Download presentation

Presentation is loading. Please wait.

Published byKoby Jason Modified over 2 years ago

1
Linguistic Summarization Using IF-THEN Rules Authors: Dongrui Wu, Jerry M. Mendel and Jhiin Joo

2
Introduction Type I & Type II Fuzzy Systems Dataset Description Linguistic Descriptions Implementation

3
Type-1 Fuzzy Sets Crisp sets, where x A or x A Membership is a continuous grade [0,1] Membership a value 1.77 0 1 Height (m) Degree of “Tall-ness” 0.6

4
Interval Type-2 Fuzzy Sets Interval type-2 fuzzy sets - interval membership grades X is primary domain J x is the secondary domain All secondary grades ( A (x,u)) equal 1 A (x) is the secondary membership function at x (vertical slice representation) A = {((x,u), 1) | x X, u J x, J x [0,1]} ~ ~

5
Interval Type-2 Fuzzy Sets Tall 0 1 Height (m) ~ Upper Membership Function Lower MF Tall Type -1 MF = FOU (explained in next slide) Membership no longer crisp

6
~ Interval Type-2 Fuzzy Sets Fuzzification: 1.8 0.42 Tall 0 1 Height (m) ~ 0.78 Tall (1.8) = [0.42,0.78]

7
Interval Type-2 Fuzzy Sets FOU Vertical slice of a Type 2 membership function – Indicating 3D structure of Type 2 Mendel Jerry M. and. Bob John Robert I, “Type-2 Fuzzy Sets Made Simple.” IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 10, NO. 2, APRIL 2002.

8
Haberman’s survival Data set - UIUC From a study conducted between 1958 and 1970 at the University of Chicago's Billings Hospital on the survival of patients who had undergone surgery for breast cancer. Attribute Information: 1. Age of patient at time of operation (numerical) 2. Patient's year of operation (year - 1900, numerical) 3. Number of positive axillary nodes detected (numerical) 4. Survival status (class attribute) -- 1 = the patient survived 5 years or longer -- 2 = the patient died within 5 year

9
Linguistic Summarizations: IF - THEN Type 1: IF AGE is 35 AND YEAR is 1962, THEN SURVIVAL is YES Type 2: IF AGE is around 35 AND YEAR is around 1962, THEN SURVIVAL is YES

10
Some parameters T – Degree of Truth; an assessment of Validity – T increases as more data satisfying antecedent also satisfy consequent

11
Some parameters C – Degree of Sufficient Coverage – Determines if sufficient data satisfies a rule (trigger) – C=f(rc) U – Degree of Usefulness – Indicates how useful a rule is – A rule is useful iff it has high degree of truth: most of the data satisfy the rule’s antecedents as well as its consequent It has sufficient coverage: enough data are described by it. – U=min(T,C) It depends on the parameters described earlier

12
Some parameters O – Degree of Outlier – Indicates if a rule describes the outliers instead of most of the data – If T=0, O=0 since no data is described by the rule – Described by the complement of T & C since they both depend on the data (not outlier)

13
Some parameters S - Degree of Simplicity Determined by the length of the summary L = number of antecedents Simplest rule: S=1 (one antecedent and one consequent)

14
MAMC Rules Multi Antecedent Multi consequent

15
Implementation Each case represented as a piecewise linear curve Blue – strength of supporting rule Red- cases violating given rule Black- Irrelevant Figure shows if C is used for ranking, T may/may not be high

16
Implementation Figure shows if U is used for ranking, high U indicates high T & C : useful rule

17
Conclusions An important method of ranking rules using the parameters: – Degree of Truth – Degree of Sufficient Coverage – Degree of Usefulness – Degree of Outlier – Degree of Simplicity

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on hydrogen fuel cell vehicles for sale Ppt on septic abortion Ppt on special types of chromosomes mutation Ppt on informal letter writing Ppt on reflection of light for class 10th Ppt on death penalty in india Ppt on natural resources and conservation job Complete ppt on cloud computing 360 degree customer view ppt on mac Ppt on amplitude shift keying transmitter