Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

In the interest of business innovation, social network companies often carry out experiments to test product changes and new ideas. such experiments, users are typically assigned one two experimental conditions with some outcome observed compared. this setting, user may be influenced by not only condition which they but also other via their connections. This challenges classical design analysis...

Mathematical programming is one of the areas to which fuq set theoq has been applied extensively. Primarily based on Bellman and Zadeh’s model of decision in fuzzy environments, models have been suggested which allow flexibility in constraints and nonlinear programming. Data envelopment analysis (DEA) is a method of evaluating relative efJiciencies for a group of similar units based on an efici...

Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also known as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirec...

For characterizing the genetic mechanisms of complex diseases familial data with multiple correlated quantitative traits are usually collected in genetic studies. To analyze such data, various multivariate tests have been proposed to investigate the association between the underlying disease genes and the multiple traits. Although these multivariate association tests may have better power perfo...