1 / 23

Fuzzy Expert System

Fuzzy Expert System. Fuzzy Expert System. Fuzzy Sets Fuzzy representation in computer Linguistic variables and hedges Operations of fuzzy sets Fuzzy rules Reasoning with fuzzy rules Fuzzy inference Building fuzzy expert system. Basic Notions. Fuzzy Logic.

patience-benjamin
Download Presentation

Fuzzy Expert System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fuzzy Expert System

  2. Fuzzy Expert System • Fuzzy Sets • Fuzzy representation in computer • Linguistic variables and hedges • Operations of fuzzy sets • Fuzzy rules • Reasoning with fuzzy rules • Fuzzy inference • Building fuzzy expert system Basic Notions

  3. Fuzzy Logic Fuzzy logic is determined as a set of mathematical principles for knowledge representation based on degrees of membership rather than on crisp membership of classical binary logic Fuzzy Logic

  4. Fuzzy Logic • Multi-valued • Deals with degree of membership • Degrees of truth • Uses continuum of logical val;ues between 0 (completely false) and 1(completely true) Fuzzy Logic

  5. Fuzzy Sets • Refer page 89 • The basic idea of fuzzy set theory ; an element belongs to a fuzzy set with certain degree of membership. • Not either true or false, but partly true(false) to any degree • Taken as a real number in the interval • Refer table 4.1, fig. 4.2. Fuzzy set

  6. Fuzzy set theory • Crisp set • Let X be the universe of discourse and its elements be denoted as x. crisp set A of X is defined as function fA(x) of A • fA(x): X  0,1 • Where

  7. Fuzzy set theory • Fuzzy set • Fuzzy set A of universe X is defined by function A(x) called membership function of set A • A(x): X  [0,1] • where A(x) = 1 if x is totally in A • A(x) = 0 if x is not in A 0 < A(x) < 1 if x is partly in A

  8. The representation of fuzzy set • Determine the membership function • Method to determine membership function • Single expert • Multiple experts • Self generated by ANN, learn the data & derive the fuzzy sets.

  9. The representation of fuzzy set • Refer ‘tall men’ example (figure 4.3, 4.4) • Fuzzy set of tall men in figure 4.3 can be represented as fit-vector Tall men = (0/180, 0.5/185, 1/190) or Tall men = (0/180, 1/190) • Fuzzy set of short and average men Short men = (1/160, 0.5/165, 0/170) or Short men = (1/160, 0/170) average men = (0/165, 1/175, 0/185)

  10. Linguistic variables and hedges • A fuzzy variable • E.g. the statement “John is tall” implies that the linguistic variable John takes the linguistic valuetall • In fuzzy ES linguistic variables are used in fuzzy rules IF wind is strong THEN sailing is good IF project duration is long THEN completion_risk is high IF the speed is slow THEN stopping_distance is short

  11. Linguistic variables and hedges • E.g. The linguistic variable speed have range between 0 and 220 km/hour may include fuzzy subsets as very slow, slow, medium, fast and very fast • Hedges - fuzzy set qualifiers • Carries by a linguistic variable • Terms that modifies fuzzy sets • Includes adverb I.e. very, somewhat, quite, more or less and slightly • Can modify verbs, adjectives, adverbs or thw whole sentence (pg 95)

  12. Linguistic variables and hedges • Hedges act as operations • Very perform concentration and creates new subset • E.g. tall men derive the subset very tall men • Dilation : the of more or less tall men is broader than the set of tall men. • Refer figure 4.5. • Refer table 4.2

  13. Fuzzy sets operations • Complement • Containment • Intersection • Union • Commutativity • Associativity • Distrubutivity • Indempotency • Identity • Involution • Transitivity • De Morgan’s law operations

  14. Fuzzy rules • Capturing human knowledge in fuzzy rules • Form of fuzzy rules: IF x is A THEN y is B Where x and y are linguistic variables; A and B are linguistic values determined by fuzzy sets

  15. Fuzzy rules • Difference with classical rules • Classical IF-THEN rule uses binary logic e.g. • Rule 1: IF speed is > 100 THEN the stopping_distance is long • Rule 2: IF speed is < 40 THEN stopping_distance is short • The variable speed can have any numerical value between 0-220km/h • The linguistic variables stopping_distance can only take either long or short.

  16. Fuzzy rules • Difference with classical rules • Fuzzy IF-THEN rules uses binary logic e.g. • Rule 1: IF speed is fast THEN the stopping_distance is long • Rule 2: IF speed is slow THEN stopping_distance is short • The variable speed can have any numerical value between 0-220km/h but include fuzzy sets range , slow, medium and fast • The linguistic variables stopping_distance can be between 0 and 300m and may take fuzzy sets as short, medium or long • Fuzzy expert systems merge the rules and consequently cut the number of rules at least 90%

  17. Reasoning with Fuzzy rules • Includes 2 distinct part • Evaluating the rule antecedent (the IF part) • Implication or applying the result to the consequent (the THEN part) • Mechanism • In classical rule based system • If the rule antecedent is true, the consequent is also true • In fuzzy systems, • All rules fires to some extent, • Partially fire • If the antecedent is true to some degree of membership, then the consequent is also true to that same degree • Discuss fig. 4.8, 4.9

  18. Reasoning with Fuzzy rules • A fuzzy rule can have • Multiple parts of antecedent • Multiple parts of consequent (see example pg 105) • In general fuzzy expert system incorporates not one but several rules that describe expert knowledge

  19. Reasoning with Fuzzy rules • The output of each rule is a fuzzy set but need to obtain a single number representing the ES output • The output of the fuzzy sets are combined and transformed into a single number by.. • Aggregates all output fuzzy sets into a single output fuzzy set • Then defuzzifies the resulting fuzzy set into a single number • Fuzzy inference

  20. Fuzzy inference • A process of mapping from a given input to an output using the fuzzy theory. • Mamdani-style inference • Sugeno-style inference

  21. Fuzzy inference • Mamdani-style inference • Involve 4 steps • Fuzzification of the input variables • Rule evaluation • Aggregation of the rule output • Defuzzification • Refer example in pg 106-112

  22. Building fuzzy ES • An iterative process that involves defining fuzzy sets and fuzzy rules, evaluating and the tuning the system to meet the specified requirement.

  23. Building fuzzy ES • Specify the problem and define linguistic variables • Determine fuzzy sets • Elicit and construct fuzzy rules • Encode the fuzzy sets, fuzzy rules and procedures to perform fuzzy inference into the ES • Evaluate and tune the system 5 steps

More Related