Granular Computing: A new problem Solving Paradigm
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Granular Computing: A new problem Solving Paradigm
Tsau Young (T.Y.) Lin
Department of Computer Science
San Jose State University
San Jose, CA 95192
tylin@cs.sjsu.edu
Outline
1. SummaryRough Computing
Equivalence Relation
Neighborhood Concept
Binary Relation
2. Details
Rough Computing
A partition is a set of (1) disjoint subsets,
(2) a cover
Class A
Class B
f, g, h i, j, k
Class Cl, m, n
Rough Computing
• X Y (equivalence)
if and only if
• both belong to the same class
Rough Computing
An Equivalence Relation
Class A
Class B
f g h i j k
Class Cl m n
Equivalence Relation
• X X (Reflexive)
• X Y implies Y X (Symmetric)
• X Y, Y Z implies X Z (Transitive)
Neighborhood Concept
• i j k Class B
i j k Class B In spite of a technical error,
• the idea was, and still is, fascinating
Introduction
• An aggressive model (ACWSP) was proposed by Lin the same year (1989) that keeps the same spirit and corrects the error
• Lost some Strength
Introduction
• Lost Interests until
• A practical way of construction ACWSP was introduced 2000
Brewer and Nash Requirements
• A set of impenetrable Chinese Great Walls
• No corporate data that are in conflict can be stored in the same side of Walls
Brewer and Nash -Theory
• Corporate data are decomposed into
Conflict of Interest Classes(CIR-classes)
• Walls are built around the CIR-classes
• Corporate data is called an object (tradition)
BN -Theory
All objects
Class A
Class B
f, g, h i, j, k
Class Cl, m, n
Is CIR Transitive?
• US (conflict) Russia
• UK Russia
• UK ? US
Is CIR Reflexive?
• US (conflict) US ?
• Is CIR self conflicting?
Is CIR Symmetric?
• US (conflict) USSR
implies
• USSR (conflict) US ?
• YES
BN -Theory• Can they be partitioned?
BN -Theory
CUS, Russia
UK?
France, German
CIR-classes
• CIR classes do overlap (Conflict of Interests)
US, UK, Iraq, . . .
USSR
CIR & IAR
• Complement of CIR: an equivalence relation
Iraq, . . .US, UK, . . .
German, . . .
ACWSP
• CIR: Anti-reflexive, symmetric, anti-transitive
CIR-class IJAR-classes
IJAR-classes
ACWSP
• CIR: Anti-reflexive, symmetric, anti-transitive
CIR-class IJAR-classes
IJAR-classes
ACWSP
• CIR: Anti-reflexive, symmetric, anti-transitive
CIR-class IJAR-classes
IJAR-classes
Trojan Horses
Direct Information flow(DIF)
Professor
Grader
StudentsCIF
DIF Trojan horse(DIF)
ACWSP
• CIR (with three conditions) only allows information sharing within one IJAR-class
• An IJAR-class is an equivalence class; so there is no danger the information will spill to outside.
• No Trojan horses could occur
SCWSP
• Simple CWSP (SVWSP)
No DIF: x y (direct information flow)(x, y) CIR
ACWSP
• Strong CWSP(ACSWP)
No CIF: x . . . y ((composite) information flow)
(x, y) CIR
ACWSP
• Theorem If CIR is anti-reflexive, symmetric and anti-transitive, then
• Simple CWSP Strong CWSP
ACWSP
CIF =a sequence of DIFs
CIF: X=X0 X1 . . . Xn=Y
YCIRX
• To derive a contradiction
ACWSP
• X=X0 X1 implies
X1 [X] CIRX = CIRX1
. . .
Y=Xn [X] CIRX = CIRXn = CIRY
Y CIRX Contradiction
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