a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

To tackle the problem with inexact, uncertainty and vague knowl- edge, constructive method is utilized to formulate lower and upper approx- imation sets. Rough set model over dual-universes in fuzzy approximation space is constructed. In this paper, we introduce the concept of rough set over dual-universes in fuzzy approximation space by means of cut set. Then, we discuss properties of rough se...

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

The aim of this paper is to study the properties of t-cut set, strong t-cut set, t-quasi-cut set, strong t-quasi-cut set and ∈ ∨q-cut set of a fuzzy set μ. For any intuitionistic fuzzy A =< μA, νA > and α, β ∈ [0, 1], we define and study the properties of upper (α, β) cut setA(α,β), strong upper (α, β) cut setA(α, β) ̇ , lower (α, β) cut set A, strong lower (α, β) cut set A (α, β) ̇ , upper (α, β...

fault tree analysis (fta) as a probabilistic risk assessment (pra) method is used to identify basic causes leading to an undesired event, to represent logical relation of these basic causes in leading to the event, and finally to calculate the probability of occurrence of this event. to conduct a quantitative fta, one needs a fault tree along with failure data of the basic events (bes). someti...

The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...