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Abstract In this paper, some strong and Δ-convergence results are proved for Suzuki generalized nonexpansive mappings in the setting of CAT(0) $\mathit{CAT}(0)$ spaces using the K iteration process. We also give an example to show the efficiency of the K iteration process. Our results are the extension, improvement and generalization of many well-known results in the literature of fixed point theory in CAT(0) $\mathit{CAT}(0)$ spaces.

ABSTRACT OBJECTIVES: To assess and evaluate prescription pattern and prescription errors using World Health Organization (WHO) drug use indicators in the medical ward of Leady Reading Hospital, Peshawar, Pakistan. METHODS: This retrospective study of 200 in-patient’s prescriptions was conducted to investigate the WHO drug use indicators (average number of drugs prescribed per prescription, percentage of prescriptions encounter with an injection(s) prescribed, percentage of prescriptions encounter with an antibiotic(s) prescribed, percentage of drugs prescribed with generic names, percentage of drugs prescribed from the WHO’s Essential Drug List (EDL), drugs prescribed from the National Essential Drug List (NEDL) and prescriptions errors. RESULTS: Drugs prescribed for 200 admitted patients were 1410 and average number of drugs prescribed per prescription were 7.05 (n=1410). Prescriptions with an injection(s) prescribed were 704/1410 (49.9%), prescriptions with an antibiotic(s) prescribed were 241/1410 (17.1%), prescriptions with drugs prescribed by generic names was none. Number of drugs prescribed from the WHO EDL were 704 (49.9%). NEDL was not available. A total of 572 (40.6%) errors in prescription writing were observed including 211/572 (36.9%) errors having absent strength of drugs, 267/572 (46.7%) contains an illegible hand writing prescriptions, 48(n=572; 8.4%) prescriptions have missing frequency of drugs and 46 (n=572; 8.04%) prescriptions had improper abbreviations. Decision errors were observed in 703 (n=1410;49.86%) cases for drug-drug interactions. CONCLUSION: Illegible hand writing, absence of strength of drugs, no mentioning of frequency of drugs and improper abbreviations were main types of prescription errors while error in drug-drug interactions was the main decision error in our study. KEY WORDS:Medical Errors (MeSH); Medication Errors (MeSH); Inappropriate Prescribing (MeSH); Prescription Errors (Non-MeSH); Prescription Pattern (Non-MeSH); Drug Use Indicators (Non-MeSH); Drug-Drug Interactions (Non-MeSH)

In this article, we introduce the class of enriched Suzuki nonexpansive (ESN) mappings. We show that this new class of mappings properly contains the class of Suzuki nonexpansive as well as the class of enriched nonexpansive mappings. We establish existence of fixed point and convergence of fixed point in a Hilbert space setting under the Krasnoselskii iteration process. One of the our main results is applied to solve a split feasibility problem (SFP) in this new setting of mappings. Our main results are a significant improvement of the corresponding results of the literature.

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises.

In this article, the recently introduced iterative scheme of Hassan et al. (Math. Probl. Eng. 2020) is re-analyzed with the connection of Reich–Suzuki type nonexpansive (RSTN) maps. Under mild conditions, some important weak and strong convergence results in the context of uniformly convex Banach spaces are provided. To support the main outcome of the paper, we provide a numerical example and show that this example properly exceeds the class of Suzuki type nonexpansive (STN) maps. It has been shown that the Hassan et al. iterative scheme of this example is more useful than the many other iterative schemes. We provide an application of our main results to solve split feasibility problems in the setting of RSTN maps. The presented outcome is new and compliments the corresponding results of the current literature.

In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α,β)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of [0, 1] that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from [0, 1] intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

As q-rung orthopair fuzzy set (q-ROFS) theory can effectively express complex fuzzy information, this study explores its application to social network environments and proposes a social network group decision-making (SNGDM) method based on the q-ROFS. Firstly, the q-rung orthopair fuzzy value is used to represent the trust relationships between experts in the social network, and a trust q-rung orthopair fuzzy value is defined. Secondly, considering the decreasing and multipath of trust in the process of trust propagation, this study designs a trust propagation mechanism by using its multiplication operation in the q-ROFS environment and proposes a trust q-ROFS aggregation approach. Moreover, based on the trust scores and confidence levels of experts, a new integration operator called q-rung orthopair fuzzy-induced ordered weighted average operator is proposed to fuse experts’ evaluation information. Additionally, considering the impact of consensus interaction on decision-making results, a consensus interaction model based on the q-ROF distance measure and trust relationship is proposed, including consistency measurement, identification of inconsistent expert decision-making opinions and a personalized adjustment mechanism. Finally, the SNGDM method is applied to solve the problem of evaluating online teaching quality.

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives.

Vesicular drug delivery systems have gained wide attention in the field of nanotechnology. Among them proniosomes become the superior over other vesicular carriers. Proniosomes are dry formulations of water soluble nonionic surfactant coated carrier system which immediately forms niosomes upon hydration. They have the capability to overcome the instability problems associated with niosomes and liposomes and have the potential to improve solubility, bioavailability, and absorption of various drugs. Furthermore, they offer versatile drug delivery concept for enormous number of hydrophilic and hydrophobic drugs. They have the potential to deliver drugs effectively through different routes at specific site of action to achieve controlled release action and reduce toxic effects associated with drugs. This review discusses the general preparation techniques of proniosomes and mainly focus on the applications of proniosomes in drug delivery and targeting. Moreover, this review demonstrates critical appraisal of the literature for proniosomes. Additionally, this review extensively explains the potential of proniosomes in delivering drugs via different routes, such as oral, parenteral, dermal and transdermal, ocular, oral mucosal, vaginal, pulmonary, and intranasal. Finally, the comparison of proniosomes with niosomes manifests the clear distinction between them. Moreover, proniosomes need to be explored for proteins and peptide delivery and in the field of nutraceuticals and develop pilot plant scale up studies to investigate them in industrial set up.

Abstract Background Traditional knowledge of indigenous plants is pivotal in developing strategies to feed livestock sustainably in low input systems. Likewise, in Pakistan the indigenous people of Central Punjab have been using their regional grasses as a ruminant fodder for centuries. This study evaluated the indigenous traditional knowledge to ascertain the value of various fodder grasses to optimise their use to feed livestock in Central Punjab. Methods The snowball technique was employed to identify key informants who had relevant knowledge about different grasses in the study area. Semi-structured questionnaires, face-to-face interviews and site visits were used for describing the fodder grasses. The data were then analysed by using relative frequency citation and pairwise comparison methods to determine the order of priority among the listed fodder grasses. Furthermore, SPSS 22 software was used for descriptive statistics and interpretation of associations among studied parameters. Microsoft Excel was used to present data as % values and graphs. Results Overall, 53 grasses were described with ethnobotanical information regarding their uses for fodder, ethnoveterinary and other purposes. All these grasses belonged to the family Poaceae where the subfamily Panicoideae had the maximum number of 30 grasses. We categorized these grasses into high (A), medium (B) and low priority (C) groups where the group A grasses were reported as not only the most abundant but also the most palatable forages to all ruminants. Their higher demand was reflected by the feeding systems of both ad libitum grazing and feeding after cutting and mixing with other feeds. The study also revealed 37 previously unreported ethnoveterinary uses of these grasses. Conclusions The results have reinforced the value of conserving ethnobotanical knowledge, being poorly documented previously, in developing strategies to feed livestock. It indicated the preferred fodder grasses as well as the possible reasons of their preference. The reported data need to be validated for nutritional and health benefits. This information could help the smallholder farmers in association with regional governments to propagate suitable fodder grasses for their use in sustainable livestock feeding to produce safe and healthy food for indigenous communities.

The current study was conducted to determine the synergistic effects of dietary nano selenium (Nano Se) and vitamin C on growth, feeding, and physiological parameters of juvenile mahseer, Tor putitora. L-ascorbyl-2-polyphosphate (APP) was used as a source of vitamin C. Four semi-purified experimental diets were prepared. A basal diet kept without the supplementation of any micronutrient and the other three diets were formulated such that three different levels of APP (100, 200, and 300 mg kg−1) were used in combination with a pre-determined dose of Nano Se (0.68 mg kg−1). The results showed that both the micronutrients positively synergized the effects of each other. APP at the rate of 300 mg kg−1 showed strong interaction with Nano Se. The APP300 + Nano Se0.68 mg kg−1 diet supplemented diet significantly decreased (P

A gastric bezoar is a compact mass of indigestible foreign materials that accumulate and consolidate in the stomach; however, it can be found in other sites of the gastrointestinal tract. The causative manner of this condition is complex and multifactorial. The main purpose of the review was to raise awareness among clinicians, particularly gastroenterologists, that patients with certain risk factors or comorbid conditions are predisposed to gastric bezoar formation. Early diagnosis and prompt intervention are crucial to avoid bezoar-induced complications. Upper gastrointestinal endoscopy is the standard diagnostic and therapeutic method for gastric bezoars. However, for large size bezoars, surgical intervention is needed.

The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature.

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized α -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.

T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.

Bioavailability of the colloidal particles is of great concern. It is because about 40% of the newly discovered colloidal agents are poorly water soluble and thus poorly bioavailable. Various colloidal technologies have been adopted to enhance the bioavailability of such drugs. In this review, advanced colloidal technologies are discussed to understand the mechanism of bioavailability enhancement of drugs, coding latest references from the literature. Additionally, advantages and disadvantages of the concerned colloidal technologies are discussed to understand the potential usage of each process. All these colloidal technologies effectively enhance the bioavailability of poorly bioavailable drugs, either by protecting them from the environment of the gastrointestinal or by prolonging their intended therapeutic effect. Furthermore, complexation of the drug molecule with potential carries, particle size reduction to nanoscale, co-crystallization and self-emulsifying drug delivery system are also discussed which not only enhance the bioavailability but also reduce the potential toxicities of the loaded drugs. It is therefore important to understand the vital colloidal technologies with their recent advancements, potential applications and future challenges, which is discussed in this review. Finally, this article concludes that the advanced colloidal technologies, including freeze-dried liposome, solid lipid nanoparticle, polymeric nanoparticle (polymeric micelles), dendrimers and solid emulsifying drug delivery systems, have the potential to achieve improved bioavailability and targeted drug delivery.

To evaluate aortic stiffness in renal transplant patients and to determine the correlation of renal insufficiency and estimated glomerular filtration rate (eGFR) with aortic pulse wave velocity (APWV), we studied 96 renal transplant patients followed-up at our center. We measured the APWV using transcutaneous Doppler flow recordings and the foot-to-foot method, and calculated the eGFR using the Modification of Diet in Renal Disease equation. The study included 81 (84.4%) males and 15 (15.6%) females. The mean age of the patients was 37.84 ± 10.10 years. The mean duration of transplant was 47.90 ± 34.40 months. The eGFR of the patients ranged from 1 to 120 mL/min, with a mean GFR of 72.6 ± 23.2 mL/min. Sixty-seven (69.8%) patients had eGFR > 60 mL/min and hence had stages 1 and 2 chronic kidney disease (CKD), 27 (28.1%) patients had eGFR 30-60 mL/min and hence had stage 3 CKD and two (2.1%) patients had eGFR

The objective of this study is to determine the prevalence of peripheral vascular disease (PVD) in patients with chronic kidney disease (CKD). Seventy-two patients with CKD stage 3 or above were included in this study. Blood samples were taken from each patient to determine complete blood counts, serum albumin, electrolytes, lipid profile and blood sugar random/fasting. The glomerular filtration rate (GFR) was estimated with the Cockcroft-Gault formula. The ankle-brachial index (ABI) was determined to identify the presence of PVD. A standardized Doppler ultrasound device was used. ABI of 0.05). However, the mean total cholesterol was significantly higher among patients with PVD. The prevalence of PVD was significantly high in patients with stage 5 CKD (P

(1) Background. Snake venom phosphodiesterases (SVPDEs) are among the least studied venom enzymes. In envenomation, they display various pathological effects, including induction of hypotension, inhibition of platelet aggregation, edema, and paralysis. Until now, there have been no 3D structural studies of these enzymes, thereby preventing structure−function analysis. To enable such investigations, the present work describes the model-based structural and functional characterization of a phosphodiesterase from Crotalus adamanteus venom, named PDE_Ca. (2) Methods. The PDE_Ca structure model was produced and validated using various software (model building: I-TESSER, MODELLER 9v19, Swiss-Model, and validation tools: PROCHECK, ERRAT, Molecular Dynamic Simulation, and Verif3D). (3) Results. The proposed model of the enzyme indicates that the 3D structure of PDE_Ca comprises four domains, a somatomedin B domain, a somatomedin B-like domain, an ectonucleotide pyrophosphatase domain, and a DNA/RNA non-specific domain. Sequence and structural analyses suggest that differences in length and composition among homologous snake venom sequences may account for their differences in substrate specificity. Other properties that may influence substrate specificity are the average volume and depth of the active site cavity. (4) Conclusion. Sequence comparisons indicate that SVPDEs exhibit high sequence identity but comparatively low identity with mammalian and bacterial PDEs.

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

The pharmaceutical clay montmorillonite (MMT) is, for the first time, explored as a carbon monoxide-releasing material (CORMat). MMT consists of silicate double layered structure; its exfoliation feature intercalate the CORM-2 [RuCl(μ-Cl)(CO)3]2 inside the layers to suppress the toxicity of organometallic segment. The infrared spectroscopy (IR) confirmed the existence of ruthenium coordinated carbonyl ligand in MMT layers. The energy-dispersive X-ray spectroscopy (EDX) analysis showed that ruthenium element in this material was about 5%. The scanning electron microscopy (SEM) and transmission electron microscope (TEM) images showed that the layer-structure of MMT has been maintained after loading the ruthenium carbonyl segment. Moreover, the layers have been stretched out, which was confirmed by X-ray diffraction (XRD) analysis. Thermogravimetric (TG) curves with huge weight loss around 100−200 °C were attributed to the CO hot-release of ruthenium carbonyl as well as the loss of the adsorbed solvent molecules and the water molecules between the layers. The CO-liberating properties have been assessed through myoglobin assay. The horse myoglobin test showed that the material could be hydrolyzed to slowly release carbon monoxide in physiological environments. The half-life of CO release was much longer than that of CORM-3, and it has an excellent environmental tolerance and slow release effect.

The CO-releasing materials (CORMats) are used as substances for producing CO molecules for therapeutic purposes. Carbon monoxide (CO) imparts toxic effects to biological organisms at higher concentration. If this characteristic is utilized in a controlled manner, it can act as a cell-signaling agent for important pathological and pharmacokinetic functions; hence offering many new applications and treatments. Recently, research on therapeutic applications using the CO treatment has gained much attention due to its nontoxic nature, and its injection into the human body using several conjugate systems. Mainly, there are two types of CO insertion techniques into the human body, i.e., direct and indirect CO insertion. Indirect CO insertion offers an advantage of avoiding toxicity as compared to direct CO insertion. For the indirect CO inhalation method, developers are facing certain problems, such as its inability to achieve the specific cellular targets and how to control the dosage of CO. To address these issues, researchers have adopted alternative strategies regarded as CO-releasing molecules (CORMs). CO is covalently attached with metal carbonyl complexes (MCCs), which generate various CORMs such as CORM-1, CORM-2, CORM-3, ALF492, CORM-A1 and ALF186. When these molecules are inserted into the human body, CO is released from these compounds at a controlled rate under certain conditions or/and triggers. Such reactions are helpful in achieving cellular level targets with a controlled release of the CO amount. However on the other hand, CORMs also produce a metal residue (termed as i-CORMs) upon degradation that can initiate harmful toxic activity inside the body. To improve the performance of the CO precursor with the restricted development of i-CORMs, several new CORMats have been developed such as micellization, peptide, vitamins, MOFs, polymerization, nanoparticles, protein, metallodendrimer, nanosheet and nanodiamond, etc. In this review article, we shall describe modern ways of CO administration; focusing primarily on exclusive features of CORM’s tissue accumulations and their toxicities. This report also elaborates on the kinetic profile of the CO gas. The comprehension of developmental phases of CORMats shall be useful for exploring the ideal CO therapeutic drugs in the future of medical sciences.

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators.

Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work.

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies’ results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work.

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.

We propose and analyse a medium access control (MAC) protocol for low energy critical infrastructure monitoring (LECIM) networks. As the packet drop probability plays crucial role in LECIM applications, we propose framed slotted aloha based MAC for LECIM using linearly increased contention window size to reduce the packet drop probability. We present a mathematical model of our proposed MAC under both saturated and nonsaturated traffic scenarios. We use probabilistic approach to find the performance metrics such as collision probability, packet drop probability, throughput, and energy consumption. Also, we obtain the probability-generating function of the head-of-line (HoL) delay of packet. The analytical results match with simulations. Our results can be used in the design of a system by providing the optimum system parameters for endpoints satisfying the given quality of service requirements on packet drop probability, energy consumption, and delay.

Normally, individuals use smartphones for a variety of purposes like photography, schedule planning, playing games, and so on, apart from benefiting from the core tasks of call-making and short messaging. These services are sources of personal data generation. Therefore, any application that utilises personal data of a user from his/her smartphone is truly a great witness of his/her interests and this information can be used for various personalised services. In this paper, we present Lifestyle Pattern MIning (LPaMI), which is a personalised application for mining the lifestyle patterns of a smartphone user. LPaMI uses the personal photograph collections of a user, which reflect the day-to-day photos taken by a smartphone, to recognise scenes (called objects of interest in our work). These are then mined to discover lifestyle patterns. The uniqueness of LPaMI lies in our graph-based approach to mining the patterns of interest. Modelling of data in the form of graphs is effective in preserving the lifestyle behaviour maintained over the passage of time. Graph-modelled lifestyle data enables us to apply variety of graph mining techniques for pattern discovery. To demonstrate the effectiveness of our proposal, we have developed a prototype system for LPaMI to implement its end-to-end pipeline. We have also conducted an extensive evaluation for various phases of LPaMI using different real-world datasets. We understand that the output of LPaMI can be utilised for variety of pattern discovery application areas like trip and food recommendations, shopping, and so on.

The design and fabrication of sustained/controlled release dosage forms, employing new excipients capable of extending/controlling the release of drugs from the dosage forms over prolonged periods, has worked well in achieving optimally enhanced therapeutic levels of the drugs. In this sense, the objective of this study was to investigate the suitability of selected cellulose ether derivatives for use in direct compression (DC) and as efficient drug release controlling agents. Controlled release matrix tablets of ciprofloxacin were prepared at different drug-to-polymer (D : P) ratios by direct compression using a fine particle sized ethylcellulose ether derivative (ETHOCEL Standard Premium 7FP) as rate controlling polymer. The tablets obtained were evaluated for various physico-chemical characteristics and in-vitro drug release studies were conducted in phosphate buffer (pH 7.4) using PharmaTest dissolution apparatus at constant temperature of 37∘C±0.1. Similarity factor 𝑓2 was employed to the release profiles of test formulations and were compared with marketed ciprofloxacin conventional tablets. Drug release mechanism and the kinetics involved were investigated by fitting the release profile data to various kinetic models. It was found that with increasing the proportion of ethylcellulose ether derivative in the matrix, the drug release was significantly extended up to 24 hours. The tablets exhibited zero order or nearly zero order drug transport mechanism. In vivo drug release performance of the developed controlled release tablets and reference conventional tablets containing ciprofloxacin were determined in rabbit serum according to randomized two-way crossover study design using High Performance Liquid Chromatography. Several bioavailability parameters of both the test tablets and conventional tablets including 𝐶max, 𝑇max and AUC0-𝑡 were compared which showed an optimized 𝐶max and 𝑇max (𝑃