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Performance Evaluation Method- Grey Relation Analysis

Performance Evaluation Method- Grey Relation Analysis. Rong-Tsu Wang. Origin and History. originated by Professor Deng Ju-Long one of Grey System Theory 1979: 參數不完全大系統的最小信息鎮定 1981:Control Problems of Unknown Systems (the first time described about Grey System)

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Performance Evaluation Method- Grey Relation Analysis

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  1. Performance Evaluation Method- Grey Relation Analysis Rong-Tsu Wang

  2. Origin and History • originated by Professor Deng Ju-Long • one of Grey System Theory • 1979:參數不完全大系統的最小信息鎮定 • 1981:Control Problems of Unknown Systems (the first time described about Grey System) • 1982:Control Problems of Grey Systems (enter into the international market)

  3. Grey System Theory • Definition

  4. Grey System Theory • Scope • Grey Generating • Grey Relation Analysis • Grey Model Construction • Grey Prediction • Grey Decision Making • Grey Control

  5. Definition-1 • Greyness: information is incomplete or unknown • Grey element: an element from an incomplete message • Grey relation: the measurement of changing relations between two systems or between two elements that occur in a system over time

  6. Definition-2 • Grey Relation Analysis based on the degree of similarity or difference of development trends among elements to measure the relation among elements

  7. Characteristics-1 • To analysis the relation grade between “Discrete Series”, is liked as ”Regression Analysis” in traditionally • Weakness of Regression Analysis: • Interactive must be existed among variables • Big sample size is required • Typical distribution of samples • Small variable factors

  8. Characteristics-2 Conduct the data which: • Uncertainty • Multi-input • Discrete data • Small sample size • Unknown distribution of samples

  9. Characteristics-3 • Explanation in Figure 1.0 0.8 X0 ） 0.6 k X1 （ X2 0.4 Xi X3 0.2 0.0 1 2 3 4 5 6 7 8 9 10 k

  10. Basic Math Concept-1 • Factor Space:{P(X);Q} P(X):theme Q:relationship satisfy the following four characteristics: • Existence of key factor • Count ability of factor • Expansion of factor • Independence of factor

  11. Basic Math Concept-2 • Comparison of sequence Suppose a sequence existed as following: Satisfy the following three conditions: • Non-dimension • Scaling • Polarization

  12. Basic Math Concept-3 • Grey Relation Space: • composed of factor space and satisfying comparison • :magnitude of measure

  13. Basic Math Concept-4 • Four axioms of grey relation measure • Axiom 1: Norm Interval

  14. Basic Math Concept-5 • Four axioms of grey relation measure • Axiom 2: Duality Symmetric

  15. Basic Math Concept-6 • Four axioms of grey relation measure • Axiom 3: Wholeness

  16. Basic Math Concept-7 • Four axioms of grey relation measure • Axiom 4: Approachability decrease along with increasing

  17. Basic Math Concept-8 • Grey Relation Grade is called as “Grey Relation Grade” if the function and satisfy the four axioms described as above

  18. Grey Relation Grade-1 • Grey Relation Coefficient if a sequence existed in the grey relation space as following

  19. Grey Relation Grade-1 • Grey Relation Coefficient (Localize) x0:referential sequence; xi:comparative sequence

  20. Grey Relation Grade-2 • Grey Relation Coefficient (Globalize) xi:referential sequence; xj:comparative sequence

  21. Grey Relation Grade-3 • Distinguished coefficient • To reduce its numerical value by getting large • To effect its loss-authenticity and to heighten the remarkable difference among relation coefficients

  22. Grey Relation Grade-4 • Grey Relation Grade if the weight of factor is considered:

  23. Grey Relation Grade-5 • Grey Relation Ordinal suppose if “the relation grade of xi to x0 is superior to xj to x0” represented by be called as “Grey Relation Ordinal of xi and xj”

  24. The Steps for Grey Relation Analysis • Step 1:Vector Normalization

  25. The Steps for Grey Relation Analysis • Step 2:To Calculate Grey Relation Grade

  26. The Steps for Grey Relation Analysis • Step 3:To Group Indicators • Rules of group “high relation grade within the same group” “similar grey relation ordinal within the same group”

  27. The Steps for Grey Relation Analysis • Step 3:To Group Indicators • Illustration of group

  28. The Steps for Grey Relation Analysis • Step 3:To Group Indicators • Illustration of group

  29. The Steps for Grey Relation Analysis • Step 4:To Select Representative Indicators • Principal of selection “the degree of relationship between an indicator and the other indicators in the same group”

  30. The Steps for Grey Relation Analysis • Step 4:To Select Representative Indicators • Method of selection:”Relative Total Score”

  31. illustration • Vector Normalization

  32. illustration • Grey Relation Grade BM1 BM2 BM3 BM4 BM5 BM6 BM7 BM8 BM9 BM10 BM11 BM12 BM13 BM14 BM15 BM16 ================================================================================================= BM1 NA 0.705 0.888 0.594 0.7680.755 0.875 0.689 0.814 0.831 0.600 0.508 0.778 0.544 0.518 0.604 BM2 0.665 NA 0.729 0.772 0.567 0.820 0.606 0.791 0.645 0.714 0.758 0.671 0.478 0.446 0.447 0.461 BM3 0.873 0.738 NA 0.592 0.651 0.7720.755 0.642 0.927 0.932 0.599 0.532 0.804 0.610 0.606 0.604 BM4 0.604 0.738 0.647 NA 0.559 0.701 0.584 0.757 0.639 0.659 0.967 0.785 0.564 0.530 0.533 0.522 BM5 0.799 0.635 0.713 0.494 NA 0.695 0.873 0.568 0.803 0.695 0.498 0.423 0.704 0.595 0.610 0.588 BM6 0.7550.831 0.769 0.664 0.631 NA 0.750 0.645 0.766 0.762 0.700 0.618 0.501 0.420 0.422 0.438 BM7 0.888 0.691 0.833 0.565 0.850 0.751 NA 0.641 0.793 0.766 0.569 0.398 0.809 0.595 0.579 0.657 BM8 0.657 0.810 0.715 0.807 0.641 0.740 0.614 NA 0.678 0.618 0.818 0.715 0.520 0.473 0.476 0.485 BM9 0.784 0.666 0.921 0.566 0.7570.7640.771 0.620 NA 0.904 0.573 0.413 0.630 0.567 0.580 0.577 BM10 0.787 0.626 0.831 0.566 0.633 0.760 0.759 0.563 0.892 NA 0.576 0.439 0.708 0.666 0.659 0.692 BM11 0.610 0.727 0.654 0.968 0.564 0.705 0.589 0.806 0.647 0.667 NA 0.800 0.567 0.531 0.535 0.524 BM12 0.611 0.597 0.686 0.724 0.557 0.534 0.571 0.593 0.662 0.694 0.694 NA 0.831 0.798 0.803 0.783 BM13 0.723 0.460 0.685 0.469 0.768 0.551 0.764 0.493 0.707 0.741 0.471 0.377 NA 0.861 0.868 0.858 BM14 0.647 0.499 0.633 0.414 0.663 0.541 0.676 0.418 0.684 0.742 0.415 0.401 0.886 NA 0.977 0.944 BM15 0.630 0.496 0.624 0.417 0.675 0.535 0.660 0.425 0.685 0.733 0.417 0.399 0.891 0.986 NA 0.951 BM16 0.733 0.513 0.672 0.423 0.685 0.554 0.767 0.444 0.738 0.761 0.424 0.392 0.884 0.947 0.952 NA

  33. illustration • Group Indicators

  34. illustration • Representative Indicators

  35. Application of Program • Turbo PASCAL 7.0 • Interactive • Man-Machine

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