This paper deals with the hyperstructures called Hv-modules. The main tools concerning the class of Hv-modules with the ordinary modules are the fundamental relations. The fundamental relations in Hv -modules and fuzzy Hv-submodules are studied in this paper. In particular, the product structure of fuzzy sets on Hv-modules is studied.

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persis...

The basic reproduction ratio, R0, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R0 indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small n...

In infectious disease epidemiology the basic reproductive ratio, R0, is defined as the average number of new infections caused by a single infected individual in a fully susceptible population. Many models describing competition for hosts between non-interacting pathogen strains in an infinite population lead to the conclusion that selection favors invasion of new strains if and only if they ha...

In this paper, we introduce a generalized class of an Hv-semigroup obtained from an LA-semigroup H. This generalized Hv-structure is called an Hv-LA-semigroup. We provide several examples of Hv-LA-semigroups. Moreover, with the help of an example we obtain that each LA-semigroup endowed with an equivalence relation can induce an Hv-LA-semigroup. We also investigate isomorphism theorems with the...

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

A positive answer to the open problem of Iorgulescu on extending weak-R 0 algebras and R 0-algebras to the noncommutative forms is given. We show that pseudo-weak-R 0 algebras are categorically isomorphic to pseudo-IMTL algebras and that pseudo-R 0 algebras are categorically isomorphic to pseudo-NM algebras. Some properties, the noncommutative forms of the properties in weak-R 0 algebras and R ...

The basic reproductive rate (R0) is a measure of the severity of an epidemic. On the basis of replicated Latin hypercube sampling, the authors performed an uncertainty and sensitivity analysis of the basic reproductive rate of tuberculosis (TB). The uncertainty analysis allowed for the derivation of a frequency distribution for R0 and the assessment of the relative contribution each of the thre...

The most simplified axiom systems of pseudo-weak-R0 algebras and pseudo-R0 algebras are obtained, and the mutually independence of axioms is proved. We introduce the notions of filters and normal filters in pseudo-weak-R0 algebras. The structures and properties of the generated filters and generated normal filters in pseudo-weak-R0 algebras are obtained. These can be seen as noncommutative gene...