There are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. -ey introduced the concept of soft rough sets, in which parameterized
subsets of a universe set serve as the building blocks for lower and upper approximations of a subset. Topological notions play a vital role in rough sets and soft rough sets. So, the basic objectives of the current work are as follows: first, we find answers to some very important questions, such as how to determine the probability that a subset of the universe is definable.
Some more similar questions are answered in rough sets and their extensions. Secondly, we enhance soft rough sets from topological perspective and introduce topological soft rough sets. We explore some of their properties to improve existing techniques. A comparison has been made with some existing studies to show that accuracy measure of proposed technique shows an improvement. Proposed technique has been employed in decision-making problem for diagnosing heart failure. For this two algorithms have been given.

This paper puts forward some rough approximations which are motivated from topology. Given a subset R ⊆ U × U, we can use 8 types of E-neighborhoods to construct approximations of an arbitrary X⊆ U on the one hand. On the other hand, we can also
construct approximations relying on a topology which is induced by an E-neighborhood. Properties of these approximations and relationships between them are studied. For convenience of use, we also give some useful and easy-to-understand examples and
make a comparison between our approximations and those in the published literature.

This year, we introduced the concept of infra soft topology as a new generalization of soft
topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under
which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

Efficient and convenient methods for the removal of toxic heavy metal ions especially Cd(II) and Pb(II) from aqueous solutions is of great importance due to their serious threat to public health and the ecological system. In this study, two magnetic metal-organic frameworks (namily: Fe₃O₄@ZIF-8, and Fe₃O₄@UiO-66–NH₂) were synthesized, fully characterized, and applied for the adsorption of Cd(II) and Pb(II) from aqueous solutions. The adsorption efficiencies for the prepared nanocomposites are strongly dependent on the pH of the aqueous solution. The maximum adsorption capacities of Fe₃O₄@UiO-66–NH₂, and Fe₃O₄@ZIF-8 at pH 6.0 were calculated to be 714.3 mg·g¹, and 370 mg·g¹ for Cd(II), respectively, and 833.3 mg·g¹, and 666.7 mg·g¹ for Pb(II), respectively. The adsorption process follows a pseudo-second-order model and fit the Langmuir isotherm model. Moreover, the thermodynamic studies revealed that the adsorption process is endothermic, and spontaneous in nature. A plausible adsorption mechanism was discussed in detail. The magnetic adsorbents: Fe₃O₄@ZIF-8, and Fe₃O₄@UiO-66–NH₂ showed excellent reusability, maintaining the same efficiency for at least four consecutive cycles. These results reveal the potential use of magnetic Fe₃O₄@ZIF-8, and Fe₃O₄@UiO-66–NH₂ as efficient adsorbents in removing Cd(II) and Pb(II) from aqueous solutions.

Cellulose–MOFs (CelloMOFs) are attractive hybrid materials that make available a range of hitherto unattainable properties by conjugating cellulosic materials with metal–organic frameworks (MOFs). CelloMOFs have demonstrated a great potential to be applied in several fields such as water remediation, air purification, gas storage, sensing/biosensing, and biomedicine. CelloMOFs can act as an efficient adsorbent to remove emerging contaminants such as metals, dyes, drugs, antibiotics, pesticides, and oils in water via adsorption. They can be also used as catalysts for catalytic degradation, reduction, and oxidation of organic pollutants. They have been applied as filters for air purification via removing greenhouse gases such as carbon dioxide (CO₂), volatile organic compounds (VOCs), and particulate matter (PMs). Biomedical applications such as antibacterial, drug delivery, biosensing were also reported for CelloMOFs materials. This review summarized the synthesis, characterization, and applications of cellulose-MOFs materials. It covered a broad overview of the status of the combination of cellulose in micron to nanoscale with MOFs. At the end of the review, the challenges and outlook regarding CelloMOFs were discussed. Hopefully, this review will be a useful guide for researchers and scientists who are looking for quick access to relevant references about CelloMOFs hybrid materials and their applications.

Removing organic contaminants such as dyes from water is essential to purify wastewater. Herein, zeolitic imidazolate framework-8 (ZIF-8) and ZnO@N-doped C are reported as effective adsorbents and photocatalysts for the adsorption and degradation of organic dyes. The materials showed effective and selective adsorption toward anionic dyes such as methyl blue (MeB) dye in the presence of fluorescein (FLU) dye. The adsorption capacities of ZnO@N-doped C for MeB and FLU dyes are 900 mg g⁻¹ and 100 mg g⁻¹, respectively. According to UV-Vis diffuse reflectance spectroscopy (DRS) data, ZnO@N-doped C has a lower bandgap (2.07 eV) than ZIF-8 (4.34 eV) and ZnO (3.12 eV). Thus, ZnO@N-doped C serves as an effective photocatalyst for the degradation of both dyes under UV exposure. The degradation efficiency capacity of the dye (50 mg L⁻¹) is >90% using 200 mg L⁻¹ of the photocatalyst. The mechanism of adsorption and photocatalysis is investigated. The photodegradation pathway of the dye involved the generation of oxidative hydroxy radicals (OH˙), which can degrade the dyes. The degradation products of FLU were recorded using mass spectrometry.

Quantum dots (QDs) have been advanced biomedical applications, including drug delivery. They can be inorganic (e.g., ZnO, CdS, CdTe, Si QDs, CuInS₂) and organic-based (e.g., carbon QDs, graphene quantum dots) materials. They exhibited advantages such as high surface area, high photostability, and can be modified merely using different approaches such as in-situ synthesis and postsynthetic method. QDs can be modified with biomolecules such as polysaccharides, proteins, polymers, and DNA leading to the formation of a hybrid QD system. Hybrid systems consist of QDs, and other molecules serve as a carrier for drug delivery of various anticancer drugs. The modification of QDs using these molecules mitigates their cytotoxicity and improves their performance as carriers. This chapter summarizes the applications of hybrid systems based on QDs for drug delivery. It also concludes a short introduction regarding QDs and their cytotoxicity. This study gives valuable insight into the fact that the performance of QDs as a carrier for drug delivery does not solely depend on a single factor but rather depends on a combination of elements from the particle formulations and the extent of cellular uptake.

Hybrid nanomaterials offer promising properties to serve as an electrode for hybrid supercapacitors. Herein, dye (rhodamine B, RhB) encapsulated zeolitic imidazolate frameworks (RhB@ZIF-8) was synthesized at room temperature via triethylamine (TEA)-assisted method. The material was used as a precursor for synthesizing zinc oxide embedded nitrogen-doped carbon (ZnO@N-doped C) via the carbonization at different temperatures (400°C, 600°C, and 800°C). The materials were characterized using X-ray diffraction (XRD), thermogravimetric analysis (TGA), differential thermal analysis (DTA), high-resolution transmission electron microscope (HR-TEM), energy-dispersive X-ray mapping (EDX), nitrogen adsorption–desorption isotherm, and X-ray photoelectron microscope (XPS). ZnO@N-doped C nanocrystals (15–20 nm) were used as an electrode for a hybrid supercapacitor. ZnO@N-doped C exhibited a high capacitance of 1200 F·g⁻¹ at a current density of 1 A·g⁻¹ without losing any capacitance (87.7% of initial capacitance) even after 1000 galvanostatic charge–discharge cycles (GCDCs). The presence of a guest molecule such as RhB improved the capacitance of the carbonized ZIF-8 two-fold compared with the carbonized materials using conventional ZIF-8.

The creation of different pore size regimes into zeolitic imidazolate frameworks (ZIFs) to form hierarchical porous structures enhanced the material's performance for various applications. This book chapter focuses on the synthetic strategies for creating ZIFs with pore structures containing multiple pore regimes and provides readers with a broader scope of the strategies available for the fabrication of hierarchical porous ZIFs. Hierarchical porous ZIFs can be synthesized using in situ and ex situ synthesis procedures. Different synthesis procedures were reported, including template-based method, template-free procedure, and three-dimensional (3D) printing. The material's porosity can be characterized using nitrogen adsorption-desorption isotherms, mercury intrusion porosimetry, transmission electron microscopy, and scanning electron microscopy. Hierarchical porous ZIFs offered a complex porous structure. Thus, the combination of different techniques to characterize the material’s porosity is highly required. Overall, this chapter offered a roadmap that may guide the scientists and researchers to design and develop hierarchical porous ZIFs materials with different pore size regimes and high molecular precision.

Cell-penetrating peptides (CPPs) are a promising non-viral vector for gene and drug delivery. CPPs exhibit high cell transfection, and are biocompatible. They can be also conjugated with organic and inorganic nanomaterials, such as magnetic nanoparticles (MNPs), graphene oxide (GO), metal-organic frameworks (MOFs), and chitosan. Nanomaterials offered a high specific surface area and provided relatively straightforward methods to be modified with biomolecules including CPPs and oligonucleotides (ONs). Novel nanomaterials conjugates with CPP/ONs complexes are therefore of interest for cell transfection with high efficiency. In this chapter, we described a summary of the non-viral vectors consisting of CPPs and nanomaterials. The book chapter also included a protocol to generate hybrid biomaterials consisting of CPPs and nanoparticles (NPs) for the delivery of oligonucleotides. The conjugation of NPs with CPPs serves as an effective platform for gene therapy with high cell transfection efficiency. The protocol is simple, offers high cell transfection compared to the CPPs-ONs complexes, and can be used for further improvements using external stimuli.