Fuzzy Neighbourhood Spaces

Abstract

Since the introduction of fuzzy neighbourhood spaces, in the sense of I

[251, many papers have appeared analyzing and making use of this notion. Some papers showed the distinguished internal characterizations of the category of fuzzy neighbourhood spaces, denoted by FNS, for example [37, 48, 49). The fuzzy topological spaces associated with the fuzzy uniform spaces in the sense of [24] and with the fuzzy proximity spaces, in the sense of [3], were shown to be fuzzy neighbourhood spaces [25, 38]. Subsequently, the notion of fuzzy syntopogeny as a unified theory of fuzzy neighbourhood spaces, Lowen fuzzy uniformities and Artico-Moresco fuzzy proximities was introduced by Katsaras [16) and Mashhour et al. [35]. Given a lower =semicontinuous triangular norm T, Morsi [42, 43]

introduced the two categories of fuzzy T-locality spaces, and of fuzzy T • 0

neighbourhood spaces, denoted by T-FLS and T-FNS, respectively. In the special case T = Min, the categories T-FLS and T-FNS coincide with the categories of fuzzy neighbourhood-base spaces, denoted by FNBS [39] and FNS [25].