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. …

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 …

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 …