The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model...

‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the col...

Using the theory of rudimentary recursion and provident sets developed in a previous paper, we give a treatment of set forcing appropriate for working over models of a theory PROVI which may plausibly claim to be the weakest set theory supporting a smooth theory of set forcing, and of which the minimal model is Jensen’s Jω. Much of the development is rudimentary or at worst given by rudimentary...

In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2),∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω1, ω∗ 1 , C, C ∗ where X is any suborder of the reals of size ...

It is well known to generalize the meagre ideal replacing ℵ 0 by a (regular) cardinal λ > ℵ 0 and requiring the ideal to be λ +-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing ℵ 0 by λ, so requiring it to be (< λ)-complete. Of course, we would welcome additional properties generalizing the one...

We provide an exposition of supercompact Radin forcing and present several methods for iterating Radin forcing. In this paper we give an exposition of supercompact Radin forcing using coherent sequences of ultrafilters. This version of Radin forcing includes as special cases the Prikry forcing and Magidor forcing, both the measurable and supercompact versions. We also introduce some methods for...

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (!2; !2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen’s combinatorial principles for L at the level !2, and therefore with the existence of an !2-Suslin tree. We also show that the axiom we ...

In this paper we consider MIMO broadcast channels with separable variance profile modelling antenna correlation at both transmit and receive sides. For large number of antennas we derive the theoretical sum-rate capacity when the transmitter performs zero-forcing or regularized zero-forcing precoding. In particular, we apply the results to volumelimited devices where the correlation originates ...

A natural question to ask is whether this result has an analogue in the context of large cardinals. The purpose of this article is to provide the strongest such analogue not ruled out by limitations imposed by the existence of Woodin cardinals. To describe the latter limitations we consider the forcing P , described as follows. Let δ be inaccessible and consider the language L(δ): (a) n ∈ R bel...

Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specifi...