Some properties of M-fuzzifying convexities induced by M-orders

In this paper, the notions of geometric interval spaces, convex geometries, and base-point orders in the theory of convexity spaces are generalized to M-fuzzifying convexity spaces. Using M-fuzzifying restricted hull operators, the M-fuzzifying convexity spaces induced by M-orders are defined conveniently. Then it is shown that M-fuzzifying convexity spaces induced by M-orders are M-fuzzifying JHC and arity ⩽2, and if the M-order is strongly anti-symmetric, then the M-fuzzifying convexity space is an M-fuzzifying convex geometry and its segment operator is an M-fuzzifying geometric interval operator.