One-sided fuzzy numbers and applications to integral equations from epidemiology

In this paper we present the algebraic and topological structure of one-sided fuzzy numbers and introduce the notion of side preserving fuzzy-number-valued function. We define the dual decomposition of a commutative monoid and prove that the sets of left-sided fuzzy numbers and right-sided fuzzy numbers realize a dual decomposition of the additive monoid of all fuzzy numbers. We prove the usefulness of right-sided fuzzy numbers in epidemiology presenting an application of these fuzzy numbers to a mathematical model for the spread of infectious diseases with a rate of contact that varies seasonally.