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Exploring Granular Computing: New Approaches to Problem Solving in Computer Science

This paper presents a novel framework in Granular Computing, discussing its benefits in problem-solving paradigms. The concept revolves around rough computing and its equivalence relations, exploring the neighborhood and partitioning principles through various classes. An example is given with Brewer and Nash’s theory on corporate data conflicts and the construction of impenetrable walls to protect sensitive information. The findings suggest that refined models can avoid data conflicts while maintaining effective information sharing within organized classes, paving the way for advancing computational intelligence.

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Exploring Granular Computing: New Approaches to Problem Solving in Computer Science

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  1. 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

  2. Outline 1. Summary Rough Computing Equivalence Relation Neighborhood Concept Binary Relation 2. Details

  3. 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

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

  5. Rough Computing An Equivalence Relation Class B i j  k f g  h Class C ClassA l  m  n

  6. Equivalence Relation • X  X (Reflexive) • X  Y implies Y X (Symmetric) • X  Y, Y Z implies X  Z (Transitive)

  7. 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

  8. 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

  9. Introduction • Lost Interests until • A practical way of construction ACWSP was introduced 2000

  10. 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

  11. 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)

  12. BN -Theory All objects Class B i, j, k f, g, h Class C ClassA l, m, n

  13. Is CIR Transitive? • US (conflict) Russia • UK Russia • UK  ? US

  14. Is CIR Reflexive? • US (conflict) US ? • Is CIR self conflicting?

  15. Is CIR Symmetric? • US (conflict) USSR implies • USSR (conflict) US ? • YES

  16. BN -Theory BN -Theory • Can they be partitioned? France, German C US, Russia UK?

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

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

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

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

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

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

  23. 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

  24. SCWSP • Simple CWSP (SVWSP) No DIF: x  y (direct information flow) • (x, y)  CIR

  25. ACWSP • Strong CWSP(ACSWP) No CIF: x . . . y ((composite) information flow) • (x, y)  CIR

  26. ACWSP • Theorem If CIR is anti-reflexive, symmetric and anti-transitive, then • Simple CWSP  Strong CWSP

  27. ACWSP CIF =a sequence of DIFs CIF: X=X0X1 . . .  Xn=Y YCIRX • To derive a contradiction

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

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