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  1. 1. Chapters 11 & 12, 13: Knowledge Acquisition, Representation and Validation <ul><li>Opening Vignette: American Express </li></ul><ul><li>Improves Approval Selection </li></ul><ul><li>with Machine Learning </li></ul><ul><li>The Problem : Loan Approval </li></ul><ul><li>85 to 90 % Predicted Accurately </li></ul><ul><li>10 to 15 % in Gray Area </li></ul><ul><li>Accuracy of Loan Officer’s Gray Area Decisions were at most 50 % </li></ul>
  2. 2. The Solution <ul><li>ES with Knowledge Acquisition Method of Machine Learning </li></ul><ul><li>Rule Induction Method </li></ul><ul><li>Gray Area: Induced Decision Tree Correctly Predicted 70 % </li></ul><ul><li>Induced Rules Explain Why Rejected </li></ul>
  3. 3. Knowledge Engineering <ul><li>Deals with knowledge acquisition, representation, validation, inferencing, explanation and maintenance </li></ul><ul><li>It is the art of building complex computer programs that represent and reason with knowledge of the world </li></ul><ul><ul><li>(Feigenbaum and McCorduck [1983]) </li></ul></ul>
  4. 4. Knowledge Engineering Process Activities <ul><li>Knowledge Acquisition </li></ul><ul><li>Knowledge Representation </li></ul><ul><li>Knowledge Validation </li></ul><ul><li>Inference </li></ul><ul><li>Explanation and Justification </li></ul>
  5. 5. Knowledge Acquisition <ul><li>Knowledge acquisition is the extraction of knowledge from sources of expertise and its transfer to the knowledge base and sometimes to the inference engine </li></ul><ul><ul><li>Documented (books, manuals, etc.) </li></ul></ul><ul><ul><li>Undocumented (in people's minds) </li></ul></ul><ul><ul><ul><li>From people, from machines </li></ul></ul></ul><ul><ul><li>Knowledge Acquisition from Databases </li></ul></ul><ul><ul><li>Knowledge Acquisition Via the Internet </li></ul></ul>
  6. 6. Difficulties in Knowledge Acquisition <ul><li>Expressing the Knowledge </li></ul><ul><ul><li>expert’s “rules” are compiled and often difficult to articulate </li></ul></ul><ul><ul><li>not available to conscious introspection </li></ul></ul><ul><ul><li>knowledge engineer’s domain “knowledge” </li></ul></ul><ul><li>Transfer to a Machine </li></ul><ul><li>Number of Participants </li></ul><ul><li>Structuring the Knowledge </li></ul>
  7. 7. <ul><li>Experts may lack time or not cooperate </li></ul><ul><li>Testing and refining knowledge is complicated </li></ul><ul><li>Poorly defined methods for knowledge elicitation </li></ul><ul><li>System builders may collect knowledge from one source, but the relevant knowledge may be scattered across several sources </li></ul><ul><li>Collect documented knowledge rather than use experts </li></ul><ul><li>The knowledge collected may be incomplete </li></ul><ul><li>Difficult to recognize specific knowledge when mixed with irrelevant data </li></ul><ul><li>Experts may change their behavior when observed and/or interviewed </li></ul><ul><li>Problematic interpersonal communication between the knowledge engineer and the expert </li></ul>Other Reasons
  8. 8. Overcoming the Difficulties <ul><li>Knowledge acquisition tools with ways to decrease the representation mismatch between the human expert and the program (“learning by being told”) </li></ul><ul><ul><li>Simplified rule syntax </li></ul></ul><ul><ul><li>Natural language processor to translate knowledge to a specific representation </li></ul></ul><ul><li>Critical </li></ul><ul><ul><li>The ability and personality of the knowledge engineer </li></ul></ul><ul><ul><li>Must develop a positive relationship with the expert </li></ul></ul><ul><ul><li>The knowledge engineer must create the right impression </li></ul></ul><ul><li>Computer-aided knowledge acquisition tools </li></ul>
  9. 9. Required Skills and Characteristics of Knowledge Engineers <ul><li>Computer skills </li></ul><ul><li>Tolerance and ambivalence </li></ul><ul><li>Effective communication abilities </li></ul><ul><li>Broad educational background </li></ul><ul><li>Advanced, socially sophisticated verbal skills </li></ul><ul><li>Fast-learning capabilities (of different domains) </li></ul><ul><li>Must understanding organizations and individuals </li></ul><ul><li>Wide experience in knowledge engineering </li></ul><ul><li>Intelligence </li></ul><ul><li>Empathy and patience </li></ul><ul><li>Persistence </li></ul><ul><li>Logical thinking </li></ul><ul><li>Versatility and inventiveness </li></ul><ul><li>Self-confidence </li></ul>
  10. 10. Methods of Knowledge Acquisition: An Overview <ul><li>Manual </li></ul><ul><ul><li>Interviewing ( Structured, Semistructured, Unstructured ) </li></ul></ul><ul><ul><li>Tracking the Reasoning Process </li></ul></ul><ul><ul><li>Observing </li></ul></ul><ul><li>Manual methods: slow, expensive and sometimes inaccurate </li></ul><ul><li>Semiautomatic </li></ul><ul><ul><li>Support Experts Directly </li></ul></ul><ul><li>Automatic (Computer Aided) </li></ul><ul><ul><li>Expert’s and/or the knowledge engineer’s roles are minimized (or eliminated) </li></ul></ul><ul><ul><li>Induction Method </li></ul></ul>
  11. 11. Recommendation <ul><li>Before a knowledge engineer interviews the expert(s) </li></ul><ul><li>1. Interview a less knowledgeable (minor) expert </li></ul><ul><ul><li>Helps the knowledge engineer </li></ul></ul><ul><ul><ul><li>Learn about the problem </li></ul></ul></ul><ul><ul><ul><li>Learn its significance </li></ul></ul></ul><ul><ul><ul><li>Learn about the expert(s) </li></ul></ul></ul><ul><ul><ul><li>Learn who the users will be </li></ul></ul></ul><ul><ul><ul><li>Understand the basic terminology </li></ul></ul></ul><ul><ul><ul><li>Identify readable sources </li></ul></ul></ul><ul><li>2. Next read about the problem </li></ul><ul><li>3. Then, interview the expert(s) (much more effectively) </li></ul>
  12. 12. Tracking Methods <ul><li>Techniques that attempt to track the reasoning process of an expert </li></ul><ul><li>From cognitive psychology </li></ul><ul><li>Most common formal method: </li></ul><ul><li>Protocol Analysis </li></ul>
  13. 13. Protocol Analysis <ul><li>Protocol : a record or documentation of the expert's step-by-step information processing and decision-making behavior </li></ul><ul><li>The expert performs a real task and verbalizes his or her thought process (think aloud) </li></ul>
  14. 15. Observations and Other Manual Methods <ul><li>Observe the Expert Work </li></ul><ul><li>card sorting </li></ul><ul><li>information display boards </li></ul><ul><li>Case analysis </li></ul><ul><li>Critical incident analysis </li></ul><ul><li>Discussions with the users </li></ul><ul><li>Commentaries </li></ul><ul><li>Conceptual graphs and models </li></ul><ul><li>Brainstorming </li></ul><ul><li>Multidimensional scaling </li></ul>
  15. 16. Expert-driven Methods <ul><li>Knowledge Engineers Typically </li></ul><ul><ul><li>Lack Knowledge About the Domain </li></ul></ul><ul><ul><li>Are Expensive </li></ul></ul><ul><ul><li>May Have Problems Communicating With Experts </li></ul></ul><ul><li>Knowledge Acquisition May be Slow, Expensive and Unreliable </li></ul><ul><li>Can Experts Be Their Own Knowledge Engineers? </li></ul><ul><li>Two approaches </li></ul><ul><ul><li>Manual </li></ul></ul><ul><ul><li>Computer-Aided (Semiautomatic) </li></ul></ul><ul><ul><ul><li>To reduce or eliminate the potential problems </li></ul></ul></ul><ul><ul><ul><ul><li>E.g. REFINER+ - case-based system </li></ul></ul></ul></ul><ul><ul><ul><ul><li>TIGON - to detect and diagnose faults in a gas turbine engine </li></ul></ul></ul></ul>
  16. 17. Manual Method: Expert's Self-reports <ul><li>Problems with Experts’ Reports and Questionnaires </li></ul><ul><ul><li>1. Requires the expert to act as knowledge engineer </li></ul></ul><ul><ul><li>2. Reports are biased </li></ul></ul><ul><ul><li>3. Experts often describe new and untested ideas and strategies </li></ul></ul><ul><ul><li>4. Experts lose interest rapidly </li></ul></ul><ul><ul><li>5. Experts must be proficient in flowcharting </li></ul></ul><ul><ul><li>6. Experts may forget certain knowledge </li></ul></ul><ul><ul><li>7. Experts are likely to be vague </li></ul></ul>
  17. 18. Machine Learning <ul><li>Manual and semiautomatic elicitation methods: slow and expensive </li></ul><ul><li>Other Deficiencies </li></ul><ul><ul><li>Frequently weak correlation between verbal reports and mental behavior </li></ul></ul><ul><ul><li>Sometimes experts cannot describe their decision making process </li></ul></ul><ul><ul><li>System quality depends too much on the quality of the expert and the knowledge engineer </li></ul></ul><ul><ul><li>The expert does not understand ES technology </li></ul></ul><ul><ul><li>The knowledge engineer may not understand the business problem </li></ul></ul><ul><ul><li>Can be difficult to validate acquired knowledge </li></ul></ul>
  18. 19. Computer-aided Knowledge Acquisition, or Automated Knowledge Acquisition Objectives <ul><li>Increase the productivity of knowledge engineering </li></ul><ul><li>Reduce the required knowledge engineer’s skill level </li></ul><ul><li>Eliminate (mostly) the need for an expert </li></ul><ul><li>Eliminate (mostly) the need for a knowledge engineer </li></ul><ul><li>Increase the quality of the acquired knowledge </li></ul>
  19. 20. Automated Knowledge Acquisition (Machine Learning) <ul><li>Rule Induction </li></ul><ul><li>Case-based Reasoning </li></ul><ul><li>Neural Computing </li></ul><ul><li>Intelligent Agents </li></ul>
  20. 21. Machine Learning <ul><li>Knowledge Discovery and Data Mining </li></ul><ul><li>Include Methods for Reading Documents and Inducing Knowledge (Rules) </li></ul><ul><li>Other Knowledge Sources (Databases) </li></ul><ul><li>Tools </li></ul><ul><ul><li>KATE-Induction </li></ul></ul><ul><ul><li>CN-2 </li></ul></ul>
  21. 22. Automated Rule Induction <ul><li>Induction : Process of Reasoning from Specific to General </li></ul><ul><li>In ES: Rules Generated by a Computer Program from Cases </li></ul><ul><li>Interactive Induction </li></ul>
  22. 25. Case-based Reasoning (CBR) <ul><li>Adapt solutions used to solve old problems for new problems </li></ul><ul><li>CBR </li></ul><ul><ul><li>Finds cases that solved problems similar to the current one, and </li></ul></ul><ul><ul><li>Adapts the previous solution or solutions to fit the current problem, while considering any difference between the two situations </li></ul></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  23. 26. Finding Relevant Cases Involves <ul><ul><li>Characterizing the input problem, by assigning appropriate features to it </li></ul></ul><ul><ul><li>Retrieving the cases with those features </li></ul></ul><ul><ul><li>Picking the case(s) that best match the input best </li></ul></ul><ul><ul><li>Extremely effective in complex cases </li></ul></ul><ul><ul><li>Justification - Human thinking does not use logic (or reasoning from first principle) </li></ul></ul><ul><ul><li>Process the right information retrieved at the right time </li></ul></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  24. 27. CBR Construction - Special Tools - Examples <ul><li>ART*Enterprise and CBR Express (Inference Corporation) </li></ul><ul><li>KATE (Acknosoft) </li></ul><ul><li>ReMind (Cognitive Systems Inc.) </li></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  25. 28. Example: College Major Advisor <ul><li>who are the experts? </li></ul><ul><li>what do they do? </li></ul><ul><li>how do they do it? </li></ul><ul><li>how do we know? </li></ul><ul><li>how can we represent their knowledge and reasoning process? </li></ul><ul><li>how can the system mimic their reasoning process? </li></ul>
  27. 30. APTITUDE INTERESTS FINANCIAL NEED RECOMMENDATION OF A MAJOR College Major Advisor: Expanded Block Diagram math skills prog. skills manual dexterity computers problem solving repair things desk vs. field job at graduation
  28. 31. math? (yes, no) programming (yes, no) manual dexterity (yes, no) computers (yes, no) problem solving (yes, no) place (desk, field) repair (yes, no) finance (yes, no) APTITUDE INTERESTS SUGGESTED MAJOR College Major Advisor: Dependency Diagram
  29. 32. Induction Table Example <ul><li>Induction tables (knowledge maps) focus the knowledge acquisition process </li></ul><ul><li>Choosing a site for a hospital clinic facility </li></ul>
  30. 34. <ul><li>Row 1: Factors </li></ul><ul><li>Row 2: Valid Factor Values and Choices (last column) </li></ul><ul><li>Table leads to the prototype ES </li></ul><ul><li>Each row becomes a potential rule </li></ul><ul><li>Induction tables can be used to encode chains of knowledge </li></ul>
  31. 35. Knowledge Representation <ul><li>a variety of alternative representations have been developed: rules, frames, semantic nets </li></ul><ul><li>efficiency and effectiveness criteria </li></ul><ul><li>incorporation into ES development software </li></ul>
  32. 36. Major Advantages of Rules <ul><li>Easy to understand (natural form of knowledge) </li></ul><ul><li>Easy to derive inference and explanations </li></ul><ul><li>Easy to modify and maintain </li></ul><ul><li>Easy to combine with uncertainty </li></ul><ul><li>Rules are frequently independent </li></ul>
  33. 37. Production Rules: Drawbacks <ul><li>variables </li></ul><ul><ul><li>unwieldy for large body of knowledge </li></ul></ul><ul><ul><li>only stand-alone, unrelated facts </li></ul></ul><ul><li>production rules </li></ul><ul><ul><li>have to embed all context into antecedent </li></ul></ul><ul><ul><li>not appropriate for all types of problem solving or expertise </li></ul></ul>
  34. 38. Frames <ul><li>an abstraction of a single object or a concept </li></ul><ul><ul><li>frame representing a car </li></ul></ul><ul><li>slots are used to define properties and attributes of a frame </li></ul><ul><li>efficient for hierarchical knowledge structures: supports inheritance </li></ul><ul><li>inference can be done with production rules based on value expectations </li></ul>
  35. 39. KR With Frames ANIMALS MAMMALS REPTILES BIRDS FISH DOG HUMAN WHALE PENGUIN LONG JOHN SILVER Reproduce: Yes Life-Form: Yes Scales: Yes Warmblooded: No Warmblooded: Yes Spinal Cord: Yes Legs: 4 Legs: 2 Legs: 1 Legs: 0 Fins: Yes Legs: 2 Wings: Yes Feathers: Yes Feathers: No Scales: Yes Fins: yes
  36. 40. Semantic Networks <ul><li>network of nodes and links </li></ul><ul><ul><li>nodes = concepts </li></ul></ul><ul><ul><li>links = relationships </li></ul></ul><ul><li>supports certain types of inference </li></ul><ul><ul><li>“ is-a” = inheritance (generalization/specialization) </li></ul></ul><ul><ul><li>“ has-a” = property aggregation </li></ul></ul><ul><ul><li>“ part-of” = physical component aggregation </li></ul></ul>
  38. 42. Semantic Networks <ul><li>advantages </li></ul><ul><ul><li>supports limited inferencing </li></ul></ul><ul><ul><li>good model of long-term memory organization? </li></ul></ul><ul><ul><li>easy to understand </li></ul></ul><ul><li>disadvantages </li></ul><ul><ul><li>quickly becomes unwieldy </li></ul></ul><ul><ul><li>doesn’t distinguish between objects, attributes, or values </li></ul></ul>
  39. 43. KR with Multiple Schemes IF Battery-Age < 5 and Battery_terminals are Uncorroded THEN Battery can work If Battery can work and Fuse is Functional and Wiring is Functional THEN Electric Circuit can work ELECTRIC SUBSYSTEM IGNITION HEADLIGHT LIGHT BULB ELECTRIC CIRCUIT Working Head Light Functional Light Bulb Functional Circuit Working Battery Functional Fuse Functional Wiring 5-Years Old Uncorroded Terminals HAS-A HAS-A HAS-A HAS-A NEEDS-A HAS-A NEEDS-A
  40. 44. Choosing a Representation Scheme <ul><li>should support acquisition, retrieval, and reasoning </li></ul><ul><li>naturalness, uniformity, and comprehensibility </li></ul><ul><li>degree of explicitness </li></ul><ul><li>Modularity and flexibility of the knowledge base </li></ul><ul><li>efficiency of knowledge retrieval and heuristic power </li></ul>
  41. 45. Validation & Verification of the Knowledge Base <ul><li>Evaluation </li></ul><ul><ul><li>Assess an expert system's overall value </li></ul></ul><ul><ul><li>Analyze whether the system would be usable, efficient and cost-effective </li></ul></ul><ul><li>Validation </li></ul><ul><ul><li>Deals with the performance of the system (compared to the expert's) </li></ul></ul><ul><ul><li>Was the “right” system built (acceptable level of accuracy?) </li></ul></ul><ul><li>Verification </li></ul><ul><ul><li>Was the system built &quot;right&quot;? </li></ul></ul><ul><ul><li>Was the system correctly implemented to specifications? </li></ul></ul>
  42. 47. Method for Validating ES <ul><li>Test </li></ul><ul><ul><li>1. The extent to which the system and the expert decisions agree </li></ul></ul><ul><ul><li>2. The inputs and processes used by an expert compared to the machine </li></ul></ul><ul><ul><li>3. The difference between expert and novice decisions </li></ul></ul><ul><li>(Sturman and Milkovich [1995]) </li></ul>
  43. 48. ES Elements to be Validated <ul><li>output, recommendations </li></ul><ul><ul><li>internal validity: completeness and consistency </li></ul></ul><ul><ul><li>external validity: test cases, Turing test </li></ul></ul><ul><li>reasoning </li></ul><ul><li>system/user interface </li></ul><ul><li>efficiency </li></ul><ul><ul><li>hardware, software </li></ul></ul><ul><ul><li>KR and response time </li></ul></ul><ul><li>cost-effectiveness </li></ul>
  44. 49. Inferencing Methods <ul><li>objective </li></ul><ul><ul><li>find logical reasoning path between known data and conclusions </li></ul></ul><ul><li>backward chaining </li></ul><ul><ul><li>goal-directed search </li></ul></ul><ul><ul><li>start with where you want to end up and see if data will get you there </li></ul></ul><ul><li>forward chaining </li></ul><ul><ul><li>data-directed search </li></ul></ul><ul><ul><li>start with what you know and see where it takes you </li></ul></ul>
  45. 50. Example Variables: A = have $10,000 B = younger than 30 C = education at college level D = annual income > = $40,000 E = invest in securities F = invest in growth stocks G = invest in IBM stocks Rules: R1: if A and C then E R2: if D and C then F R3: if B and E then F R4: if B then C R5: if F then G Initial Facts: A and B
  46. 51. Inferencing Methods <ul><li>which way should you go? </li></ul><ul><ul><li>forward chaining tends to collect more data </li></ul></ul><ul><ul><li>forward chaining is good for design problems </li></ul></ul><ul><ul><li>backward chaining tends to examine more rules </li></ul></ul><ul><ul><li>backward chaining is good for diagnosis problems </li></ul></ul><ul><li>vp-expert is backward chaining </li></ul><ul><li>other expert system shells are forward chaining, backward chaining, or both </li></ul>
  47. 52. Inferencing with Uncertainty <ul><li>Uncertainty in AI - Three-step Process </li></ul><ul><li>1. An expert provides inexact knowledge in terms of rules with likelihood values. Also, users may be uncertain with respect to inputs. </li></ul><ul><li>2. The inexact knowledge of the basic set of events can be directly used to draw inferences in simple cases (Step 3) </li></ul><ul><li>3. Working with the inference engine, experts can adjust the Step 1 input after viewing the results in Steps 2 and 3. </li></ul><ul><ul><li>In Step 2: Often the various events are interrelated. </li></ul></ul><ul><ul><li>Necessary to combine the information provided in Step 1 into a global value for the system </li></ul></ul><ul><li>Major integration methods: Bayesian probabilities, theory of evidence, certainty factors and fuzzy sets </li></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  48. 53. Theory of Certainty (Certainty Factors) <ul><li>Uncertainty is represented as a Degree of Belief or Certainty Factor </li></ul><ul><li>Certainty Factors (CF) express belief in an event (or fact or hypothesis) based on evidence (or the expert's assessment) </li></ul><ul><li>CFs are NOT probabilities </li></ul><ul><li>CFs need not sum to 100 </li></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  49. 54. <ul><ul><li>Rule 9 </li></ul></ul><ul><ul><li>if wine_color = red </li></ul></ul><ul><ul><li>and body = full </li></ul></ul><ul><ul><li>and sweetness = dry </li></ul></ul><ul><ul><li>then wine = cabernet_sauvignon cnf 80 </li></ul></ul><ul><ul><li>because &quot;This is a good wine~&quot;; </li></ul></ul><ul><ul><li>Rule 1 </li></ul></ul><ul><ul><li>if main_component = meat </li></ul></ul><ul><ul><li>then wine_color = red; </li></ul></ul><ul><ul><li>  </li></ul></ul><ul><ul><li>Rule 3 </li></ul></ul><ul><ul><li>if has-sauce = yes </li></ul></ul><ul><ul><li>and sauce_type = creamy </li></ul></ul><ul><ul><li>then body = full cnf 90 </li></ul></ul><ul><ul><li>because &quot;Creamy sauce needs full bodied wine&quot;; </li></ul></ul><ul><ul><li>   </li></ul></ul><ul><ul><li>Rule 8 </li></ul></ul><ul><ul><li>if likes = dry </li></ul></ul><ul><ul><li>then sweetness = dry; </li></ul></ul><ul><ul><li>INPUTS: Meat cnf=100; has_sauce=95; creamy=70; likes dry=.60 </li></ul></ul><ul><ul><li>INTERMEDIATE: wine-color=red 100; body=full 63 [min(95,70)*90]; sweetness=dry 60 </li></ul></ul><ul><ul><li>FINAL: wine=cabernet sauvignon 48 [(min 100, 63, 60)*80] </li></ul></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  50. 55. Calculating Confidence Factors <ul><li>For conjunction (AND): </li></ul><ul><ul><li>take min CNF of conditions </li></ul></ul><ul><li>For disjunction (OR): </li></ul><ul><ul><li>when one condition only is true take the CNF of true condition </li></ul></ul><ul><ul><li>when both conditions are true: </li></ul></ul><ul><ul><li>CNF antecedent=max CNF of conditions </li></ul></ul><ul><ul><li>CNF Rule: Antecedent CNF*Consequent CNF </li></ul></ul>
  51. 56. AND <ul><ul><li>IF inflation is high, CF = 50 percent, (A), AND </li></ul></ul><ul><ul><li>IF unemployment rate is above 7 percent, CF = 70 percent, (B), AND </li></ul></ul><ul><ul><li>IF bond prices decline, CF = 100 percent, (C) </li></ul></ul><ul><ul><li>THEN stock prices decline </li></ul></ul><ul><li>CF(A, B, and C) = Minimum[CF(A), CF(B), CF(C)] </li></ul><ul><li>The CF for “stock prices to decline” = 50 percent </li></ul><ul><li>The chain is as strong as its weakest link </li></ul>
  52. 57. <ul><li>IF inflation is low, CF = 70 percent; OR </li></ul><ul><li>IF bond prices are high, CF = 85 percent; THEN stock prices will be high </li></ul><ul><li>Only one IF need be true </li></ul><ul><li>Conclusion has a CF with the maximum of the two </li></ul><ul><ul><li>CF (A or B) = Maximum [CF (A), CF (B)] </li></ul></ul><ul><li>CF = 85 percent for stock prices to be high </li></ul>OR Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  53. 58. Combining Two or More Rules <ul><li>Example: </li></ul><ul><ul><li>R1: IF the inflation rate is less than 5 percent, </li></ul></ul><ul><ul><li>THEN stock market prices go up (CF = 0.7) </li></ul></ul><ul><ul><li>R2: IF unemployment level is less than 7 percent, </li></ul></ul><ul><ul><li>THEN stock market prices go up (CF = 0.6) </li></ul></ul><ul><li>Inflation rate = 4 percent and the unemployment level = 6.5 percent </li></ul><ul><li>Combined Effect </li></ul><ul><ul><li>CF(R1,R2) = CF(R1) + CF(R2)[1 - CF(R1)]; or </li></ul></ul><ul><ul><li>CF(R1,R2) = CF(R1) + CF(R2) - CF(R1)  CF(R2) </li></ul></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ
  54. 59. Assume an independent relationship between the rules <ul><li>Example: Given CF(R1) = 0.7 AND CF(R2) = 0.6, then: </li></ul><ul><li>CF(R1,R2) = 0.7 + 0.6(1 - 0.7) = 0.7 + 0.6(0.3) = 0.88 </li></ul><ul><li>ES tells us that there is an 88 percent chance that stock prices will increase </li></ul>Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ