Fuzzy Sets and Fuzzy Differential Equations

Solution of real world problems often rely on solutions of mathematical models of empirical phenomena. It is well known that the precision and exactness necessary during the construction and solution of such models are not always true in real situations. The major difficulty encountered by a model builder is to express imprecise notions in a seemingly precise form. Conventional mathematics is not equipped to handle vagueness. As researchers and mathematical model builders continue their efforts to construct intelligent systems they are coming to grip with the issue of uncertainty in human knowledge and reasoning. As new fields of study like general system theory, robotics, artificial intelligence and language theory continue to grow, we are forced to specify imprecise notions and analyze them. In 1965, Zadeh [31] introduced a modification of set theory known as fuzzy set theory to study notions with prescribed vagueness.