Introduction to Fuzzy Logic & Theory

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 In the real world, more often than not things are not black and white, or in binary terms 0 and 1. Instead, there are a million shades in between black and white, which in a way can be represented by different decimal numbers between 0 and 1. This is basically the key concept behind the advent of Fuzzy Theory.

Instead of talking about absolutes 0 and 1, Fuzzy theory talks about the plethora of numbers in between 0 and 1(inclusive) to represent the degrees of membership. For example, let's say you want to quantify How hot is the weather right now? Now, you can say the weather is hot( value of 1) or the weather is not hot( value of 0), but the fact of the matter is that this definition does not capture the true human interaction. In  the real world, if you ask somebody this question "How hot is the weather right now?", they are more likely to reply along the following lines : 

  • The weather is very hot.
  • The weather is somewhat hot
  • The weather is okay (neither hot nor cold)
  • The weather is somewhat cold.
  • The weather is very cold. 

This is what being fuzzy means, instead of just sticking to absolutes 0 and 1 , you try to make use of multiple values. For instance, the above problem can be defined as follows :

Non- fuzzy approach :



Fuzzy approach:




where y represents the function to compute the degree of membership.

 




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