13th International Conference on Membrane Computing - MTA Sztaki

Membranes with local environments
– The requirements from the base set point of view are:
• PASM(U) is bounded in occurrences by n (n ∈ N), if for all M ∈ B
M(a) ≤ n for all a ∈ U;
• PASM(U) is single layered, if B ∈ B, B ′ ∈ B \ {B} then B ⋢ B ′ for
all B ∈ B;
• PASM(U) is one–layered, if B 1 ⊓ B 2 = ∅ for all B 1 , B 2 ∈ B, B 1 ≠ B 2 .
– The requirements from the set D B point of view are:
• PASM(U) is a set–type union partial mset approximation space, if B 1 ⊔
B 2 ∈ D B for all B 1 , B 2 ∈ B;
• PASM(U) is a minimal set–type union partial mset approximation space,
if D B is given by the following inductive definition:
1. ∅ ∈ D B ;
2. B ⊆ D B ;
3. if B 1 , B 2 ∈ B, then B 1 ⊔ B 2 ∈ D B ;
• PASM(U) is a strict set–type union partial mset approximation space,
if D B is given by the following inductive definition:
1. ∅ ∈ D B ;
2. B ⊆ D B ;
3. if B ′ ⊆ B, then ⊔ B ′ ∈ D B ;
• PASM(U) is a mset–type union partial mset approximation space, if
B 1 ⊕ B 2 ∈ D B for all B 1 , B 2 ∈ B;
• PASM(U) is an intersection type partial mset approximation space, if
B 1 ⊓ B 2 ∈ D B for all B 1 , B 2 ∈ B;
• PASM(U) is total, if for all M ∈ MS