Category «fuzzy-logic»

What is Fuzzy Set Theory?

Problems in the real world turn out to be quite complex, due to uncertainty in the parameters that define the problem and due to uncertainty in the situations in which that particular problem occurs. Probability theory is an age old theory, which excellently handles this uncertainty. But this probability theory can be applied only to …

Operations on Crisp Sets

As you may already know, Crisp Sets consists of well-defined collection of objects. Well-defined in the sense that the objects either belong to or doesn’t belong to a set. Here are some of the most important operations of Crisp sets: Union The union of two sets A and B is a set containing the elements …

Implication in Fuzzy Logic

If P, Q, R are Fuzzy propositions defined on sets A, B, C of their respective universe of discourses, then the fuzzy propositions P, Q, R are given by P : x is A, A ⊂ XQ : y is B, B ⊂ YR : y is C, C ⊂ Y P → Q : …

The Compound Proposition Exclusive NOR

The compound proposition exclusive NOR is represented as Logical Proofs :- P : a person is engineer Q : a person is mathematician R : a person is logical thinker S : a person who believes in magic Hypothesis :- Engineers are mathematicians. Logical thinkers don’t believe in magic. Mathematicians are logical thinkers. Conclusion:- Engineers …

State and Prove Modus Ponens and Modus Tollens

Modus Ponens :- If A and B are two simple propositions defined on Universe of discourse X then the compound proposition tautology Proof :- Modus Tollens :- When A and B are two simple propositions defined on Universe of elements X then the compound proposition Proof :-

What are Tautologies

Tautologies :- Compound propositions that are always true irrespective of the truth values of the individual simple propositions are called tautologies. For example, if A1 = 2 | A2 = 3 | A3 = 5then the compound proposition “Ai is not divisible by 6″ is a tautology. Some common tautologies defined on universe of discourse …