# 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 $\left[0,1\right]$ , 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-value$1$

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 ${\mu }_{a}^{}$ the sentence $b$ has truth-value ${\mu }_{b}^{}$ , then the sentence $a\wedge b$ can be defined to have the truth-value ${\mu }_{\wedge }^{}=min{\mu }_{a}^{},{\mu }_{b}^{}$ , the sentence $a\vee b$

can be defined to have the truth-value ${\mu }_{\vee }^{}=max{\mu }_{a}^{},{\mu }_{b}^{}$

and the sentence $¬a$ can be defined to have the truth-value${\mu }_{¬}^{}=1-{\mu }_{a}^{}$

.

### References:

• Dubois, D. and Prade, H., An Introduction to Possibilistic and Fuzzy Logics, Non-Standard Logics for Automated Reasoning ( Smets, P., Mamdani, E.H., Dubois, D. and Prade, H. , eds.), Academic Press , London, 1988, pp.287--326.