Evolution of Fuzzy Set Theory under Monotonic Constraints

Fuzzy Set Theory (FST) has proved advantageous in various areas of research ever since it was proposed by Prof. Lotfi A Zadeh in 1965. The work on FST has grown manifolds since then resulting in many extensions of FST, one of them being the development of FST under Monotonic Constraints (MC). The notion of Monotonic Fuzzy Set Theory (M-FST) was first presented in 2000 by P Lindskog and L Ljung. It has since seen various augmentations of its own with expansions over various extensions of FST. The applications of M-FST include classification, regression, and prediction. In this paper, the evolution of FST under MC has been studied. First, the evolution of FST has been presented which is then extended to FST under MC. The benefits, challenges, and applications along with the future scopes of FST under MC have also been studied and presented.