Fuzzy systems, pioneered by Lotfi A. Zadeh in the 1960s, basically deal with how human beings handle imprecise and uncertain information. They mimic how human beings use approximate reasoning in dealing with imprecision, uncertainty, inaccuracy, inexactness, ambiguity, vagueness, qualitativeness, subjectivity, and perception that are experienced in everyday decision making.
Fuzzy systems are capable of handling imprecise terms such “quite”, “very”, and “extremely” that are normally part of natural language. This directly feeds into the concept of "computing with words" (CW) in contrast to that of manipulating numbers and symbols. The former deals with linguistics and perceptions while the latter deals with crisp and exact measurements.
"Soft computing" was coined by Zadeh. This area, he says, is a partnership of techniques and methodologies among which are fuzzy logic (FL), neuro-computing (NC) and probabilistic reasoning (PR), with the latter subsuming genetic algorithms (GA), chaotic systems, belief networks, and parts of learning theory.
Fuzzy logic is a superset of the conventional boolean logic that has been extended to handle the concept of partial truth -- truth values between "completely true" and "completely false". The transition of truth values from "completely true" to "completely false" is exhibited in the fuzzy sets and not in crisp sets.
In crisp sets, such as a set A of old ages
{ A | A >= 35 }there is a sharp distinction or boundary between members of the set, and those that are non-members of the set. In the example, only those ages greater than or equal to 35 are regarded as members of set A, and the other ages are non-members. But how about 34.8? Shouldn't it be considered already old? Would an age of 35 and 85 carry the same concept of being "old"? In other words, how old is "old"? The same issue arises in classifying other measurements like coldness of temperature, tallness in height, and expensiveness of prices. Such imprecision and uncertainty of terms as well as flexibility in truth values can be handled in fuzzy sets but not in crisp sets.
In fuzzy sets, the transition from membership to non-membership in sets is gradual and not abrupt. Shown below is the difference between a crisp set of old ages, and a fuzzy set of old ages.
Crisp Set A and Fuzzy Set A of Old Ages
In the illustration of fuzzy set A, ages 35 years or below are still members of fuzzy set A of old ages but their degrees of membership are lower. Degrees of membership in fuzzy sets are in the range of 0.0 (non-membership) to 1.0 (full-membership) in contrast to only either 0.0 (member) or 1.0 (non-member) in crisp sets. Generally, membership degrees in the fuzzy set of old ages decrease as ages decrease. If we have another fuzzy set B of young ages, we expect the membership degree to increase with age.
From the above firgure, an age of 45 may be perceived in fuzzy logic as “old” at a degree of around 0.95 and as “young” at a degree of around 0.5. Thus, we move from exact, crisp measurements to inexact, fuzzy perceptions which are normally associated to words or linguistic terms.
Fuzzy logic is applied in expert systems to handle linguistic uncertainties which experts use when they verbalize their knowledge about a particular domain. Degrees of uncertainty are used not only in representing expert knowledge, but also in processing expert tasks.
Knowledge are represented in fuzzy expert systems using linguistic variables, linguistic values, linguistic terms, fuzzy sets, membership functions, and fuzzy IF-THEN rules.
