TASK 2

                                                       A Picture Describing Fuzzy Logic

Fuzzy Logic is a form of  computing where the real value may be between 1 and 0 but never either of them. It is mainly about"truths and degrees" than usual "True and False". It is a form of many-valued logic where the value can be abstract.The idaes of Fuzzy Logic was first used by DR. Lotfi Zadeh of
University of California in the 1960s. He as working on the problem of computer understanding of natural language.Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. (Whether everything is ultimately describable in binary terms is a philosophical question worth pursuing, but in practice much data we might want to feed a computer is in some state in between and so, frequently, are the results of computing.) It may help to see fuzzy logic as the way reasoning really works and binary or Boolean logic is simply a special case of it.

Fuzzy Logic contains 0 and 1 as an extreme case of truth(like a state of matter) and also includes various state of truths in between 1 and 0.It is closer to how our brain works and it. We aggregate data and form a number of partial truths which we aggregate further into higher truths which in turn, when certain thresholds are exceeded, cause certain further results such as decision making.

Classical logic only permits conclusions which are either true or false. However, there are also propositions with variable answers, such as one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum.Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first, but fuzzy logic uses degrees of truth as a mathmatical model of vaguness, while probability is a mathematical model of ignorance

The process of Fuzzy Logic are

1. Fuzzify all input values into fuzzy membership functions.
2. Execute all applicable rules in the rule base to compute the fuzzy output functions.
3. De-fuzzify the fuzzy output functions to get "crisp" output values.

Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner.

Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators AND, OR, NOT must be available. There are several ways to this. A common replacement is called the Zadeh operators.

For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. As it is used in many day to day critical concept.

                                                                

References

                                                             

Novák, V.; Perfilieva, I.; Močkoř, J. (1999). Mathematical principles of fuzzy logic. Dordrecht: Kluwer Academic.