The aim of this paper is to introduce and study some new neutrosophic fuzzy pairwise notian via neutrosophic fuzzy ideals. In addition to generalize the concept of NFPL-continuity and NFPL-open functions. Relationships between the above new neutrosophic fuzzy pairwise notions and there other relevant neutrosophic fuzzy classes are investigated.

In recent decades, Information and Communication Technology (ICT) has been advanced and widely spread around the globe in addition to ICT revolution and technological advances are considered the major role in the evolution of modern age, which is called "Digital Transformation Age". Therefore, Electronic Technology (E-Technology) has become one of the most prominent approaches such as Electronic Learning (E-Learning), Electronic Training (E-Training), Mobile Learning (M-Learning), Virtual Lab (V-Lab), Virtual University, etc. E-Technology includes some features, for instance anyone, anywhere, anytime and reducing of geographical barriers. ETechnology is a great trend and influences many fields and sectors such as Learning, Training, Military, Navy, Aviation, Medicine, and Digital space. According to nature of usage, E-Technology can be used in positive or negative trends. E-Technology is considered as a valuable tool in providing several opportunities for learning and training processes for individuals and organizations, especially in critical issues. Finally, we give a quick overview of neutrosophic data and some recent applications.

The neutrosophic logic and theory has been established by the Italian Mathematician Florentin Smarandache on 1995. The first publication on neutrosophic logic was released since 1995 by the article entitled (Neutrosophic Logic and Set), this paper discussed a new branch of philosophy and mathematics which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra , therefore, the word (Neutrosophic) has been coined for the first time at 1995 and it is constructed of two syllables ( the first syllable is Latin [ Neuro]in French [ Neutre] which means Neutral, the second syllable is [Sophia] which is a Greek word means skill or wisdom, so the word (Neutrosophic) means (the knowing of the neutrality thought). This article will spot light to this mathematical concept, wherein a brief history about the studies that dealt with this topic would presented, specifically by Arabian researchers, and the role of them in developing the neutrosophic logic.

In this paper, the definition of neutrosophic bimatrix. The main objective is to define a neutrosophic bipolynomial. And to find neutrosophic biinverse for neutrosophic bimatrix, and finding the biinverse of the square neutrossophic bimatrix using the Kayley-Hamilton theorem, Also defining the eigenvalues of the neutrosophic bimatrix and diagonalizing the neutrosophic bimatrix.