Abstract:
Classical or standard logic is the two-valued logic that governs deductions in standard mathematics. The mathematical systems of this logic were introduced and studied in the late 19th and early 20th centuries by mathematicians such as Frege, Russell, Hilbert, Tarski, and Gödel. But in natural languages, we encounter cases that seem to be inconsistent with classical logic. The history of examining these matters goes back to ancient times and the works of philosophers such as Aristotle. But the study of the mathematical systems of these logics has started in the 20th century in a similar way to the classical logic systems. Some of these non-classical logics are extensions of classical logic and are compatible with it, such as modal logic. But some other logic is made by abandoning some principles and rules of classical logic, such as fuzzy logic. In this public lecture, we will review some preliminary concepts in fuzzy logic. We deal with the mathematical aspects of this logic, which is called fuzzy logic in a narrow sense. On the other hand, fuzzy logic in a broad sense deals with various applications of the concept of fuzzy set and its generalizations.