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Fuzzy soft set theory presented by Maji et al. (J Fuzzy Math 9(3):589–602, 2001) and soft set theory presented by Molodtsov (Comput Math Appl 37(3):19–31, 1999) are important ideas in decision-making problems. They can be used to model uncertainty and make decisions under uncertainty. A single-valued neutrosophic soft set (svnf-set) is a hybrid model of a single-valued neutrosophic set and fuzzy soft set that is shown in this paper. The novel concept of single-valued neutrosophic soft topology (svnft) is defined to discuss topological structure of (svnf-set). Some fundamental properties of svnft and their related results are studied. It is good to use the proposed models of svnf-sets and svnft to figure out how to deal with uncertainty in real life. Thus, svnft is a generalization of fuzzy soft topology and fuzzy intuitionistic soft topology. Moreover, after giving the definition of a single-valued neutrosophic soft base svnf-base, we also added the concept of svnft. Finally, we set up the concept of single-valued neutrosophic soft closure spaces and show that the initial single-valued neutrosophic soft closure structures are real, which is what we did. From this fact, the category SVNSC is considered as a topological category over SET. [ABSTRACT FROM AUTHOR]

In this paper, a new class of fuzzy ideal sets, namely the r - (τ i , τ j) - θ -generalized fuzzy ideal closed sets, is introduced for fuzzy bitopological spaces in Šostak sense. This class falls strictly in between the class of r - (τ i , τ j) - θ -fuzzy ideal closed sets and the class of r - (τ i , τ j) -generalized fuzzy ideal closed sets. Furthermore, by using the class of r - (τ i , τ j) - θ -generalized fuzzy ideal closed sets we establish a new fuzzy closure operator which generates fuzzy bitopological spaces in Šostak sense. Finally, the (i , j) strongly- θ -fuzzy ideal continuous, (i , j) - θ -generalized fuzzy ideal continuous and (i , j) - θ -generalized fuzzy ideal irresolute mappings are introduced, and we show the (i , j) - θ -generalized fuzzy ideal continuous properly fuzzy ideal bitopological spaces in Šostak sense (for short, fibtss) in between (j , i) strongly- θ -fuzzy ideal continuous and (i , j) -generalized fuzzy continuous mappings. [ABSTRACT FROM AUTHOR]

This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings ( F · V · M s). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities. [ABSTRACT FROM AUTHOR]

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ -pre-invex interval-valued mappings ( C · L · R - ℏ -pre-invex Ι · V - M ), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte's type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes. [ABSTRACT FROM AUTHOR]

This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal is established. Additionally, the concept of a single-valued neutrosophic open local function for a single-valued neutrosophic topological space is presented. We introduce an operator based on a single-valued neutrosophic primal, illustrating that the single-valued neutrosophic primal topology is finer than the single-valued neutrosophic topology. Lastly, the concept of single-valued neutrosophic open compatibility between the single-valued neutrosophic primal and single-valued neutrosophic topologies is introduced, along with the establishment of several equivalent conditions related to this notion. [ABSTRACT FROM AUTHOR]

This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak's sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations. [ABSTRACT FROM AUTHOR]

This study presents new fuzzy adaptations of Ostrowski's integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived. [ABSTRACT FROM AUTHOR]

Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak's sense, which is considered as a generalization of fuzzy ideals in Šostak's sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations. [ABSTRACT FROM AUTHOR]

Hip fractures are common orthopedic injuries that have significant impacts on patients and healthcare systems. Previous studies have shown varying outcomes for hip fracture management in different settings, with diverse postoperative outcomes and complications. While teaching hospital settings have been investigated, no studies have specifically examined hip fracture outcomes in teaching hospitals in Jordan or the broader Middle East region. Therefore, the aim of this study was to investigate this important outcome. A cohort comprising 1268 patients who underwent hip fracture fixation from 2017 to 2020 was analyzed for nine distinct outcomes. These outcomes encompassed time to surgery, ICU admissions, perioperative hemoglobin levels, length of hospital stay, readmission rates, revision procedures, and mortality rates at three time points: in-hospital, at 6-months, and at 1-year post-surgery. The analysis of 1268 patients (616 in teaching hospitals, 652 in non-teaching hospitals) showed shorter mean time to surgery in teaching hospitals (2.2 days vs. 3.6 days, p < 0.01), higher ICU admissions (17% vs. 2.6%, p < 0.01), and more postoperative blood transfusions (40.3% vs. 12.1%, p < 0.01). In-hospital mortality rates were similar between groups (2.4% vs. 2.1%, p = 0.72), as were rates at 6-months (3.1% vs. 3.5%, p = 0.65) and 1-year post-surgery (3.7% vs. 3.7%, p = 0.96). Geriatric hip fracture patients in teaching hospitals have shorter surgery times, more ICU admissions, and higher postoperative blood transfusion rates. However, there are no significant differences in readmission rates, hospital stays, or mortality rates at various intervals. [ABSTRACT FROM AUTHOR]

In the current paper, particular acheivments of single-valued neutrosophic continuity on a singlevalued neutrosophic topological space (𝔗 ̃, 𝜏̃𝛾̃, 𝜏̃𝜂̃, 𝜏̃𝜇̃) are introduced. Some necessary implications between them are illustrated. The theories of r-single-valued neutrosophic compact, r-single-valued neutrosophic ideal compact, r-single-valued neutrosophic quasi H-closed and r-single-valued neutrosophic compact modulo an single-valued neutrosophic ideal I~ are presented and investigated. [ABSTRACT FROM AUTHOR]