1 Pertemuan 21 MEMBERSHIP FUNCTION Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menjelaskan konsep fungsi keanggotaan pada logika fuzzy.

3 Outline Materi Pengertian Fungsi keanggotaan. Derajat keanggotaan.

4 FUZZY LOGIC Lotfi A. Zadeh “Fuzzy Sets”, Information and Control, Vol 8, pp ,1965. Clearly, the “class of all real numbers which are much greater than 1,” or “the class of beautiful women,” or “the class of tall men,” do not constitute classes or sets in the usual mathematical sense of these terms (Zadeh, 1965).

5 PROF. ZADEH Fuzzy theory should not be regarded as a single theory, but rather a methodology to generalize a specific theory from being discrete, to being more continuous

6 WHAT IS FUZZY LOGIC  Fuzzy logic is a superset of conventional (boolean) logic  An approach to uncertainty that combines real values [0,1] and logic operations  In fuzzy logic, it is possible to have partial truth values  Fuzzy logic is based on the ideas of fuzzy set theory and fuzzy set membership often found in language

7 WHY USE FUZZY LOGIC ?  An Alternative Design Methodology Which Is Simpler, And Faster Fuzzy Logic reduces the design development cycle Fuzzy Logic simplifies design complexity Fuzzy Logic improves time to market  A Better Alternative Solution To Non-Linear Control Fuzzy Logic improves control performance Fuzzy Logic simplifies implementation Fuzzy Logic reduces hardware costs

8 WHEN USE FUZZY LOGIC Where few numerical data exist and where only ambiguous or imprecise information maybe available.

9 FUZZY SET In natural language, we commonly employ: classes of old people Expensive cars numbers much greater than 1 Unlike sharp boundary in crisp set, here boundaries seem vague Transition from member to nonmember appears gradual rather than abrupt

10 CRISP AND FUZZY

11 FUZZY SET AND MEMBERSHIP FUNCTION Universal Set X – always a crisp set. Crisp set assigns value {0,1} to members in X Fuzzy set assigns value [0,1] to members in X These values are called the membership functions . Membership function of a fuzzy set A is denoted by : A: X  [0,1] A: [x1/  1, x2/  …, xn/  n}

12 HIMPUNAN CRISP DAN FUZZY Himpunan kota yang dekat dengan Bogor A = { Jakarta, Sukabumi, Cibinong, Depok }  CRISP B = { (0.7 /Jakarta), (0.6 /Sukabumi), (0.9 /Cibinong), (0.8/Depok) }  FUZZY Angka 0.6 – 0.9 menunjukkan tingkat keanggotaan ( degree of membership )

13 CONTOH CRISPFUZZY

14 TINGGI BADAN

15 SEASONS Time of the year Membership SpringSummerAutumnWinter

16 AROUND Measurements Membership

17 AGE Age Membership old more or less old young very young not very young

18 MEMBERSHIP FUNCTION (a)(d)(g)(j) (b) (e) (h)(k) (c) (f) (i) (l)

19 SET OPERATION Membership A B A  BA  BA  B

20 SET OPERATION A B A  B A  B  A

21 LINGUISTIC VARIABLES Linguistic variable is ”a variable whose values are words or sentences in a natural or artificial language”. Each linguistic variable may be assigned one or more linguistic values, which are in turn connected to a numeric value through the mechanism of membership functions.

22 LINGUISTIC VARIABLES Fuzzy linguistic terms often consist of two parts: 1) Fuzzy predicate : expensive, old, rare, dangerous, good, etc. 2) Fuzzy modifier: very, likely, almost impossible, extremely unlikely, etc. The modifier is used to change the meaning of predicate and it can be grouped into the following two classes: a)Fuzzy truth qualifier or fuzzy truth value: quite true, very true, more or less true, mostly false, etc. b)Fuzzy quantifier: many, few, almost, all, usually, etc.

23 FUZZY PREDICATE Fuzzy predicate – If the set defining the predicates of individual is a fuzzy set, the predicate is called a fuzzy predicate Example – “z is expensive.” – “w is young.” – The terms “expensive” and “young” are fuzzy terms. Therefore the sets “expensive(z)” and “young(w)” are fuzzy sets

24 FUZZY PREDICATE When a fuzzy predicate “x is P” is given, we can interpret it in two ways : P(x) is a fuzzy set. The membership degree of x in the set P is defined by the membership function  P(x)  P(x) is the satisfactory degree of x for the property P. Therefore, the truth value of the fuzzy predicate is defined by the membership function : Truth value =  P(x)

25 FUZZY VARIABLES Variables whose states are defined by linguistic concepts like low, medium, high. These linguistic concepts are fuzzy sets themselves. LowHigh Very high Temperature Membership Trapezoidal membership functions

26 FUZZY VARIABLES Usefulness of fuzzy sets depends on our capability to construct appropriate membership functions for various given concepts in various contexts. Constructing meaningful membership functions is a difficult problem –GAs have been employed for this purpose.

27 EXAMPLE if speed is interpreted as a linguistic variable, then its term set T (speed) could be T = { slow, moderate, fast, very slow, more or less fast, sligthly slow, ……..}. where each term in T (speed) is characterized by a fuzzy set in a universe of discourse U = [0; 100]. We might interpret slow as “ a speed below about 40 km/h" moderate as “ a speed close to 55 km/h" fast as “ a speed above about 70 km/h"

28 SPEED Values of linguistic variable speed.

29 NORMALIZED DOMAIN INPUT NB (Negative Big), NM (Negative Medium) NS (Negative Small), ZE (Zero) PS (Positive Small), PM (Positive Medium) PB (Positive Big) A possible fuzzy partition of [-1; 1].

30 MEMBERSHIP FUNCTION