Fuzzy Logic|Homanga Bharadwaj

Homanga Bharadwaj

The  multiple  milestones  of Artificial  Intelligence  have  taken  the  world  by storm  ever  since  the  advent of techniques  that could  implement the  age  old ideas of making  machines  that mimic humans. Fuzzy logic is the  mathematical formulation of approximating reality.  It is well known that binary logic has ones and  zeroes only i.e.  either  a statement is completely  true  or false.  Although it is mathematically and  computationally convenient to have such a system  in place, it does not fit in well with the ways in which humans  think  and act.  For example, when  we increase  the  temperature of the  air  conditioner, we have  a thought process akin to, “It is getting  very cold now and  so I should increase the  temperature of the  air  conditioner” and  not, ”Since  the  temperature is now 2.3 degrees below 25.6 degree Celsius, I  will increase  the  AC knob  by 2.3 degrees”.    So, instead  of saying  that something  is true  or  false,  we attach a ‘degree of certainty’ with every statement. Linguistic uncertainty (that arises in human  communication) and probabilistic uncertainty are the two major sources of randomness  that arise in a control system.  Fuzzy logic helps in mathematical modeling of the former while Probability theory  deals with the latter

Over the recent years, fuzzy theory  has proven  to be highly effective in system  identification and  modeling. It  is especially  useful in designing  rule  based expert systems where the linguistic uncertainty is high. Presently, fuzzy methods of inference have been combined  with  traditional training methods  like neural networks  to generate  more robust  systems.   Another  advantage is that in contrast to classical system  modeling, where both  the order and the type (i.e. linear or nonlinear)  of the  model are important, in fuzzy modeling we are mostly concerned  about  the  order  of the  model, which is actually  the  number  of rules included in the rule base . The design of a fuzzy model is usually carried out via a training procedure  which determines the  number  of rules needed  to describe the system  and estimates  the appropriate system  parameters

Membership  grades are used to quantify  the extent to which an element be- longs to a particular group(set). Conventionally, a membership  value runs from 0 to 1.  In Type  -I fuzzy sets, the  membership  grades  of each data  point of the input  are ”crisp”,  meaning non fuzzy or distinct. The topic of current research  is Type-II  fuzzy sets, where the membership  values are themselves  fuzzy intervals. Type -II fuzzy sets are used to model situations where we are unsure  of to what extent each data  point belongs to a given set.  Since, statistical uncertainties are always present in experimental data,  this  formulation is considered  to be more realistic

Fuzzy  logic controllers  are  increasingly  being used  in modern  AI architectures.  They  have an edge over conventional PID  controllers  in modeling a non linear  system  with  a high  degree  of accuracy.   The  input  set  is first  fuzzified by associating  membership  values to each data  point on some predefined membership  functions. Then the  input  is passed  through a ”knowledge  base”  which contains rules and also a method to determine the degree to which each rule fires. The rules applied on the fuzzified input  generate  fuzzy outputs which are finally defuzzified using various  techniques  like centre  of sets,  centroid  defuzzification etc. This  results  in a traditional ”crisp” output.

Fuzzy inference combined with other machine learning techniques  are beginning to define new standards that can be achieved  by the  current state  of the art  AI architectures. It is only a matter of time  before we build  machines  that outperform us in almost  all walks of life

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