A short note on fuzzy neighbourhood spaces
Fuzzy Sets and Systems - The fuzziness of language and cerebral processes
Fuzzy proximities compatible with Lowen fuzzy uniformities
Fuzzy Sets and Systems
Nearness concepts in fuzzy neighbourhood spaces and in their fuzzy proximity spaces
Fuzzy Sets and Systems
Fuzzy uniformities induced by fuzzy proximities
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Abstract and concrete categories
Abstract and concrete categories
Fuzzy proximities induced by functional fuzzy separation
Fuzzy Sets and Systems
Generalized possibility measures
Information Sciences—Intelligent Systems: An International Journal
Fuzzy T-neighbourhood spaces: part 3: T-separation axioms
Fuzzy Sets and Systems - Topology
Fuzzy T-neighbourhood spaces: part 2--T-neighbourhood systems
Fuzzy Sets and Systems - Mathematics
Uniform environments as a general framework for metrics and uniformities
Fuzzy Sets and Systems
International Journal of Hybrid Intelligent Systems
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This is the first one of three articles that are intended to be published consecutively in this journal. Together they constitute a three-part work on the unified subject of fuzzy T-neighbourhood spaces and their fuzzy T-proximities, where T stands for any continuous triangular norm. These new notions generalize, to arbitrary T, corresponding ones due to Artico, Höhle, Lowen and Moresco.In this part, we define and study notions of fuzzy T-proximity, one for each T. Their definition subsumes that of fuzzy proximity due to Artico and Moresco (Fuzzy Sets and Systems 21 (1987) 85), as our Min-proximity. In particular, we study proximity maps, the fuzzy topological space associated with a T-proximity (which, in the second part, will be proved a fuzzy T-neighbourhood space), T-proximities as fuzzy relations in (ordinary) power sets, T-proximal neighbourhood systems, and relationships to the Höhle-Lowen fuzzy T-uniformities (J. Math. Anal. Appl. 82 (1981) 370; Manuscripta Math. 38 (1982) 289). The second part of this three-part work will be concerned with the categories of fuzzy T-neighbourhood spaces, one for each T, Whereas we devote the third part to our T-separation axioms in those categories.