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Every information system with the above said restriction will be referred to as a situation. An information system contains explicit information about the attitude of each agent to issues being considered in the debate, and will be used to derive various implicit information, necessary to conflicts analysis. In order to express relations between agents we define three basic binary relations on the universe: conflict, neutrality and alliance. To this end we need the following auxiliary function: ⎧ ⎨ 1, if a(x)a(y) = 1 or x = y, 0, if a(x)a(y) = 0 and x = y, φa (x, y) = ⎩ −1, if a(x)a(y) = −1.

The algorithm goes as follows: every discernibility matrix M (B) and a given threshold tr ∈ (0, 1] determines a Boolean function φ(B) = [δ(x, y)], (∗) x,y∈U 2 where [δ(x, y)] = {ΠC : C ⊆ δ(x, y) is minimal such that ρC (x, y) ≥ tr}. Each prime implicant of (*) corresponds to a tr-reduct of A preserving discernibility of objects x, y such that ρA (x, y) ≥ tr. 1 then sets of attributes {a, b, e} and {d, b, e} are the only tr-reducts of the set of attributes {a, b, c, d, e} in the Middle East conflict.

Granular Computing from Rough Set Prospect. IEEE Computational Intelligence Society Newsletter, November (2004). 13. Lin, T. : Granular Computing: Examples, Intuition, and Modeling. In: The Proceedings of the 2005 IEEE International Conference on Granular Computing July 25-27, 2005, Beijing, China, 40-44. 14. : Topological Rough Sets and Granular Computing on Symmetric Binary Relations. J. of General Systems (2006) To appear. 15. : Granular Computing II: Infrastructures for AI-Engineering. In Proc.

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Access 2007 by John Hales


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