Fuzzy Logic


A fuzzy logic system is unique, because is able to simultaneously handle numerical data and linguistic knowledge. It is a non linear mapping of an input data vector into a scalar output i.e. it maps’ numbers into numbers.

Fuzzy Logic Definition

Fuzzy logic means inexact reasoning, data granulation, computing with words and so on.

Haziness is always present in any realistic process. This vagueness may come up from the analysis of the data inputs and in the directives used to describe the relationships between the informative attributes. Fuzzy logic grants an inference structure that allows the human reasoning capacities to be applied to artificial knowledge-based structures. Fuzzy logic gives a means for adapting linguistic strategy into control actions and thus offers a high-level computation.

A definition of fuzzy logic systems set mathematical determination to the emulation of certain perceptual and lingual attributes related with human cognition, where the science of neural networks provides a new computing tool with learning and adaptation capabilities. The theory of fuzzy logic gives an inference method under cognitive uncertainty, computational neural networks, fuzzy logic offer exciting benefits such as learning, adaptation, fault tolerance, parallelism, and generalization.

In the literary texts sources, we can find different kinds of explanation for fuzzy systems theory. Human knowledge these days becomes more and more important – we increase it from living through the world after only which we live and use our capability to reason to create an order in the mass of information (i.e., to formulate human knowledge in a organized manner). As we are all limited in our ability to perceive the world and to deep reasoning, we find ourselves everywhere faced by uncertainty that is a result of lack of information, in particular, miscalculation of measurements.

The other restriction factor in our request for precision is a natural language used for describing/sharing knowledge, communication, etc. We understand core meanings of word and are able to communicate without error to an adequate degree, but generally we cannot precisely agree among ourselves on the singular word or terms of communal sense meaning. In other words, ordinary languages are unclear.

Our impression of the real world is pervaded by concepts, which do not have severely defined boundaries – for example, many, tall, much larger than,young, etc. are true only to some degree, and they are false to some extent as well. These concepts can be called fuzzy or vague concepts – a human brain works with them, while computers may not do it (they reason with strings of 0s and 1s). Natural languages, which are much higher in level than programming languages, are fuzzy, while programming languages are not. The door to the development of fuzzy computers was opened in 1985 by the design of the first logic chip by Masaki Togai and Hiroyuki Watanabe at Bell Telephone Laboratories. In the years to come fuzzy computers will employ both fuzzy hardware and fuzzy software, and they will be much closer in structure to the human brain than the present-day computers are.

The Fuzzy Logic tool was introduced in 1965 by Lotfi Zadeh. It is a mathematical tool for dealing with uncertainty. It offers to a software computing system the important concept of computing with words’. It grants a technique to deal with vagueness and information granularity. The fuzzy theory provides a mechanism for representing linguistic constructs such as “many,” “low,” “medium,” “often,” “few.”

Basically, the fuzzy logic provides an inference organization that enables proper human reasoning capabilities that machines do not have. In the other hand, the traditional binary set theory describes crisp events, events that have two options: one or zero. It uses probability theory to explain whether an event is about to happen, measuring the chance with which a given event is expected to come about. The premise of fuzzy logic is based leading the concept of relative graded connection and so are the functions of awareness and cognitive processes.

It is important to keep in mind that there is a close connection between Fuzziness and Complexity. As the complexity of a task, or of a system for performing that task, exceeds a certain limit, the system must unavoidably become fuzzy in nature. Zadeh, initially an engineer and systems scientist, was concerned with the fast turn down in information afforded by common mathematical models as the complexity of the target system increased.

As he stressed, with the increasing of complexity our skill to make accurate and yet major statements about its behavior diminishes. Real world problems are too complex, and the difficulty involves thedegree of vagueness – as uncertainty increases, so does the involvedness of the problem. Habitual system modeling and analysis techniques are too precise for such problems, and in order to make complexity less daunting we set up appropriate simplifications, assumptions, etc. to accomplish a reasonable compromise between the information we have and the amount of uncertainty we are willing to accept. In this aspect, fuzzy systems theory is similar to other engineering theories, because almost all of them describe the real world in an approximate manner.

Engineers define fuzzy logic as a useful tool with diverse applications; especially on solving problems that linear computing is not able to do. A good example of this functionality is the capability for image recognition, since human brain is capable to distinguish an object from an image even if is blur, meanwhile linear computing is able to read just pixels as set of colors. There is an analog factor: vagueness, images may have fuzzy maps.

Fuzzy sets grants means to model the ambiguity associated with vagueness, imprecision, and lack of information concerning a dilemma or a plant, etc. Consider the significance of a “short person.” For an entity X, the short person may be one whose height is below 4.20. For another individual Y, the short person may be one whose height is beneath or equal to 3.9. This “short” is called as a linguistic descriptor. The term “short” informs the same meaning to the individuals X and Y, but it is establish that they both do not supply a unique definition. The term “short” would be conveyed successfully, only when a computer compares the given height value with the pre-assigned value of “short.” This variable “short” is called as linguistic variable, which represents the elusiveness existing in the system.