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					|  |  |  | Nearly all applications of Fuzzy logic rely on the notion of | 
			
		
	
		
			
				
					|  |  |  | linguistic variables. These are variables whose values are words rather than | 
			
		
	
		
			
				
					|  |  |  | cold hard numbers. Something like "it is nice outside" is an examples of a linquistic | 
			
		
	
		
			
				
					|  |  |  | variable. These are values which don't necessarily directly relate to | 
			
		
	
		
			
				
					|  |  |  | cold hard numbers, but, they do in a roundabout way. When I say that it is nice | 
			
		
	
		
			
				
					|  |  |  | outside, that is subjective to my opinion; other people may have different opinions | 
			
		
	
		
			
				
					|  |  |  | on what is considered nice outside. That is why this is called fuzzy logic: each | 
			
		
	
		
			
				
					|  |  |  | fuzzy set carries some tolerance for imprecision. The tolerance for ambiguity helps us model | 
			
		
	
		
			
				
					|  |  |  | the world in a more realistic form by using language rather than cold hard numbers. | 
			
		
	
		
			
				
					|  |  |  | With words we can quickly convey ideas like "young" and "old" and quickly make actions | 
			
		
	
		
			
				
					|  |  |  | based on this knowledge. Since there is no definitive answer on what is the | 
			
		
	
		
			
				
					|  |  |  | cut of for being old/young, we can use fuzzy logic to deal with partial truth values. | 
			
		
	
		
			
				
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					|  |  |  | # Fuzzy Sets | 
			
		
	
		
			
				
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					|  |  |  | Classical sets are mutually exclusive. In other words: things can only belong | 
			
		
	
		
			
				
					|  |  |  | to one set at a time. | 
			
		
	
		
			
				
					|  |  |  | In a fuzzy set, elements can belong to multiple sets with some degree of membership. | 
			
		
	
		
			
				
					|  |  |  | As an example, someone who is 30 may be 33% in the young set and 66% in the old set. | 
			
		
	
		
			
				
					|  |  |  | Fuzzy sets are usually are represented by trapezoids; however, other shapes such as gaussian can | 
			
		
	
		
			
				
					|  |  |  | be used. | 
			
		
	
		
			
				
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					|  |  |  | ## Temperature Example | 
			
		
	
		
			
				
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					|  |  |  | # Fuzzy Rules | 
			
		
	
		
			
				
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					|  |  |  | # Fuzzy Logic System | 
			
		
	
		
			
				
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					|  |  |  | # Example |