Assoc. Prof. Dr. Zlatogor Minchev - SysSec Project Website · Assoc. Prof. Dr. Zlatogor Minchev...
Transcript of Assoc. Prof. Dr. Zlatogor Minchev - SysSec Project Website · Assoc. Prof. Dr. Zlatogor Minchev...
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Assoc. Prof. Dr. Zlatogor Minchev
IMI-BAS, OR Department
IICT-BAS, JTSAC
E-mail: [email protected]
September 12-16, 2011 Borovets, Bulgaria
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- The Model
- The Task
- An Algebraic Interpretation & Optimization Usage
- But, how certain we are?
- Conclusions
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I-SCIP http://www.syssec-project.eu/
*Minchev & Petkova, “Information Processes and Threats in Social Networks: A Case Study”, 2010.
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???
*Moving the objects in-between the four cluster zones (Red, Green, Blue, Yellow) defined in accordance with the Influence/Dependence values measured in percentages [0,100] from the interval [0,1] in I-SCIP program Sensitivity Diagram - SD.
http://www.syssec-project.eu/
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Directed Weighted Graph G = (V,A) V1
V2 Vn
A1
A2
An
A= {A1, A2,….,qi,…,An} with Q weights, where Q = {q1, q2,…qi,…,qn}, q N, q [1, 100]
Z = (qi - )2 + ( pj - )2, s.t. 0 < qi , 0 < pj i=1,…,n, j=1,…,m; , - desired position in the cluster set Minimize Z
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x12
x21
x13
x31
x32
x23
Minimize the Objective Function Z:
S.t. the following constraints:
Solution: ## The following warning was issued while solving: necessary conditions met but sufficient conditions not satisfied Objective value: 0. x12 = 50. x13 = 0. x21 = 50. x23 = 30. x31 = 0. x32 = 15.
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?
Initial Configuration
New Configuration after the Q optimization
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Oden, Moser & Ghattas, “Computer Predictions with Quantified Uncertainty”, SIAM NEWS, November 12, 2010.
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- Use Intuitionistic Fuzzy Sets for Q sets weights values calculation of the arcs A: Influence – A(x), Dependence – A (x)
- Create an IFS Map - Use IFS operators & experts opinion to move around the IFS Map
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*Atanassov, K. “Intutionistic Fuzzy Sets: Theory & Applications”, Springer - Verlag, 1999.
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*Minchev, Z. “Intelligent Scenario Development for CAX”, IOS Press, 2007.
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A
A
0
0
IFS Map
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Nodes uncertainty dynamics example
*Sugihara & May, “Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series”, Nature 344, 734 - 741, 1990.
yi
yi+p
Approximate the solution of the inverse task of the one posed in Sugihara & May, 1990*, taking into account:
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- The presented quadratic optimization application allows fast and easy movement in-between the cluster zones of the model vertices;
- What however is important to be included in this solution is to keep track of the uncertainty changes;
- A possible solution of the uncertainty changes could be obtained by utilization of IFS, experts opinion and IFS operators;
- An interesting future research work could be in the field of IFS map interpretation in 3D space and dynamic uncertainty correction.
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