Explain: Fuzzy Logic.

·         Fuzzy Logic is a form of many-valued logic in which the truth value of variables may be any real number b/w 0 and 1.

·         Fuzzy Logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false.

     ·         Ex.:

         The complex sentence Tall (Anil) ˄ Heavy (Anil) has a fuzzy truth value, which is a function of the truth values of its components.

         ·        The standard rules to evaluate the fuzzy truth (T), of a complex sentence are – T (A˄B) = min (T (A), T (B))

T (A˅B) = max (T (A), T (B)) T (¬A) = 1 – T (A)

     ·        Thus, fuzzy logic is a truth functional system. And hence, it causes serious difficulties.

·         This problem arises from the inability of a truth functional approach to take correlations or anti-correlations among the component propositions into account.

     ·  Ex.:

Suppose, T (Tall (Anil)) = 0.6 and T (Heavy (Anil)) = 0.4. Then we have T (Tall (Anil)) ˄ T (Heavy (Anil)) = 0.4.

This seems reasonable.

But, we also get T (Tall (Anil)) ˄ ¬ T (Tall (Anil)) = 0.4, which does not seem reasonable.