Fuzzy Computing

In the real word there exists much fuzzy knowledge, that is, knowledge which is vague, imprecise,uncertain, ambiguous, inexact, or probabilistic in nature.

Human can use such information because the human thinking and reasoning frequently involve fuzzy information, possibly originating from inherently inexact human concepts and matching of similar rather than identical experience.

The computing system, based upon classical set theory and two-valued logic, cannot give answers to some questions as a human does, because they do not have completely true answers.

We want the computing systems not only to give human-like answers but also to describe their reality levels. These levels need to be calculated using imprecision and the uncertainty of facts as well as rules that were applied.

Fuzzy sets

Fuzzy Logic is built on The Fuzzy Set Theory which was introduced to the world by Lotfi Zadeh in 1965 for the first time. The invention, or proposition, of Fuzzy Sets was motivated by the need to capture and represent the real world with its fuzzy data due to uncertainty. Uncertainty can be caused by imprecision in measurement due to imprecision of tools or other factors. Uncertainty can also becaused by vagueness in the language objects and situations. Lotfi Zadeh realized that the Crisp Set Theory is not capable of representing those descriptions and classifications in many cases. In fact, Crisp Sets do not provide adequate representation. We use linguistic variables often to describe, and maybe classify, physical objects and situations.

Instead of avoiding or ignoring uncertainty, Lotfi Zadeh developed a set theory that captures this uncertainty. The goal was to develop a set theory and a resulting logic system that are capable of coping with the real world. Therefore, rather than defining Crisp Sets, where elements are either in or out of the set with the absolute certainty, Zadeh proposed the concept of a Membership Function. An element can be in the set with a degree of membership and out of the set with a degree of membership. Figure illustrates the use of Fuzzy Sets to represent the notion of a tall person. It also shows how we can differentiate between the notions of talland very tall, resulting in a more accurate model than the classical set theory.