In this paper, relations between hull operators which correspond to convex structures formed by cut sets of a given M-fuzzifying convex structure and cut sets of the hull operator of that M-fuzzifying convex structure are discussed. Then concepts of M-fuzzifying Join-Hull Commutativity property and M-fuzzifying Peano property are introduced and characterized, respectively. Also, it is proved that an M-fuzzifying convex structure which has M-fuzzifying JHC property is of arity ≤ 2 and that the segment operator of an M-fuzzifying convex structure of arity ≤2 has M-fuzzifying JHC property iff it has M-fuzzifying Peano property.
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