International Journal of Neutrosophic Science

Better classroom evaluation may have positive effects on students' learning, according to research and practice from the past ten years. United Arab Emirates (UAE) values the assessment of procedures used in teaching, as an integral part in the evaluation of their effectiveness. Through evaluation, the results realized, help in measuring the effectiveness of curricula and methods used in teaching. This, therefore, affects stakeholders in education, the teachers, and most importantly, the students. This study aims at cross-examining students’ performance in mathematics, especially at the high school level, in the UAE. Also, this evaluation has a multi-criteria so the concept of multi-criteria decision-making is used in this paper. But this process has vague and uncertain information, so the neutrosophic theory is used to solve this problem. The neutrosophic sets integrated with the MCDM methodology. The neutrosophic AHP method is used to compute the weights of criteria and evaluate the classroom.

NeutroGeometries are those geometric structures where at least one definition, axiom, property, theorem, among others, is only partially satisfied. In AntiGeometries at least one of these concepts is never satisfied. Smarandache Geometry is a geometric structure where at least one axiom or theorem behaves differently in the same space, either partially true and partially false, or totally false but its negation done in many ways. This paper offers examples in images of nature, everyday objects, and celestial bodies where the existence of Smarandechean or NeutroGeometric structures in our universe is revealed. On the other hand, a practical study of surfaces with characteristics of NeutroGeometry is carried out, based on the properties or more specifically NeutroProperties of the famous quadrilaterals of Saccheri and Lambert on these surfaces. The article contributes to demonstrating the importance of building a theory such as NeutroGeometries or Smarandache Geometries because it would allow us to study geometric structures where the well-known Euclidean, Hyperbolic or Elliptic geometries are not enough to capture properties of elements that are part of the universe, but they have sense only within a NeutroGeometric framework. It also offers an axiomatic option to the Riemannian idea of Two-Dimensional Manifolds. In turn, we prove some properties of the NeutroGeometries and the materialization of the symmetric triad <Geometry>, <NeutroGeometry>, and <AntiGeometry>.

In this paper, a new fuzzy integral transform is introduced and called “fuzzy Mohand transform” which is based on a mathematical formula of the classical Mohand transform. The fuzzy technique that is well-established from fuzzy Laplace transform, agrees with the neutrosophic logic. In fact, in mathematical field, neutrosophic logic, which is based on the idea of indeterminacy, is introduced as a generalization of fuzzy logic. In Neutrosophic logic, there are three values, grade of membership of Truth values (T), Indeterminate values (I) and False values (F). To demonstrate this mixed technique, a realistic example about heating system is discussed as an illustrative example for solving an ordinary differential equation of first order using fuzzy Mohand transform with neutrosophic numbers as an initial condition.