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What Buddha saw of the world, Matisse sought in his paintings, and Heisenberg found in the quantum, was a simple fact that “Precision is not the truth”. They all found out in different novel ways that things can be a certain degree true, and a certain degree false at the same time. Drawing absolutes can certainly increase precision, but cannot make it perfectly precise as is clear from the finite word length effects in the digital domain. In a quest to seek the ultimate, in a bid to imitate the human capabilities, we have constantly resorted to the continuum of phenomenon and not discreteness. This is the world of **fuzzy logic**.

**History**

**Fuzzy Logic**date back to the time when intelligent life forms evolved and they all can be classified as fuzzy systems. While Aristotle, presented the system of two valued logic, it was Plato who laid the foundations of what would be known as fuzzy logic by proposing that there was an intermediate third region in between ‘true’ and ‘not true’ where some part might be true, while some part might not be. The subject then never found any mention in history while probability continued to thrive until the early 1900’s when Lukasiewicz proposed the idea of three valued logic True-Possible-False [0, 1, 2].

**fuzzy logic**

**controller**to control the speed of a small steam engine and achieved great success. The oriental countries of Japan and China readily accepted the concept and started developing it. While the US were still contemplating over the childishness of the name, Japan built a train controlled by

*which is said to have such smooth functions that if one was standing inside one such moving train, he couldn’t tell if the train was moving at all unless he saw the world flashing by in the windows.*

**fuzzy logic****Fuzzy Logic**can be viewed as a super set of Boolean logic, as a multi-valued logic. It adds degrees between the absolute truth and absolute false to cover partial truth in between. In simple terms, fuzzy logic involves classifying objects and functions into fuzzy sets which could be given linguistic phrases. It is a form of reasoning that is neither exact, nor absolutely inexact. For example, too hot, little slow, phrases which do not give the idea of absolute, but a fuzzy estimate. While 33 degrees might be warm enough for a person from the equator, someone from the arctic might find the heat unbearable, or too hot. It is not possible to classify them into strict sets with defined boundaries which leads to the idea of fuzziness.

*Fig. 1: Image Showing Comparison Between Bivalent And Fuzzy Sets*

## Working

**System Requirements:**Define control objectives, specifications, criteria, type of response needed, possible failure modes etc.

**Input/Output relationship:**Choosing the minimum number of fuzzy variables for inputs and their relation to the output. These can be linguistic variables, for example for error measurements, large positive error, zero error, small negative error etc.

**Create FL Membership Functions:**These define the values of Input/output terms used in the rules. These represent graphically, the magnitude of participation of an input and associate a weight to each input which determines their influence on the final output. These functions seldom have simple shapes, and may range from triangular to bell shaped, trapezoidal or exponential. The degree of membership is determined by having the input on the x-axis and projecting it to the upper boundary of membership function.

*Fig. 2: Graph Showing FL Membership Functions For Velocity In Speed Controller*

**Rule Based Engine Structure:**FL systems are based more on intuitive reasoning with If-Then clauses for all the possible cases. There is no Else clause, which means that all the conditions are checked. A rule matrix is initially formed to tabulate all the possible number of rules. Though all might not be needed, it helps mapping out the possible inputs while keeping the system under control.

**Create Routines:**In case of software, pre and post-processing routines, and in hardware programs, putting rules into the FL Engine.

**Defuzzification:**The firing strength of each rule is determined and logical products of each rule are inferred through techniques like max-min’d, root-sum-squared, max-dot’d etc. before passing them to the defuzzification phase. Defuzzification involves the conversion of the fuzzy data into a crisp output using the Fuzzy Centroid Algorithm.

**Testing and Evaluation:**The objective is to try and try again until the goal is achieved. The rules are changed and new rules may be added to tune the system to achieve the desired performance.

## Hardware & Application

*Fig. 3: Typical Linear First Order System Curves Using Conventional Control And Fuzzy Logic*

## Comments

## fuzzy logics has been in use

fuzzy logics has been in use from the very beginning of any civilizations. i completely agree with logics as the basis for any discovery as well as any invention. there are only two answers to any or every question i.e yes or no , true or false , zero or one. the word "probable" is just analogous to probability in mathematics having probability between 0 or 1 . fuzzy logics are also defined in electronics system and forms the basis for any electronic circuit in the binary form as 0 and 1.every electronic circuit works on the principle of 0 and 1 i.e if it is a zero or one as the input or output which is used to drive other circuits input output.

## I see, I spupose that would