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Crude oil, the backbone of modern industry, holds unparalleled significance as a global energy cornerstone. Unlocking its potential hinges on effective pretreatment techniques, ensuring purity, and maximizing efficiency. This study extends the established Spherical Fuzzy Set paradigm to explore the domain of Disc Spherical Fuzzy Sets (D-SFSs) in critical decision-making for crude oil preparation. Investigating D-SFSs within the Aczel Alsina norm, the research employs comparison rules, conversion rules, and distance metrics. Primary operations of the Aczel Alsina norm in D-SFSs are examined, laying the groundwork for introducing unique aggregation operations within this framework. The paper's primary aim is to propose a hybrid method, termed MEREC-SWARA-MARCOS-D-SFSs Multiple Attribute Group Decision Making, which integrates the aforementioned aggregation procedures. A case study on crude oil pretreatment validates the effectiveness of the proposed method. Furthermore, a comprehensive comparison with CoCoSo underscores the reliability of the method. This study represents a significant stride in enhancing decision-making by providing a robust framework to tackle complex situations, particularly in the critical domain of crude oil pretreatment. [ABSTRACT FROM AUTHOR]

Achieving household food security is the tumbling issue of the century. This article explores the factors affecting household food security and solutions by utilizing a synergy of statistical and mathematical models. The methodology section is divided into two portions namely sociological and mathematical methods. Sociologically, 379 household heads were interviewed through structured questions and further analyzed in terms of descriptive and binary logistic regression. The study found that 4 independent variables (poverty, poor governance, militancy, and social stratification) showed a significant association (P = 0.000) to explain variations in the dependent variable (household FS). The Omnibus test value (χ2= 102.386; P = 0.000) demonstrated that the test for the entire model against constant was statistically significant. Therefore, the set of predictor variables could better distinguish the variation in household FS. The Nagelkerke's R Square (R2 =.333) helps to interpret that the prediction variable and the group variables had a strong relationship. Moreover, 23% to 33% variation in FS was explained by the grouping variables (Cox and Snell R2 = 0.237 and Nagelkerke's R2 = 0.333). The significant value of Wald test results for each variable confirmed that the grouping variables (poor governance P = 0.004, militancy P = 0.000, social stratification P = 0.021 and poverty P = 0.000) significantly predicted FS at the household level. Mathematically, all the statistics were validated further through the application of spherical fuzzy mathematics (TOPIS and MADM) to explore what factors are affecting household FS. Thus, the study found that F3 (poverty) > F2 (militancy) > F4 (social stratification) > F1 (poor governance) respectively. Thus, it could be concluded from these findings that the prevalence of poverty dysfunctional all the channels of household FS at the macro and micro levels. Therefore, a sound and workable model to eradicate poverty in the study area by ensuring social safety nets for the locals was put forward some of the policy implications for the government are the order of the day. [ABSTRACT FROM AUTHOR]

Spherical q-linear Diophantine fuzzy sets (Sq-LDFSs) showed a significant improvement to handling uncertainty in multi-criteria decision-making (MADM). It is advantageous for two-parametric data as well as for data with three variable parameters. One of the most crucial functions of supply chain management is to increase competitive pressure. The study's standout innovation, Multi-Attributive Ideal Real Comparative Analysis (MAIRCA), has been implemented to give powerful group decision-making. An ecological perspective is becoming more prevalent due to the competitive climate and customer perception. Green supplier selection (GSS) has become a significant issue. In this study, we address the problem of GSS, which aims for flexibility, robustness, ecological sensitivity, leanness, and feasibility. The feasibility criteria in recycling, environmental, carbon footprints, and water consumption are different from those in standard supplier selection. The aim of our work is to introduced the weighted Average/Geometric aggregation operators based on Sq-LDFSs. For this we defined some operational rules as a foundation of aggregation operators. Secondly we proposed a MAIRCA approach for Sq-LDFSs to address these issues. The MAIRCA strategy, which uses multi-criteria group decision-making (MCGDM) to evaluate and choose traditional and environmental conventionalities, is used to reduce instability and ambiguity. The spherical q-linear Diophantine fuzzy MAIRCA approach provides comparative analysis of decision-makers and criteria. By merging Sq-LDFS and MAIRCA, a hybrid strategy is formed, successfully selecting the best provider among options based on the order of significance. These numerical examples demonstrate the suggested MCGDM approaches that were applied in actual situations, giving a realistic appreciation of their efficacy. The comparative study of the final ranking further supports the idea that these strategies are dependable in decision-making processes in addition to being practical and usable. [ABSTRACT FROM AUTHOR]

The key objective of this article is to introduce the innovative idea of a complex intuitionistic hesitant fuzzy set (CIHFS), which blends the intuitionistic hesitant fuzzy set with the complex fuzzy set to address the uncertain information in real-life complex problems. In CIHFS, the range of the membership functions is extended from the subset of the real number to the unit disc under the hesitant environment. To determine how well the CIHFSs can be distinguished from one another, we first propose generalized distance measures and weighted generalized distance measures based on the Hamming, Euclidean, and Hausdorff metrics. Some interesting properties and their relationships are thoroughly discussed. Furthermore, a decision-making framework for selecting the optimal option from the feasible set has been proposed, which is grounded in these distance metrics. For the purpose of proving the method's efficacy, we included examples from pattern recognition and medical diagnostics. [ABSTRACT FROM AUTHOR]

This article presents a higher-order circular intuitionistic fuzzy time series forecasting method for predicting the stock change index, which is shown to be an improvement over traditional time series forecasting methods. The method is based on the principles of circular intuitionistic fuzzy set theory. It uses both positive and negative membership values and a circular radius to handle uncertainty and imprecision in the data. The circularity of the time series is also taken into consideration, leading to more accurate and robust forecasts. The higher-order forecasting capability of this method provides more comprehensive predictions compared to previous methods. One of the key challenges we face when using the amount featured as a case study in our article to project the future value of ratings is the influence of the stock market index. Through rigorous experiments and comparison with traditional time series forecasting methods, the results of the study demonstrate that the proposed higher-order circular intuitionistic fuzzy time series forecasting method is a superior approach for predicting the stock change index. [ABSTRACT FROM AUTHOR]

This paper aims to assess and deal with the challenges experienced by medical professionals caring for infectious diseases. In Pakistan, public health is still a serious concern and the main contributor to morbidity and mortality is infectious diseases. The major issue is a resemblance in the clinical symptoms of infectious diseases such as tuberculosis, hepatitis, COVID-19, dengue, and malaria. Early detection of infectious disease is crucial in order to start treatment with counseling and medication. This can only be done if several infections with similar clinical traits can be diagnosed depending on several criteria, including the availability of various kits, the ability to carry out diagnostic procedures, money, and technical staff. But woefully Pakistan's economy is badly battered due to several circumstances. Therefore, we are unable to provide patients with enough diagnostic testing kits and broadly accessible therapy choices, which makes diagnosis more difficult and create hesitancy with fuzziness and randomness. For this purpose, we introduced the new concept of the complex probabilistic hesitant fuzzy N-soft set. We defined its fundamental operations (like restricted and extended union, restricted and extended intersection, weak, top and bottom weak complements, as well as soft max-AND or soft min-OR) with examples. We also discussed their many properties with their proofs and theorems. Furthermore, we developed the algorithms for decision-making where doctors use the complex probabilistic hesitant fuzzy N-soft information to identify a particular disease. Furthermore, we explained numerical illustration of two case studies. Moreover, a sensitive and comparative analysis is discussed. In the last, we conclude the whole study. [ABSTRACT FROM AUTHOR]

One of the hottest areas for applying the solutions currently available is the internet of things-based smart housing society architecture and its uncertainty analysis. When intelligent parking, waste management, public transportation, public safety, and other automatic methods for housing society's growth were implemented, it became even more crucial. An intelligent, smart system is necessary to manage these problems and provide smooth services. Additionally, it will be helpful in reducing issues with time waste and societal safety. However, the issue comes up when describing accurate, approximate, or questionable parking, transit, safety, and waste management areas. This paper discusses several mathematical solutions for the smart housing society that use fuzzy rough sets, probabilistic hesitant fuzzy sets, and their extensions with neutrosophic sets. For further growth, a few studies on the graphic display of the evolution of the smart housing society are also considered. The rough set theory can be useful when dealing with imprecise, incomplete, or indeterminate data sets. The core contribution of this work is the construction of a novel generalized notion of a single-valued neutrosophic probabilistic hesitant fuzzy rough set (SV-NPHFRS), which is a hybrid structure of the single-valued neutrosophic set, the probabilistic hesitant fuzzy set, and the rough set. In contrast to the present literature, the underlying idea of SV-NPHFRS is that it is a powerful mathematical tool for managing uncertainty and imperfect information. This method is particularly beneficial when there are a number of competing criteria to consider. The aggregation technique plays an important role in decision-making concerns, especially when more competing criteria are present. In the study's comparison phase, the suggested decision support system is compared to relevant existing approaches. The results suggest that, in terms of choice flexibility, the suggested technique has the potential to outperform the drawbacks of the current decision-making tools. The proposed study is expected to be useful for a number of researchers conducting future work on housing societies, waste management, public safety diagnostics, and hybridization. [ABSTRACT FROM AUTHOR]

Zadeh's Z̆-numbers are able to more effectively characterize uncertain information. Combined with "constraint" and "reliability". It is more powerful at expressing human knowledge. While the reliability of data can have a direct impact on the precision of decisions. The key challenge in solving a Z̆-number issue is reasoning about both fuzzy and probabilistic uncertainty. Existing research on the Z̆-number measure is only some, and most studies cannot adequately convey the benefits of Z̆-information and the properties of Z̆-number. Considering this study void, this work concurrently investigated the randomness and fuzziness of Z̆-number with Spherical fuzzy sets. We first introduced the spherical fuzzy Z-numbers (SFZNs), whose elements are pairwise comparisons of the decision-maker's options. It can be used effectively to make true ambiguous judgments, reflecting the fuzzy nature, flexibility, and applicability of decision making data. We developed the operational laws and aggregation operators such as the weighted averaging operator, the ordered weighted averaging operator, the hybrid averaging operator, the weighted geometric operator, the ordered weighted geometric operator, and the hybrid geometric operator for SFZ̆Ns. Furthermore, two algorithm are developed to tackle the uncertain information in the form of spherical fuzzy Z̆-numbers based to the proposed aggregation operators and TODIM methodology. Finally, we developed the relative comparison and discussion analysis to show the practicability and efficacy of the suggested operators and approach. [ABSTRACT FROM AUTHOR]

Due to the frequent occurrence of numerous emergency events that have significantly damaged society and the economy, the need for emergency decision-making has been manifest recently. It assumes a controllable function when it is critical to limit property and personal catastrophes and lessen their negative consequences on the natural and social course of events. In emergency decision-making problems, the aggregation method is crucial, especially when there are more competing criteria. Based on these factors, we first introduced some basic concepts about SHFSS, and then we introduced some new aggregation operators such as the spherical hesitant fuzzy soft weighted average, spherical hesitant fuzzy soft ordered weighted average, spherical hesitant fuzzy weighted geometric aggregation, spherical hesitant fuzzy soft ordered weighted geometric aggregation, spherical hesitant fuzzy soft hybrid average, and spherical hesitant fuzzy soft hybrid geometric aggregation operator. The characteristics of these operators are also thoroughly covered. Also, an algorithm is developed within the spherical hesitant fuzzy soft environment. Furthermore, we extend our investigation to the Evaluation based on the Distance from Average Solution method in multiple attribute group decision-making with spherical hesitant fuzzy soft averaging operators. And a numerical illustration for "supply of emergency aid in post-flooding the situation" is given to show the accuracy of the mentioned work. Then a comparison between these operators and the EDAS method is also established in order to further highlight the superiority of the established work. [ABSTRACT FROM AUTHOR]

In modern civilization, individuals are increasingly concerned with evaluating the quality of medical services. Evaluation of the quality of medical services enables medical care providers to monitor and improve their service quality. The evaluation of medical service quality is efficiently addressed by the novel concept of Aczel–Alsina operators in an intuitionistic hesitant fuzzy (IHF) environment as multicriteria decision-making (MCDM) problem. Thus, this paper presents the IHF Aczel–Alsina weighted geometric operators for IHF information. We first apply the Aczel–Alsina norms to IHF scenarios and present novel operations of intuitionistic hesitant fuzzy sets. This article develops a unique strategy for evaluating the quality of medical services based on the specified operators, including a quantitative framework for evaluating medical service quality and a novel MCDM technique. Finally, this article presents a numerical example of the novel approach used to evaluate medical services for hospitals and compares it to conventional MCDM methods to highlight the suggested superiority method. According to the comparative results, our strategy outperforms the insufficiency of lacking decision flexibility in the existing MAGDM method. [ABSTRACT FROM AUTHOR]

Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases. [ABSTRACT FROM AUTHOR]

The control of spreading of COVID-19 in emergency situation the entire world is a challenge, and therefore, the aim of this study was to propose a spherical intelligent fuzzy decision model for control and diagnosis of COVID-19. The emergency event is known to have aspects of short time and data, harmfulness, and ambiguity, and policy makers are often rationally bounded under uncertainty and threat. There are some classic approaches for representing and explaining the complexity and vagueness of the information. The effective tool to describe and reduce the uncertainty in data information is fuzzy set and their extension. Therefore, we used fuzzy logic to develop fuzzy mathematical model for control of transmission and spreading of COVID19. The fuzzy control of early transmission and spreading of coronavirus by fuzzy mathematical model will be very effective. The proposed research work is on fuzzy mathematical model of intelligent decision systems under the spherical fuzzy information. In the proposed work, we will develop a newly and generalized technique for COVID19 based on the technique for order of preference by similarity to ideal solution (TOPSIS) and complex proportional assessment (COPRAS) methods under spherical fuzzy environment. Finally, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested method, along with a sensitivity analysis and comparative analysis, showing the feasibility and reliability of its results. [ABSTRACT FROM AUTHOR]

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method's capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects. [ABSTRACT FROM AUTHOR]

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method's capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects. [ABSTRACT FROM AUTHOR]

Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry approach to get a foothold within a system and move laterally throughout the organization. In recent decades, powerful attacks such as Stuxnet, Duqu, Flame, and Havex have served as wake-up calls for industrial units. All organizations are faced with the rise of security challenges in technological innovations. This paper aims to develop aggregation operators that can be used to address the decision-making problems based on a spherical fuzzy rough environment. Meanwhile, some interesting properties of idempotence, boundedness, and monotonicity for the proposed operators are analyzed. Moreover, we use this newly constructed framework to select ICS security suppliers and validate its acceptability. Furthermore, a different test has been performed based on a new operator to strengthen the suggested approach. Additionally, comparative analysis based on the novel extended TOPSIS method is presented to demonstrate the superiority of the proposed technique. The results show that the conventional approach has a larger area for information representation, better adaptability to the evaluation environment, and higher reliability of the evaluation results. [ABSTRACT FROM AUTHOR]

As a generalization of Pythagorean fuzzy sets and picture fuzzy sets, spherical fuzzy sets provide decision makers more flexible space in expressing their opinions. Preference relations have received widespread acceptance as an efficient tool in representing decision makers' preference over alternatives in the decision-making process. In this paper, some new preference relations are investigated based on the spherical fuzzy sets. Firstly, the deficiency of the existing operating laws is elaborated in detail and three cases are described to identify the accuracy of the proposed operating laws in the context of t-spherical fuzzy environment. Also, a novel score function is proposed to obtain the consistent value in ranking of the alternatives. The backbone of this research, t-spherical fuzzy preference relation, consistent t-spherical fuzzy preference relations, incomplete t-spherical fuzzy preference relations, consistent incomplete t-spherical fuzzy preference relations, and acceptable incomplete t-spherical fuzzy preference relations are established. Additionally, some ranking and selection algorithms are established using the proposed novel score function and preference relations to tackle the uncertainty in real-life decision-making problems. Finally, evaluation of the product quality of the online shopping platform problem is demonstrated to show the applicability and reliability of proposed technique. [ABSTRACT FROM AUTHOR]

The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers' unknown weights as well as attributes' weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to present the notion of probabilistic hesitant fuzzy rough (PHFR) set and their basic operations. As a generalization of the sets, PHFR set is a more profitable way to express the uncertainties in the data. For it, firstly, we define the basic operational laws like, the union, intersection and the composition of probabilistic hesitant fuzzy approximation spaces with some basic properties are discussed in details. Secondly, presented the novel decision-making technique based on the PHFR sets over two nonempty fixed sets to deal with uncertainty in decision-making problems. Finally, two numerical examples are provided with some comparative study to validate the proposed approach. [ABSTRACT FROM AUTHOR]

The spherical fuzzy set (SFS) is one of the most important concepts to accommodate more uncertainties than the intuitionistic fuzzy set, Pythagorean fuzzy set, picture fuzzy set and hence its applications are more extensive. Keeping the feature and the importance of the SFS, the objective of this paper is to present some robust symmetric operational laws for SFSs. Associated with these laws, we define some series of new aggregation operators named as spherical fuzzy (SF) symmetric weighted averaging, SF ordered weighted averaging and SF hybrid weighted averaging operators to aggregate the SF information. Afterwards, we present a group decision making technique to solve the multi attribute group decision making (MAGDM) based on proposed symmetric aggregation operators and illustrate with a numerical example of renewable energy source selection as a real-life practical example to validate it. A comparative analysis is also conducted to show the superiorities of the proposed method. [ABSTRACT FROM AUTHOR]

Among the most prevalent and serious retinal illnesses are glaucoma, diabetic retinopathy, hypertension caused by diabetes, cataracts, and age-related macular degeneration. If these disorders are not identified at an early stage, permanent eyesight loss ensues. Numerous anomalies in the retina, including microaneurysms, neovascularization, hemorrhages, soft exudates or cotton wool patches, and macular edema, serve as illustrations. Ophthalmologists employ automated technologies that analyze ophthalmic imaging modalities to quickly screen for and diagnose these illnesses. Due to the complexity of numerous diseases that have overlapping symptoms, accurate disease diagnosis has become more difficult in modern times. When it comes to medical diagnosis, this complexity presents a huge challenge for specialists working in health departments. Many academics and researchers are actively attempting to create novel approaches and solutions to deal with the difficulties in medical diagnostics. The goal of this research initiative is to develop cutting-edge techniques that can help professionals make more accurate disease diagnoses. The present work introduces the notion of confidence level for neutrosophic average and aggregation operators, which contrasts with neutrosophic rough average and geometric aggregation operators, which do not take into account the experts’ familiarity with the objects being examined during the initial assessment. A more sophisticated structure of neutrosophic rough sets is used to calculate the confidence level, allowing for a more thorough review procedure. The fundamental traits of the suggested operators are also covered in the paper. [ABSTRACT FROM AUTHOR]

Emergency decision-making is vital for nations or communities because it increases emergency management's effectiveness and legitimacy, which in turn greatly minimizes environmental damage, fatalities, and economic loss. The evaluation of emergency judgements must take into account significant inaccuracy, fuzzyness, and ambiguity. While high risk and uncertainty are frequently characteristics of emergency decision-making (EDM) circumstances. The current EDM methodologies do not take into account the psychological behavior of the decision makers in addition to the various emergency situations and the various responses. In this paper, we presented a new method based on a Complex Probabilistic Hesitant Fuzzy Soft Set (CPHFSS) as represented by membership in 2-D with hesitant probability. The idea that is being put forth captures the ambiguity and takes into account emergency situations while also taking into account the psychological state of the decision-makers involved in the EDM procedure. The introduction of a new score function for the CPHFSS serves as the second objective of this paper, which is to address a number of comparability issues. We examine a novel family of hybrid operators for CPHFSS that utilize numerous independent variables as a solution to these unforeseen issues. The group decision-making strategy and EDAS technique are then suggested employing these operators. Later, an emergency decision-making situation involving a major fire in China is used to demonstrate the validity of the algorithms. • Concept of complex probabilistic hesitant fuzzy soft set is presented. • Introduce a new score function for the CPHFSS. • Group decision-making strategy and EDAS technique presented. • Emergency decision-making problems discussed in the study. • Case study related to industrial disaster emergency decision-making discuss. [ABSTRACT FROM AUTHOR]

In this paper, we introduce spherical fuzzy sets (SFSs) which is an advanced tool of the fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets. We investigate the basic properties of SFSs and compare the idea SFSs with picture fuzzy sets. The spaces of spherical membership grades and picture membership grades are examined by graphically. Some useful operation such as spherical fuzzy t'-norms and spherical fuzzy t'-conorms are introduced. Also introduced spherical fuzzy negator and some classifications of spherical fuzzy t'-norms and spherical fuzzy t′-conorms which are useful for development the aggregation operator to aggregate the spherical fuzzy information. Finally, a food circulation center evaluation problem is given as a practical application to demonstrate the usage and applicability of the proposed ranking approach. [ABSTRACT FROM AUTHOR]

The novel concept of spherical fuzzy set consists of positive, neutral and negative membership grades which satisfy the conditions that the square sum of its membership grades is less than or equal to 1. In this paper, we investigate the family of novel similarity measures between spherical fuzzy sets based on cosine function by considering the positive, neutral, negative and refusal grades in SFSs. To implement the proposed similarity measures, we provide some numerical applications of decision-making problems. A comparative study of the proposed and existing similarity measures is established. The proposed method is more advance as compare to the previous all reflexive. [ABSTRACT FROM AUTHOR]

The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm. In this paper, we discussed generalized form of weighted geometric aggregation operator for picture fuzzy information. Further, the proposed geometric aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. Also, we propose the TOPSIS method to aggregate the picture fuzzy information. To implement the proposed models, we provide some numerical applications of group decision making problems. Also compared with previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

The key objective of the present proposed work in this paper is introduced a new version of picture fuzzy set so called spherical fuzzy sets (SFS). spherical fuzzy set is a new extension of picture fuzzy sets and Pythagorean fuzzy sets. In spherical fuzzy sets, membership degrees are gratifying the condition 0 ⩽ P2 (x) + I2 (x) + N2 (x) ⩽1 instead of 0 ⩽ P (x) + I (x) + N (x) ⩽1 as is in picture fuzzy sets. In this paper, we investigate the basic operations of spherical fuzzy sets and discuss some related results. We extend operational laws to aggregation operators and introduce weighted averaging and weighted geometric aggregation operators based on spherical fuzzy number's. Further a multi attribute decision making method is developed and these aggregation operators are utilized. Finally, we constructed a numerical approach for implementation of proposed technique. [ABSTRACT FROM AUTHOR]

The key objective of the proposed work in this paper is to introduce a new version of picture linguistic fuzzy set, so-called spherical linguistic fuzzy sets. The novel concept of spherical linguistic fuzzy set consists of linguistic term, positive, neutral and negative membership degrees which satisfies the conditions that the square sum of its membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of spherical linguistic fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose spherical linguistic fuzzy Choquet integral weighted averaging (SLFCIWA) operator based on spherical fuzzy numbers. Further, the proposed SLFCIWA operator of spherical fuzzy number is applied to multi-attribute group decision-making problems. Also, we propose the GRA method to aggregate the spherical fuzzy information. To implement the proposed models, we provide some numerical applications of group decision-making problems. Also compared with the previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-579-611-1441). The authors, therefore, gratefully acknowledge DSR technical and financial support. [ABSTRACT FROM AUTHOR]

Reference 1 Qiyas M, Abdullah S, Khan S. Multi-attribute group decision making based on sine trigonometric spherical fuzzy aggregation operators. Retraction Note to: Soft Computing (2021) 25:8549-8572 https://doi.org/10.1007/s00500-021-057... The Editors-in-Chief have retracted this article because it is highly similar to a previously published article by Qiyas et al. ([1]). [Extracted from the article]

Department of Mathematics, Khawaja Farid University of Engineering and Information Technology, Rahim Yar Khan, Pakistan In the Acknowledgements section, "Muhammad Naeem would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4310396DSR02)." now reads: "Muhammad Naeem would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4310396DSR06)." Shahzaib Ashraf was incorrectly affiliated with 'Department of Mathematics and Statistics, Bacha Khan University, Charsadda, KPK, Pakistan'. [Extracted from the article]

We developed a multicriteria decision-making method based on the list of novel single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) weighted averaging and geometric aggregation operators to address the uncertainty and achieve the sustainability of the manufacturing business. In addition, a case study on choosing the optimum elements for a sustainable manufacturing sector was carried out. The proposed decision support method is then compared to other relevant methodologies, and a validity test is performed to show the reliability and validity of the new methodology. Sustainability is one of the most important issues the world economy is facing today. Several industrial businesses have incurred large financial losses as a result of their ignorance of sustainability issues. Manufacturers in industrialized countries have done a decent job of making sure that their businesses are sustainable over the long run. Modern companies use a lot of modern technologies. These include blockchain, artificial intelligence (AI), the Internet of Things (IoT), big data analytics (BDA), and fuzzy logic (fuzziness). These modern technologies support the continuation of life, either directly or indirectly. Therefore, it is of utmost importance to concentrate on those elements that encourage the adoption of sustainability. The goal of this study is to provide a framework for using cutting-edge technology to increase the adoption of sustainability in manufacturing firms. Under the guidance of single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) aggregate information, it was advised to place a strong emphasis on addressing sustainability, waste management, environmental protection, manufacturing cost savings, and chemicals and resources. The results suggest that the proposed technique can solve the inadequacy of the existing decision method by the SV-NHFR aggregation operators in terms of decision adaptability. [ABSTRACT FROM AUTHOR]

We developed a multicriteria decision-making method based on the list of novel single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) weighted averaging and geometric aggregation operators to address the uncertainty and achieve the sustainability of the manufacturing business. In addition, a case study on choosing the optimum elements for a sustainable manufacturing sector was carried out. The proposed decision support method is then compared to other relevant methodologies, and a validity test is performed to show the reliability and validity of the new methodology. Sustainability is one of the most important issues the world economy is facing today. Several industrial businesses have incurred large financial losses as a result of their ignorance of sustainability issues. Manufacturers in industrialized countries have done a decent job of making sure that their businesses are sustainable over the long run. Modern companies use a lot of modern technologies. These include blockchain, artificial intelligence (AI), the Internet of Things (IoT), big data analytics (BDA), and fuzzy logic (fuzziness). These modern technologies support the continuation of life, either directly or indirectly. Therefore, it is of utmost importance to concentrate on those elements that encourage the adoption of sustainability. The goal of this study is to provide a framework for using cutting-edge technology to increase the adoption of sustainability in manufacturing firms. Under the guidance of single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) aggregate information, it was advised to place a strong emphasis on addressing sustainability, waste management, environmental protection, manufacturing cost savings, and chemicals and resources. The results suggest that the proposed technique can solve the inadequacy of the existing decision method by the SV-NHFR aggregation operators in terms of decision adaptability. [ABSTRACT FROM AUTHOR]

In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems. [ABSTRACT FROM AUTHOR]

This paper aims to resolve the issue of the ranking of the fuzzy numbers in decision analysis, artificial intelligence, and optimization. In the literature, many ideas have been established for the ranking of the fuzzy numbers, and those ideas have some restrictions and limitations. We propose a method based on spherical fuzzy numbers (SFNs) for ranking to overcome the existing restrictions. Further, we investigate the basic properties of SFNs, compare the idea of spherical fuzzy set with the picture fuzzy set, and establish some distance operators, namely spherical fuzzy distance-weighted averaging (SFDWA), spherical fuzzy distance order-weighted averaging (SFDOWA), and spherical fuzzy distance order-weighted average weighted averaging (SFDOWA WA) operators with the attribute weights' information incompletely described. Further, we design an algorithm to solve decision analysis problems. Finally, to validate the usage and applicability of the established procedure, we assume the child development influence environmental factors problem as a practical application. [ABSTRACT FROM AUTHOR]

Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative. [ABSTRACT FROM AUTHOR]

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

Keeping in mind the importance and well growing Pythagorean fuzzy sets, in this paper, some novel operators for Pythagorean fuzzy sets and their properties are demonstrated. In this paper, we develop a comprehensive model to tackle decision-making problems where strong points of view are in the favour and against the some projects, entities or plans. Therefore, a new approach, based on Pythagorean fuzzy set models by means of Pythagorean fuzzy Dombi aggregation operators is proposed. An approach to deal with decision-making problems using Pythagorean Dombi averaging and Dombi geometric aggregation operators is established. This model has a stronger capability than existing averaging, geometric, Einstein, logarithmic averaging and logarithmic geometric aggregation operators for Pythagorean fuzzy information. Finally, the proposed method is demonstrated through an example of how the proposed method helps us and is effective in decision-making problems. [ABSTRACT FROM AUTHOR]

Recently, neutrosophic sets are found to be more general and useful to express incomplete, indeterminate and inconsistent information. The purpose of this paper is to introduce new aggregation operators based on logarithmic operations and to develop a multi-criteria decision-making approach to study the interaction between the input argument under the single valued neutrosophic (SVN) environment. The main advantage of the proposed operator is that it can deal with the situations of the positive interaction, negative interaction or non-interaction among the criteria, during decision-making process. In this paper, we also defined some logarithmic operational rules on SVN sets, then we propose the single valued neutrosophic hybrid aggregation operators as a tool for multi-criteria decision-making (MCDM) under the neutrosophic environment and discussd some properties. Finally, the detailed decision-making steps for the single valued neutrosophic MCDM problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative. [ABSTRACT FROM AUTHOR]

The problem of energy crisis and environmental pollution has been mitigated by the generation and use of solar power; however, the choice of locations for solar power plants is a difficult task because the decision-making process includes political, socio-economic, and environmental aspects. Thus, several adverse consequences have been created by the choice of suboptimal locations. The objective of this paper is to address the integrated qualitative and quantitative multicriteria decision-making framework for the selection of solar power plant locations. Neutrosophic sets (NSs) are the latest extension of the ordinary fuzzy sets. The main characteristic of the neutrosophic sets is satisfying the condition that the sum of the truth, indeterminacy, and falsity grades must be at least zero and at most three. In this research, we establish novel operational laws based on the Yager t-norm and t-conorm under neutrosophic environments (NE). Furthermore, based on these Yager operational laws, we develop a list of novel aggregation operators under NE. In addition, we design an algorithm to tackle the uncertainty to investigating the best solar power plant selection in five potential locations in Pakistan. A numerical example of solar power plant location problem is considered to show the supremacy and effectiveness of the proposed study. Also, a detailed comparison is constructed to evaluate the performance and validity of the established technique. [ABSTRACT FROM AUTHOR]

The information aggregation operator plays a key rule in the group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely picture fuzzy Einstein weighted and Einstein ordered weighted operators are proposed in this paper. Some properties of these aggregation operators are discussed in detail. Further, a group decision making problem is illustrated and validated through a numerical example. A comparative analysis of the proposed and existing studies is performed to show the validity of the proposed operators. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models. [ABSTRACT FROM AUTHOR]

Diminished estimate techniques for image quality assessment examine the overall quality using only partially retrieved features from the reference image. The main goal of these methods is to make objective evaluation flexible enough to accommodate the influence of any new visual distortion. The research provides a rapid approach for quality assessment of color photographs based on this concept by altering the structural similarity index measure (SSIM) index in a neutrosophic environment. The SSIM family is a set of parameters that have demonstrated a promising approach in the analysis of reference picture tasks. The current study deals with the exploitation of the concept to use Single-Valued Neutrosophic Sets (SVNSs) for evaluating image quality. Neutrosophic divergence was being constructed for an image and its comparison with other SSIM is presented. Resultantly, a correlation was observed between the proposed divergence and SSIM, which gave accurate informatics. Additionally, the results were presented on a real line which reflects clear information on image convergence and divergence. The uncertainty in the allocation of membership is called the hesitation degree, fuzzy sets have gained a lot of traction in numerous domains of signal and image processing. Based on generalized exponential fuzzy entropy, a trustworthy Image Quality Assessment is proposed. [ABSTRACT FROM AUTHOR]

In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this investigation. It is suggested that these processes be simulated using a method utilizing a hesitant fuzzy set, a rough set, and a probabilistic single-valued neutrosophics set. The proposed approach is employed in the decision-making process, while taking into consideration the decision-makers' (DMs') level of confidence in the data they have obtained in order to deal with ambiguity, incomplete data, and uncertainty in lower and upper approximations. The major goal was to outline the issue's complexities in order to pique interest among experts in the health care sector and encourage them to evaluate SMDs using various evaluation standards. The analysis of the technique's outcomes demonstrated that the rankings and the results themselves were adequate and trustworthy. The effectiveness of our suggested improvements is also demonstrated through a symmetrical analysis. The symmetry behavior shows that the current techniques address more complex and advanced data. [ABSTRACT FROM AUTHOR]

The advantages of the intuitionistic fuzzy set, Pythagorean fuzzy set, and q-rung orthopair fuzzy set are all carried over into the linear Diophantine fuzzy set by extending the restrictions on the grades. Linear Diophantine fuzzy sets offer a wide range of practical applications because the reference parameters allow evaluation andto express their judgments about membership and nonmembership degrees in a variety of ways. Linguistic-valued information cannot be described by linear Diophantine fuzzy numbers since precise numbers are used in linear Diophantine fuzzy systems. In this paper, we first present the novel idea of a linguistic linear Diophantine fuzzy set, which is the hybrid structure of the linear Diophantine fuzzy set and the linguistic term set. Furthermore, some basic operational rules with novel distance measures, namely, Hamming, Euclidean, and Chebyshev distance measures, are established. Based on the newly defined concept of distance measure, an extended TOPSIS technique is presented to tackle the linguistic uncertainty in real-world decision support problems. A numerical example is illustrated to support the applicability of the proposed methodology and to analyze symmetry of the optimal decision. A comparison analysis is constructed to show the symmetry, validity, and effectiveness of the proposed method over the existing decision support techniques. [ABSTRACT FROM AUTHOR]

Spherical fuzzy set (SFS) is one of the most important and extensive concept to accommodate more uncertainties than existing fuzzy set structures. In this article, we will describe a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. First, we study the notion of SFSs, the score and accuracy functions of SFSs and their basic operating laws. In addition, defined the generalized distance measure for SFSs based on spherical fuzzy entropy measure to compute the unknown weights information. Secondly, the spherical fuzzy information-based decision-making technique for MAGDM is presented. Lastly, an illustrative example is delivered with robot selection to reveal the efficiency of the proposed spherical fuzzy decision support approach, along with the discussion of comparative results, to prove that their results are feasible and credible. [ABSTRACT FROM AUTHOR]

The aims of this study are to propose the linguistic picture fuzzy Dombi (LPFD) aggregation operators and decision-making approach to deal with uncertainties in the form of linguistic picture fuzzy sets. LPFD operators have more flexibility due to the general fuzzy set. Utilizing the Dombi operational rule, the series of Dombi aggregation operators were proposed, namely linguistic picture fuzzy Dombi arithmetic/geometric, ordered arithmetic/ordered geometric and Hybrid arithmetic/Hybrid geometric aggregation operators. The distinguished feature of these proposed operators is studied. At that point, we have used these Dombi operators to design a model to deal with multiple attribute decision-making (MADM) issues under linguistic picture fuzzy information. Finally, an illustrative example to evaluate the emerging technology enterprises is provided to demonstrate the effectiveness of the proposed approach, together with a sensitivity analysis and comparison analysis, proving that its results are feasible and credible. [ABSTRACT FROM AUTHOR]