Catalogue of Artificial Intelligence Techniques

   

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Fuzzy Logic

Categories: Inference and Reasoning , Knowledge Representation


Author(s): Fl\'avio Corr\^ea da Silva

Fuzzy logics were created to deal with vague sentences and partial degrees of truth. The truth-value of a sentence in a fuzzy logic is a value in the interval [0,1] , rather than true or false. Intuitively, assigning a truth-value 0 to a sentence corresponds to the concept of the sentence being false, assigning a truth-value1

corresponds to the sentence being true, and intermediate values (i.e., values between 0 and 1 ) represent distances between the truth-value of the sentence and the values true and false. Fuzzy truth-values are propagated by means of triangular norms and conorms and symmetric inversion functions. For example, if the sentence a has truth-value μa the sentence b has truth-value μb , then the sentence ab can be defined to have the truth-value μ=minμa,μb , the sentence ab

can be defined to have the truth-value μ=maxμa,μb

and the sentence ¬a can be defined to have the truth-valueμ¬=1-μa

.


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