Granular Computing: A new problem Solving Paradigm

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. Summary Rough Computing Equivalence Relation Neighborhood Concept Binary Relation 2. Details

Rough Computing A partition is a set of (1) disjoint subsets, (2) a cover Class B i, j, k f, g, h Class C ClassA l, m, n

Rough Computing • X  Y (equivalence) if and only if • both belong to the same class

Rough Computing An Equivalence Relation Class B i j  k f g  h Class C ClassA l  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 B i, j, k f, g, h Class C ClassA l, 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 BN -Theory • Can they be partitioned? France, German C US, Russia UK?

CIR-classes • CIR classes do overlap (Conflict of Interests) US, UK, Iraq, . . . USSR

CIR & IAR • Complement of CIR: an equivalence relation US, UK, . . . Iraq, . . . German, . . .

ACWSP • CIR: Anti-reflexive, symmetric, anti-transitive IJAR-classes CIR-class IJAR-classes

Trojan Horses Direct Information flow(DIF) Grader DIF Trojan horse(DIF) Professor CIF Students

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 YCIRX • To derive a contradiction

ACWSP • X=X0X1 implies X1  [X] CIRX = CIRX1 . . . Y=Xn  [X] CIRX = CIRXn = CIRY Y  CIRX Contradiction

Granular Computing: A new problem Solving Paradigm