Fure-ai, from the verb fure-au 'to come in contact with each other' or 'to touch together', has the deeper, highly positive meaning of exchange and interaction among people. It is reminiscent of the old adage 袖ふれあうも多少の縁 sode fure-au mo tashō no en -- even the brushing together of sleeves is a fated connection, based on the Buddhist philosophy that even casual incidents and connections are determined by karma.
Fure-ai is written in Chinese characters as 触れ合い or 触合い, but it is much more common to see it as hiragana ふれあい, as in the following sign:
Note that the -ai in fure-ai is etymologically the same as the -ai in kumi-ai 'cooperative'. In forming compound verbs it has the meaning of 'mutual, together'. Since kumi-ai is a fully-fledged noun referring to a specific business entity, it is always written in pure kanji as 組合, without any hiragana. On the other hand, fure-ai has gone the other way and is almost always written in hiragana.
There are several reasons for this:
A Google search in August 2003 confirms the overwhelming use of hiragana to write fure-ai on the Internet: