Penerapan Variabel Linguistik dlm Sehari-hari

While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts.[4]

A linguistic variable such as age may have a value such as young or its antonym old. However, the great utility of linguistic variables is that they can be modified via linguistic hedges applied to primary terms. The linguistic hedges can be associated with certain functions. For example, L. A. Zadeh proposed to take the square of the membership function. This model, however, does not work properly. For more details, see the references.

Contoh Aplikasi Variabel Linguistik Fuzzy

Fuzzy set theory defines fuzzy operators on fuzzy sets. The problem in applying this is that the appropriate fuzzy operator may not be known. For this reason, fuzzy logic usually uses IF-THEN rules, or constructs that are equivalent, such as fuzzy associative matrices.

Rules are usually expressed in the form:
IF variable IS property THEN action

For example, a simple temperature regulator that uses a fan might look like this:

IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain level
IF temperature IS hot THEN speed up fan

There is no "ELSE" – all of the rules are evaluated, because the temperature might be "cold" and "normal" at the same time to different degrees.

The AND, OR, and NOT operators of boolean logic exist in fuzzy logic, usually defined as the minimum, maximum, and complement; when they are defined this way, they are called the Zadeh operators. So for the fuzzy variables x and y:

NOT x = (1 - truth(x))
x AND y = minimum(truth(x), truth(y))
x OR y = maximum(truth(x), truth(y))

There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as "very", or "somewhat", which modify the meaning of a set using a mathematical formula.


Introduction of Fuzzy Logic

Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. In contrast with "crisp logic", where binary sets have binary logic, fuzzy logic variables may have a truth value that ranges between 0 and 1 and is not constrained to the two truth values of classic propositional logic.[1] Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.

Fuzzy logic emerged as a consequence of the 1965 proposal of fuzzy set theory by Lotfi Zadeh.[2][3] Though fuzzy logic has been applied to many fields, from control theory to artificial intelligence, it still remains controversial among most statisticians, who prefer Bayesian logic, and some control engineers, who prefer traditional two-valued logic.

Fuzzy logic and probabilistic logic are mathematically similar – both have truth values ranging between 0 and 1 – but conceptually distinct, due to different interpretations—see interpretations of probability theory. Fuzzy logic corresponds to "degrees of truth", while probabilistic logic corresponds to "probability, likelihood"; as these differ, fuzzy logic and probabilistic logic yield different models of the same real-world situations.


DEGREE of Truth

Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. For example, let a 100 ml glass contain 30 ml of water. Then we may consider two concepts: Empty and Full. The meaning of each of them can be represented by a certain fuzzy set. Then one might define the glass as being 0.7 empty and 0.3 full. Note that the concept of emptiness would be subjective and thus would depend on the observer or designer. Another designer might equally well design a set membership function where the glass would be considered full for all values down to 50 ml. It is essential to realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of randomness.

A probabilistic setting would first define a scalar variable for the fullness of the glass, and second, conditional distributions describing the probability that someone would call the glass full given a specific fullness level. This model, however, has no sense without accepting occurrence of some event, e.g. that after a few minutes, the glass will be half empty. Note that the conditioning can be achieved by having a specific observer that randomly selects the level for the glass, a distribution over deterministic observers, or both.

Consequently, probability has nothing in common with fuzziness, these are simply different concepts which superficially seem similar because of using the same unit interval of real numbers [0,1]. Still, since theorems such as De Morgan's have dual applicability and properties of random variables are analogous to properties of binary logic states, one can see where the confusion might arise.

Variabel Linguistik Fuzzy

Variabel linguistik adalah variabel yang bernilai kata/kalimat, bukan angka. Sebagai alasan menggunakan kata/kalimat daripada angka karena peranan linguistik kurang spesifik dibandingkan angka, namun informasi yang disampaikan lebih informatif. Variabel linguistik ini merupakan konsep penting dalam logika fuzzy dan memegang peranan penting dalam beberapa aplikasi.

Jika “kecepatan” adalah variabel linguistik, maka nilai linguistik untuk variabel kecepatan adalah, misalnya “lambat”, “sedang”, “cepat”. Hal ini sesuai dengan kebiasaan manusia sehari-hari dalam menilai sesuatu, misalnya : “Ia mengendarai mobil dengan cepat”, tanpa memberikan nilai berapa kecepatannya.

Konsep tentang variabel linguistik ini diperkenalkan oleh Lofti Zadeh. Dalam variabel linguistik ini menurut Zadeh dikarakteristikkan dengan (X, T(x), U, M) dimana :
X = nama variabel (variabel linguistik)
T(x) atau T = semesta pembicaraan untuk x atau disebut juga nilai linguistik dari x
U = jangkauan dari setiap nilai samar untuk x yang dihubungkan dengan variabel dasar U
M = aturan semantik yang menghubungkan setiap X dengan artinya.

Fungsi Keanggotaan Fuzzy

Ada dua cara mendefinisikan keanggotaan himpunan fuzzy, yaitu secara numeris dan fungsional. Definisi numeris menyatakan fungsi derajat keanggotaan sebagai vektor jumlah yang tergantung pada tingkat diskretisasi. Misalnya, jumlah elemen diskret dalam semesta pembicaraan (Lootsma, 1997).

Definisi fungsional menyatakan derajat keanggotaan sebagai batasan ekspresi analitis yang dapat dihitung. Standar atau ukuran tertentu pada fungsi keanggotaan secara umum berdasar atas semesta X bilangan real.

Definisi :
Misalkan X adalah suatu himpunan tak kosong. Suatu himpunan fuzzy di X dikarakteristikkan melalui fungsi keanggotaan

Logika Fuzzy

Logika fuzzy merupakan pengembangan dari teori himpunan fuzzy yang diprakarsai oleh Prof. Lofti Zadeh dari University California USA, pada tahun 1965. Ia berpendapat bahwa logika benar dan salah dari logika bolean tidak dapat mengatasi masalah gradasi yang berada pada dunia nyata. Untuk mengatasi masalah gradasi yang tidak terhingga tersebut, Zadeh mengembangkan sebuah himpunan fuzzy. Tidak seperti logika bolean, logika fuzzy mempunyai nilai yang kontinu. Fuzzy dinyatakan dalam derajat dari suatu keanggotaan dan derajat dari kebenaran.

Contoh berikut akan menjelaskan bagaimana konsep “umur” yang digolongkan “tua” dalam pengertian fuzzy /samar dan crisp (tegas). Misalnya diberikan suatu definisi bahwa setiap orang yang berumur 60 tahun atau lebih adalah “tua”. Dalam pengertian crisp (tegas), batas-batas antara “tua” dan tidak “tua” sangat jelas, setiap orang yang berumur ≥ 60 adalah tua, sedang yang lainnya (40,…,55) adalah tidak “tua”. Tidak ada derajat ketuaan, sedangkan dalam fuzzy setiap anggota memiliki nilai berdasarkan pada derajat keanggotaan