Fixed point theory has garnered significant interest due to its applicability across various scientific disciplines. In this manuscript, we present fixed point theorems pertaining to neutrosophic fuzzy quasi-contractions, situated within the sophisticated framework of neutrosophic fuzzy metric spaces. Furthermore, we establish several fixed point results pertinent to this field of research.

This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by concatenating some into one inequality. The main idea of this paper is to extend the existing numerical radius inequalities by providing a unified framework. We also present a numerical example to demonstrate the effectiveness of the proposed approach. Roughly, our approach combines the existing inequalities, proved in literature, into a single inequality that can be used to obtain improved or restored results. This unified approach allows us to extend the existing numerical radius inequalities and show their effectiveness through numerical experiments.

As a generalization of fuzzy soft sets, we present the idea of time-effective fuzzy soft sets (T-EFSS) in this study. Additionally, i will describe its fundamental operations complement, union intersection, AND, and OR—and examine their characteristics. I will finally provide two applications of this idea to decision-making situations. The second application that neurosophic Membership offers In addition, to demonstrate influence over variables that might impact membership values following application.

In this work, a perturbed Milne’s quadrature rule for n-times differentiable functions with $L^p$-error estimates is derived. One of the most important advantages of our result is that it is verified for p-variation and Lipschitz functions. Several error estimates involving $L^p$-bounds are proven. These estimates are useful if the fourth derivative is unbounded in $L^{\infty }$-norm or the $L^p$-error estimate is less than the $L^{\infty }$-error estimate. Furthermore, since the classical Milne’s quadrature rule cannot be applied either when the fourth derivative is unbounded or does not exist, the proposed quadrature could be used alternatively. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are also provided. The numerical experiments compare the accuracy of the proposed quadrature rule to the classical Milne rule when approximating different types of functions. The results show that, for certain types of functions, the proposed quadrature rule is more accurate than the classical Milne rule.

In this paper, we present the topological space of intervals based neutrosophic real numbers , where we clarify how neutrosophic real intervals can be expressed according to the neutrosophic partial order relation, and we use these intervals to build a topological space. On the other hand, we use a similar argument to build a topological space over the intervals of refined neutrosophic numbers, with many illustrated and related examples on open and closed sets.

Ayman A. Hazaymeh. International Journal of Fuzzy Logic and Intelligent Systems 2024;24:387-98. https://doi.org/10.5391/IJFIS.2024.24.4.387