This paper is devoted to introduce and investigate some weak forms of fuzzy open mappings, namely fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly α-open (fuzzy faintly α-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly spopen (fuzzy faintly spclosed) mappings and their fundamental properties ...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. Using the notion of intuitionistic fuzzy sets, Çoker [5] introduced the notion of intuitionistic fuzzy topological spaces. In this paper, we define the notion of intuitionistic fuzzy semiopen (r...

The concept of a preopen set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called preopen or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called preclosed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, preopen, was used for the first time by A. S. Mashhour, M. E. Abd El-Monse...

In this paper, we introduce and characterize double fuzzy weakly preopen and double fuzzy weakly preclosed functions between I-double gradation fuzzy topological spaces and also study these functions in relation to some other types of already known functions.

The purpose of this paper is to present and investigate a new class topological spaces known as Sw*-regular spaces, by utilizing the concept Sw-regular sets some its properties. which introduced in 2009 L. S. Abddullah A. B. Khalaf [1], properly contained S*- regular space [2], [3], means that Sw*- stronger form regular. Several characterizations, properties relationships with other such as, Sw...

We use realized volatilities based on after hours high frequency returns to predict next day volatility. We extend GARCH and long-memory forecasting models to include additional information: the whole night, the preopen, the postclose realized variance, and the overnight squared return. For four NASDAQ stocks ( MSFT, AMGN, CSCO, and YHOO) we find that the inclusion of the preopen variance can i...

In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.