We propose residual based tests for cointegration using local GLS detrending (Elliott, Rothemberg and Stock, 1996, ERS) applied separately to each variable of the system. We consider two cases, one where only a constant is included and one where a constant and a time trend are included. We derive the asymptotic distribution of a feasible point optimal test which allows us to derive the power en...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

This paper is divided into four sections. The first section (this section) briefly reviews topics that will be required for the rest of the paper. The second section covers the proof of Gödel’s theorem that the generalized continuum hypothesis cannot be disproved in Zermelo-Fraenkel set theory. The third section simply states the proof of Cohen’s theorem that the generalized continuum hypothesi...

In this paper, we introduce the concept of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings, which is a generalized concept of fuzzy weak bi-ideals of $Gamma$- near-rings. We also characterize some properties and examples of interval valued fuzzy weak bi-ideals of $Gamma$-near-rings.

in this work, we define a fuzzy soft set theory and its related properties. we then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.