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In this research article, we have proved strong and Δ -convergence results for mapping satisfying (R C S C) condition via M-iteration process in CAT(0) spaces. Numerical examples are provided to show the superiority of our results over other existing results and to illustrate the faster convergence of the M iterative scheme as compared to many well-known iterative schemes. In this process, many results are improved in the current literature of CAT(0) spaces. [ABSTRACT FROM AUTHOR]

The developed world has focused on Web preservation compared to the developing world, especially news preservation for future generations. However, the news published online is volatile because of constant changes in the technologies used to disseminate information and the formats used for publication. News preservation became more complicated and challenging when the archive began to contain articles from low-resourced and morphologically complex languages like Urdu and Arabic, along with English news articles. The digital news story preservation framework is enriched with eighteen sources for Urdu, Arabic, and English news sources. This study presents challenges in low-resource languages (LRLs), research challenges, and details of how the framework is enhanced. In this paper, we introduce a multilingual news archive and discuss the digital news story extractor, which addresses major issues in implementing low-resource languages and facilitates normalized format migration. The extraction results are presented in detail for high-resource languages, i.e., English, and low-resource languages, i.e., Urdu and Arabic. LRLs encountered a high error rate during preservation compared to high-resource languages (HRLs), corresponding to 10% and 03%, respectively. The extraction results show that few news sources are not regularly updated and release few new news stories online. LRLs require more detailed study for accurate news content extraction and archiving for future access. LRLs and HRLs enrich the digital news story preservation (DNSP) framework. The Digital News Stories Archive (DNSA) preserves a huge number of news articles from multiple news sources in LRLs and HRLs. This paper presents research challenges encountered during the preservation of Urdu and Arabic-language news articles to create a multilingual news archive. The second part of the paper compares two bilingual linking mechanisms for Urdu-to-English-language news articles in the DNSA: the common ratio measure for dual language (CRMDL) and the similarity measure based on transliteration words (SMTW) with the cosine similarity measure (CSM) baseline technique. The experimental results show that the SMTW is more effective than the CRMDL and CSM for linking Urdu-to-English news articles. The precision improved from 46% and 50% to 60%, and the recall improved from 64% and 67% to 82% for CSM, CRMDL, and SMTW, respectively, with improved impact of common terms as well. [ABSTRACT FROM AUTHOR]

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm. [ABSTRACT FROM AUTHOR]

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. [ABSTRACT FROM AUTHOR]

Many fuzzy concepts have been researched and described with uncertain information. Collecting data under uncertain information is a difficult task, especially when there is a difference between the opinions of experts. To deal with such situations, different types of operators have been introduced. This paper aims to develop the Maclaurin symmetric mean (MSM) operator for the information in the shape of the interval-valued spherical fuzzy set (IVSFS). In this article, a family of aggregation operators (AOs) is proposed which consists of interval valued spherical fuzzy Maclaurin symmetric mean operator (IVSFMSM), interval valued spherical fuzzy weighted Maclaurin symmetric mean (IVSFWMSM), interval valued spherical fuzzy dual Maclaurin symmetric mean (IVSFDMSM), and interval valued spherical fuzzy dual weighted Maclaurin symmetric mean (IVSFDWMSM) operators. In this paper, we studied an elucidative example to discuss the evaluation of multi-national companies for the application of the proposed operator. Then the obtained results from the proposed operators are compared. The results obtained are graphed and tabulated for a better understanding. [ABSTRACT FROM AUTHOR]

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators. [ABSTRACT FROM AUTHOR]

Vendor management systems (VMSs) are web-based software packages that can be used to manage businesses. The performance of the VMSs can be assessed using multi-attribute decision-making (MADM) techniques under uncertain situations. This article aims to analyze and assess the performance of VMSs using MADM techniques, especially when the uncertainty is of complex nature. To achieve the goals, we aim to explore Hany mean (HM) operators in the environment of complex picture fuzzy (CPF) sets (CPFSs). We introduce CPF Hamy mean (CPFHM) and CPF weighted HM (CPFWHM) operators. Moreover, the reliability of the newly proposed HM operators is examined by taking into account the properties of idempotency, monotonicity, and boundedness. A case study of VMS is briefly discussed, and a comprehensive numerical example is carried out to assess VMSs using the MADM technique based on CPFHM operators. The sensitivity analysis and comprehensive comparative analysis of the proposed work are discussed to point out the significance of the newly established results. [ABSTRACT FROM AUTHOR]

Traditional electricity networks are replaced by smart grids to increase efficiency at a low cost. Several energy projects in Pakistan have been developed, while others are currently in the planning stages. To assess the performance of the smart grids in Pakistan, this article employs a multi-attribute group decision-making (MAGDM) strategy based on power Maclaurin symmetric mean (PMSM) operators. We proposed a T-spherical fuzzy (TSF) power MSM (TSFPMSM), and a weighted TSFPMSM (WTSFPMSM) operator. The proposed work aims to analyze the problem involving smart grids in an uncertain environment by covering four aspects of uncertain information. The idempotency, boundedness, and monotonicity features of the proposed TSFPMSM are investigated. In order to assess Pakistan's smart grid networks based on the suggested TSFPMSM operators, a MAGDM algorithm has been developed. The sensitivity analysis of the proposed numerical example is analyzed based on observing the reaction of the variation of the sensitive parameters, followed by a comprehensive comparative study. The comparison results show the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

The T-Spherical fuzzy set (TSFS) is the most generalized form among the introduced fuzzy frameworks. It obtains maximum information from real-life phenomena due to its maximum range. Consequently, TSFS is a very useful structure for dealing with information uncertainties, especially when human opinion is involved. The correlation coefficient (CC) is a valuable tool, possessing symmetry, to determine the similarity degree between objects under uncertainties. This research aims to develop a new CC for TSFS to overcome the drawbacks of existing methods. The proposed CCs are generalized, flexible, and can handle uncertain situations where information has more than one aspect. In addition, the proposed CCs provide decision-makers independence in establishing their opinion. Based on some remarks, the usefulness of the new CC is reviewed, and its generalizability is evaluated. Moreover, the developed new CC is applied to pattern recognition for investment decisions and medical diagnosis of real-life problems to observe their effectiveness and applicability. Finally, the validity of the presented CC is tested by comparing it with the results of the previously developed CC. [ABSTRACT FROM AUTHOR]

A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence of Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) and their specific advantages in handling real-world problems. In the beginning, we introduce a few new q-ROF numbers (q-ROFNs) operations, including sum, product, scalar product, and power operations based on AATN and AATCN. At that point, we construct a few q-ROF AOs such as q-ROF Aczel–Alsina weighted averaging (q-ROFAAWA) and q-ROF Aczel–Alsina weighted geometric (q-ROFAAWG) operators. It is illustrated that suggested AOs have the features of monotonicity, boundedness, idempotency, and commutativity. Then, to address multi-attribute decision-making (MADM) challenges, we develop new strategies based on these operators. To demonstrate the compatibility and performance of our suggested approach, we offer an example of construction material selection. The outcome demonstrates the new technique's applicability and viability. Finally, we comprehensively compare current procedures with the proposed approach. [ABSTRACT FROM AUTHOR]

The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by S , the nonmembership degree (NMD) denoted by D , and the abstinence degree (AD) denoted by I. It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of [ 0 , 1 ] . The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn. [ABSTRACT FROM AUTHOR]

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0 ,   1 . The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established. [ABSTRACT FROM AUTHOR]

In Distributed Hash Table (DHT)-based Mobile Ad Hoc Networks (MANETs), a logical structured network (i.e., follows a tree, ring, chord, 3D, etc., structure) is built over the ad hoc physical topology in a distributed manner. The logical structures guide routing processes and eliminate flooding at the control and the data plans, thus making the system scalable. However, limited radio range, mobility, and lack of infrastructure introduce frequent and unpredictable changes to network topology, i.e., connectivity/dis-connectivity, node/link failure, network partition, and frequent merging. Moreover, every single change in the physical topology has an associated impact on the logical structured network and results in unevenly distributed and disrupted logical structures. This completely halts communication in the logical network, even physically connected nodes would not remain reachable due to disrupted logical structure, and unavailability of index information maintained at anchor nodes (ANs) in DHT networks. Therefore, distributed solutions are needed to tolerate faults in the logical network and provide end-to-end connectivity in such an adversarial environment. This paper defines the scope of the problem in the context of DHT networks and contributes a Fault-Tolerant DHT-based routing protocol (FTDN). FTDN, using a cross-layer design approach, investigates network dynamics in the physical network and adaptively makes arrangements to tolerate faults in the logically structured DHT network. In particular, FTDN ensures network availability (i.e., maintains connected and evenly distributed logical structures and ensures access to index information) in the face of failures and significantly improves performance. Analysis and simulation results show the effectiveness of the proposed solutions. [ABSTRACT FROM AUTHOR]

Low carbon and digitalization are the general trends of manufacturing upgrading and transformation. Digital technology enables the whole process of green manufacturing and breaks down the spatial barrier. To achieve the dual carbon goals, the pressure-state-response (PSR) model, in which digital technology enables the green innovation of the manufacturing industry, was theoretically analyzed in this study. The measurement system of the digital green innovation (DGI) in the manufacturing industry was constructed according to the PSR framework. An evaluation model based on the analytic hierarchy process and the deviation maximization technique for order preference by similarity to an ideal solution method was constructed to measure the level of DGI. The results of this study from Chinese manufacturing are as follows. (i) The measurement system of the level of DGI in manufacturing industry includes a pressure system, state system and response system. (ii) In the past five years, the comprehensive index of the DGI in manufacturing industry has generally shown a trend of fluctuating rise. There are overall low and unbalanced phenomena in all regions. The gap decreased from 0.1320 to 0.1187, showing a gradually narrowing trend. (iii) Compared with other regions, the composite index of DGI is generally higher in the regions with a better ecological environment in the east and a more developed economy in the north. State parameters are higher than pressure and response parameters in most areas. (iv) Compared with other regions, the composite index of DGI in western and southern regions is lower, and the parameters of pressure, status and response are basically coordinated. (v) The application degree of digital technology, the emission intensity of waste water/exhaust gas of output value of one hundred million yuan and the expenditure intensity of digital technology adopted by enterprises are the key influencing factors of DGI in the manufacturing industry. This study not only proposed an evaluation index system of the digital green innovation level, but also puts forward policy guidance and practical guidance of digital technology to accelerate the green and intelligent manufacturing industry. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets. [ABSTRACT FROM AUTHOR]

In this research, we suggest some convergence results for operators having (R C S C) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having (R C S C) condition and show that its F iterative scheme is more effective than the corresponding well known iterative schemes on this particular example. [ABSTRACT FROM AUTHOR]

Under the influence of circular economy theory, waste clothing recycling has been widely studied in the resource sector, and the waste clothing recycling channel (WCRC) is the vital link that affects the recycling efficiency of waste clothing. How to select the optimal WCRC is considered a typical multiple attribute group decision-making (MAGDM) problem. In this article, we develop sine trigonometric interaction operational laws (IOLs) (STIOLs) using Pythagorean fuzzy information. The sine trigonometric interaction Pythagorean fuzzy weighted averaging (STI-PyFWA) and sine trigonometric interaction Pythagorean fuzzy weighted geometric (STI-PyFWG) operators are advanced, and their several desirable properties are discussed. Further, we build a MAGDM framework based on the modified Pythagorean fuzzy CoCoSo (Combined Compromise Solution) method to solve the WCRC selection problem. The combined weight of attributes is determined, and the proposed aggregation operators (AOs) are applied to the CoCoSo method. A Pythagorean fuzzy distance measure is used to achieve the defuzzification of aggregation strategies. Finally, we deal with the WCRC selection problem for a sustainable environment by implementing the proposed method and performing sensitivity analysis and comparative study to validate its effectiveness and superiority. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The permanent magnet synchronous motor (PMSM) is a highly efficient energy saving machine. Due to its simple structural characteristics, good heat radiation capability, and high efficiency, PMSMs are gradually replacing AC induction motors in many industrial applications. The PMSM has a nonlinear system and lies on parameters that differ over time with complex high-class dynamics. To achieve the excessive performance operation of a PMSM, it essentially needs a speed controller for providing accurate speed tracking, slight overshoot, and robust disturbance repulsion. Therefore, this article provides an overview of different robust control techniques for PMSMs and reviews the implementation of a speed controller. In view of the uncertainty factors, such as parameter perturbation and load disturbance, the H∞ robust control strategy is mainly reviewed based on the traditional control techniques, i.e., robust H∞ sliding mode controller (SMC), and H∞ robust current controller based on Hamilton–Jacobi Inequality (HJI) theory. Based on comparative analysis, this review simplifies the development trend of different control technologies used for a PMSM speed regulation system. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM's validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work's reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future. [ABSTRACT FROM AUTHOR]

To find the correspondence between every number of attributes, the Bonferroni mean (BM) operator is most widely used and proven to be a flexible approach. To express uncertain information, the frame of the interval-valued T-spherical fuzzy set (IVTSFS) is a recent development in fuzzy settings which discusses four aspects of uncertain information using closed sub-intervals of [ 0 , 1 ] and hence reduces the information loss greatly. In this research study, we introduced the principle of BM operators with IVTSFS to develop the principle of the inter-valued T-spherical fuzzy (IVTSF) BM (IVTSFBM) operator, the IVTSF-weighted BM (IVTSFWBM) operator, the IVTSF geometric BM (IVTSFGBM) operator, and the IVTSF-weighted geometric BM (IVTSFWGBM) operator. To see the significance of the proposed BM operators, we applied these BM operators to evaluate the performance of solar cells that play an important role in the field of energy storage. To do so, we developed a multi-attribute group decision-making (MAGDM) procedure based on IVTSF information and applied it to the problem of solar cells to evaluate their performance under uncertainty, where four aspects of opinion about solar cells were taken into consideration. We studied the results obtained using BM operators with some previous operators to see the significance of the proposed IVTSF BM operators. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Does financial inclusion contribute to sustainable mountain development by providing access to financial resources and creating economic opportunities for poor mountain people? Keeping this question in mind, the present study aimed to investigate the nexus between financial inclusion and improvement in the living standards of mountain people, and reduction in socioeconomic disaster risks (economic poverty, multidimensional poverty and income inequality). For empirical investigation, the study employed Quasi Experimental Designs, Foster, Greer and Thorbecke poverty measures, Alkire et al. methodology, Gini Index and Quintile technique to assess the impact of financial inclusion on the living standards and reduction of economic poverty, multidimensional poverty and income inequality, respectively. We used the Logistic Regression technique to identify major drivers of socioeconomic disaster risks in the study area. The study collected quantitative and qualitative household level data from 424 households through structured questionnaires using multistage sampling technique for analysis. The findings of the study revealed a positive synergy among inclusive finance and living standards and a negative connection between financial inclusion and socioeconomic disaster risks in the Karakoram valleys of Pakistan. The logistic regression results also recognized financial inclusion as a potential determinant of economic poverty reduction. However, financial inclusion as a potential tool to eradicate multidimensional poverty in the study area showed insignificant results. These findings can help policy-makers and other stakeholders to understand the dynamics of socioeconomic disaster risks and the role of financial inclusion in their reduction to accomplish sustainable mountain development in the Karakoram valleys of Pakistan. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples. [ABSTRACT FROM AUTHOR]

(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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]