We survey what is known about limitwise monotonic functions and sets and discuss their applications in effective algebra and computable model theory. Additionally, we characterize the computably enumerable degrees that are totally limitwise monotonic, show the support strictly increasing 0′-limitwise monotonic sets on Q do not capture the sets with computable strong η-representations, and study...

Chebyshev’s integral inequality, also known as the covariance inequality, is an important problem in economics, finance, and decision making. In this paper we derive some covariance inequalities for monotonic and non-monotonic functions. The results developed in our paper could be useful in many applications in economics, finance, and decision making.

In this paper, we propose a constructive method to develop a fuzzy system having a monotonic input–output relationship and prove that the developed fuzzy system can approximate any continuously differentiable monotonic function with any desired degree of accuracy. The fuzzy system is constructed with complete and consistent input membership functions and imposes special parametric constraints o...

The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with two-layer monotonic functions. The existence of a solution to the given problem suggests that from two monotone functions, a monotonic function with the same...