Fuzzy if-then rules fuzzy database modeling

Transcription

1 Fuzzy if-then rules Associates a condition described using linguistic variables and fuzzy sets to a conclusion A scheme for capturing knowledge that involves imprecision fuzzy database modeling

2 Two types of fuzzy rules Fuzzy mapping rules Af functional mapping relationship between inputs and an output using linguistic terms Function approximation in system identification and artificial neural network Fuzzy implication rules A generalized logic implication relationship between two logic formula Related to classical two-valued logic and multivalued logic

3 Fuzzy implication rules A generalization of implication in two value logic. To reason with ideas and statements that are imprecise

4 Fuzzy mapping rules Function approximation techniques Global modeling Using one mathematical structure Linear, second-order d polynomial l Local modeling Fuzzy rule-based function approximation Superimposition functions (B-splines, Taylor expansions) Partition-based approximate Partitioning the input space of the function and approximate the function in each partitioned region

5 Fuzzy rule-based function Fuzzy partition approximation Allowing a sub region to partially overlap with neighboring sub region Partitioning the input space of the function

6 Partial matching Calculate the matching degree between a fuzzy input A and a fuzzy condition i A

7 Fuzzy rule-based models Fuzzy partition Mapping of fuzzy sub regions to local model Fusing of multiple local models Defuzzification

8 Classical partition A classical partition of a space is a collection of disjoint i subspaces whose union is the entire space

9 Fuzzy partition Generalizes classical partition so that the transition from one subspace into a neighbor one is smooth Fuzzy partition 9

10 Piecewise linear approximation A nonlinear global model can often be approximated dby a set of flinear local lmodels

11 Mapping of fuzzy space to local General form model Four different types of local model Crisp constant Fuzzy constant Linear model Nonlinear model

12 Fusion of local models through interpolative reasoning Interpolative reasoning If-then rule1 w 1 w 2 Overall opinion If-then rule2 w 3 w 4 If-then rule3 If-then rule

13 Interpret a possibility distribution Linguistic approximation A qualitative interpretation Defuzzification A quantitative summary Mean of maximum (MOM) Center of area (COA) The height method

14 Mean of maximum (MOM) Calculates the average of those output values that have the highest h possibility degrees

15 Center of area (COA) Calculate the center-of-gravity (the weighted sum of the results)

16 The height method 1. Convert the consequent membership function C i into crisp consequent y = c i 2. Apply the centroid defuzzification w i is the degree to which the ith rule matches the input data

17 Fuzzy rule-based models Takagi-Sugeno-Kang Standard Additive Model

18 If speed is med and distance is small then force is negative If speed is zero and distance is large then force is positive Mamdani model Linguistic rules Input form output membership of rule i Matching degree of rule i, condition j Aggregation of outputs from all rules

19 TSK model Linguistic rules To reduce the number of rules output

20 TSK model (example)

21 Standard Additive Model Linguistic rules Output

22 Comparison of SAM and Mamdani SAM Mamdani inputs crisp Crisp & fuzzy Composition scaling Clipping operator (min) Fusion method addition max Defuzzification Centroids Not insist

23 Multiconditional Approximate Reasoning

24 Step 1. Step

25

26

27