In our super-aging society we are faced with an ever-increasing problem that needs to be resolved, namely accommodation for the elderly. To solve this problem we must first clarify its nature. We know that, by 2030, 10% of the elderly will have dementia and another 40% will be living alone. Therefore, it is important that, right now, we think about the emergency measures we will need to implement on a national scale to solve these problems in 2025, when the baby boomers reach the age of 75. The elderly face not only a rising incidence of diseases such as dementia and the biological factors associated with aging, but also social factors such as lack of communication. In particular, we have found that the incidence of dementia differs significantly between those with the presence or absence of a social network. Also, the number of people moving into care facilities for the elderly has been increasing in recent years, and this trend is an important social phenomenon. Here, we performed a basic study of the process used to select facilities for the elderly. First, as a basic structure, we focused on the attributes of facilities for the elderly. Next, we examined the basic attributes of the elderly as institutional tenants. We then computed a power set by using these basic attributes as elements. From the partially ordered set (poset) we derived a possible combination of elements to use in selecting facilities for the elderly. We found that the elements of the power set obtained by using the attributes of elderly people as institutional tenants constituted fuzzy measures. We showed clearly that comprehensive evaluation by using fuzzy integration was possible.