interests but also social interests. Due to the limitations of human thinking in the evaluation process, the evaluation value of a nursing home site might be an interval grey number. Moreover, the evaluation indicator system for nursing home locations is a two-layer system that has been neglected in the literature. Therefore, the fuzzy analytical hierarchy process is extended to a new grey approach, i.e., the grey analytic hierarchy process, which can solve the evaluation problems for a two-layer indicator system under an interval grey environment. By constructing a three-point interval grey number, grey evaluation criteria are given to obtain a judgment matrix for interval grey numbers. Definitions of the initial weights, nongreyness weights and integrated weights are proposed to find the best evaluation object. Finally, the effectiveness of the method proposed by this paper is verified by comparative analyses of other grey methods.