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Inter-dependency among the decision criteria and difficulty of handling the information in form of "yes," "abstain," "no," and "refusal" are two important issues to be addressed in multicriteria group decision-making (MCGDM) problems in the environment of uncertainty. Recently, spherical fuzzy set (SFS) has gained the attention of the researchers for MCGDM problems due to their capability of handling decision makers' preferences in the form "yes," "abstain," "no," and "refusal" more efficiently than picture fuzzy set. Choquet integral operator has an edge over traditional aggregation operator in the modeling of interaction among the preferences of decision makers and decision criteria and therefore, we define Choquet integral operator for SFS. The main objective of this study is to define the spherical fuzzy Choquet integral (SFCI) operator and to extend the VIsekriterijumska optimizacija I Kmpromisno Resenje (VIKOR) for spherical fuzzy environment. In this study we define spherical fuzzy Choquet average, spherical fuzzy Choquet geometric and spherical fuzzy Choquet integral distance (SFCID) operators and propose SFCI-based VIKOR method for MCGDM problems. Proposed SFCI-based VIKOR method is applied on warehouse selection problems and results are compared with existing MCGDM methods. [ABSTRACT FROM AUTHOR]

Linear Diophantine fuzzy soft set (LDFSS) is a powerful tool to handle uncertain information more flexibly and comprehensively. The aim of this paper is to propose some information measures (similarity measure, distance measure and entropy) for the LDFSS environment. For this aim, we first redefine the notion of LDFSS from a more general perspective. Then, we extend some well-known classical distances such as Hamming distance, Euclidean distance, Minkowski distance and etc. for the LDFSS environment. Also, we give some similarity measures where some of which are constructed from the presented distance measures and introduce the entropy measure for the LDFSSs. After, we construct two different decision-making methods, one based on the presented similarity measures and the other based on the TOPSIS method with entropy. Finally, we demonstrate a numerical example related to the medical diagnosis to illustrate that the proposed methods are more objective and feasible in the applications. [ABSTRACT FROM AUTHOR]

In order to conduct an in-depth study of Zhan’s methodology pertaining to the covering of multigranulation fuzzy rough sets ( C MG FRSs), we build two families: the family of fuzzy β -minimum descriptions and the family of β -maximum descriptions. Subsequently, utilizing these notions, we proceed to develop two variations of covering via optimistic (pessimistic) multigranuation rough set samples ( CO(P) MG FRS). The axiomatic properties are examined. In this study, we examine four models of covering using variable precision multigranulation fuzzy rough sets ( CVP MG FRSs). We proceed with analyzing the features of these models. Interconnections between these planned plans are also elucidated. This study explores algorithms that aim to identify innovative strategies for addressing multiattribute group decision-making problems (MAGDM) and multicriteria group decision-making problems (MCGDM). The test examples have been elucidated to provide an inclusive grasp of the efficacy of the offered samples. Ultimately, the distinctions between our methodologies and the preexisting research have been demonstrated. [ABSTRACT FROM AUTHOR]

In this article, we develop innovative models of multigranulation rough fuzzy sets, utilizing fuzzy β -covering and incorporating a range of techniques such as fuzzy β -neighborhood, fuzzy complementary β -neighborhood, fuzzy β -minimal description, and fuzzy β -maximal description. The axiomatic characteristics of fuzzy β -neighborhoods within the context of fuzzy β -covering based multigranulation rough fuzzy sets (F β CMGRFS) are analyzed. Thus, we introduce seven new classes of F β CMGRFS and investigate their relevant properties. Furthermore, the connections and associations between these techniques are established. Thus, we provide a set of observations and propositions that highlight the value and dissimilarities of our proposed models compared to others. A test example is produced to verify the applicability of the presented strategies and treat MCGDM issues. Finally, we compare the outcomes of our approaches and the existing studies to check the reliability and the validity of our work. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new approach to deal with multi-criteria group decision-making (MCGDM) problems under type-2 single valued neutrosophic set (T2SVNS) environment. Firstly, we give the concepts of single valued neutrosophic set (SVNS) and T2SVNS, and then we define probabilistic operators with T2SVN information. Secondly, two type of binary logarithm similarity measures (BLSM) and weighted binary logarithm similarity measures (WBLSM) for T2SVNSs are defined. Hybrid binary logarithm similarity measure (HBLSM) and weighted hybrid binary logarithm similarity measure (WHBLSM) for T2SVNSs are also defined. In addition, a MCGDM model based on TOPSIS method is proposed under T2SVNS environment. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we have established Cosine Trigonometric Operational Law (CTOL) and constructed Cosine Trigonometric Neutrosophic Weighted Averaging (CT-NWA) operator in the domain of generalized neutrosophic environment, which has been endorsed in a Multi-Criteria Group Decision Making (MCGDM) technique to select the best Anti-Pegasus software. In this study, the expertize recommendations and public opinion are well taken in context of debatable Pegasus issue in the Indian political, bureaucratic and democratic aspects. The problem has been addressed and resolved by using the integrated methodology of Analytical Network Process (ANP) and Evaluation based on Distance from Average Solution (EDAS) strategies. Here, we have optimized the weight factors and the gradation values of the decision makers as well as the sub-criteria of each criterion using Linear Programming (LP) model. Finally, we have performed the comparative analysis from various aspects to justify the reliability of our results. [ABSTRACT FROM AUTHOR]

Abstract Due to the fuzziness of the medical field, q-rung orthopair fuzzy 2-tuple linguistic (q-RF2L) set is the privileged way to aid medical professionals in conveying their assessments in the patient prioritization problem. The theme of the present study is to put forward a novel approach centered around the merging of prioritized averaging (PA) and the Maclaurin symmetric mean (MSM) operator within q-RF2L context. According to the prioritization of the professionals and the correlation among the defined criteria, we apply both PA and MSM to assess priority degrees and relationships, respectively. Keeping the pluses of the PA and MSM operators in mind, we introduce two aggregation operators (AOs), namely q-RF2L prioritized Maclaurin symmetric mean and q-RF2L prioritized dual Maclaurin symmetric mean operators. Meanwhile, some essential features and remarks of the proposed AOs are discussed at length. Based on the formulated AOs, we extend the weighted aggregated sum product assessment methodology to cope with q-RF2L decision-making problems. Ultimately, to illustrate the practicality and effectiveness of the stated methodology, a real-world example of patients’ prioritization problem is addressed, and an in-depth analysis with prevailing methods is performed.

This document is a special issue of the journal "Mathematics in Engineering, Science & Aerospace" that focuses on advances in mathematical modeling and its applications. The issue covers a diverse range of topics including reliability, operation research, multi-objective optimization, machine learning, fluid dynamics, software reliability, numerical analysis, and supply chain. The articles included in this collection have been peer-reviewed and cover various domains. Some specific topics discussed in the articles include simulating wave solutions using trigonometric B-spline functions, innovation diffusion models, adaptability of origami structures, effects of voltage unbalanced on induction motors, job-shop scheduling problems, support vector machines, spectral methods for solving partial differential equations, blood flow in stenosed arteries, predator-prey cooperation dynamics, software reliability growth models, entropy measures for intuitionistic fuzzy sets, stability of chemically reacting flows, Petri net modeling of signaling pathways, and system reliability analysis. The authors express gratitude to the contributors and reviewers, as well as the editorial board of the journal. [Extracted from the article]

To measure the amount of uncertainty present in the data, fuzzy set plays crucial role and to predict the hidden information of any fuzzy set, entropy plays significant role. This research work proposes a new entropy measure specifically designed for intuitionistic fuzzy sets (IFS). The validation process verifies the efficacy of the proposed measure. In addition, specific case studied illustrates the practical applications of the proposed entropy measure in real-world multi-criteria group decision making as proposed measure has been integrated with TOPSIS methods. The findings highlight the importance of entropy measures in effectively managing uncertainty and diversity. [ABSTRACT FROM AUTHOR]

This research is devoted to diagnosing water-borne infectious diseases caused by floods employing a novel diagnosis approach, the Einstein hybrid structure of q-rung orthopair fuzzy soft set. This approach integrates parts of fuzzy logic and soft set theory to develop a robust alternative for disease detection in stressful situations, especially in areas affected by floods. Compared to the traditional intuitionistic fuzzy soft set and Pythagorean fuzzy soft set, the q-rung orthopair fuzzy soft set (q-ROFSS) adequately incorporates unclear and indeterminate facts. The major objective of this investigation is to formulate the q-rung orthopair fuzzy soft Einstein hybrid weighted average (q-ROFSEHWA) operator and its specific characteristics. Moreover, our stated operator is implementing intelligent multi-criteria group decision-making (MCGDM) methodology. Floods are severe natural catastrophes that raise the risk of diseases and epidemics, particularly those caused by contaminants in the water, such as gastrointestinal diseases, respiratory infections, vector-borne diseases, skin infections, and water-borne parasites. The designed MCGDM strategy tackles the prevalence of certain conditions in flood-affected patients. A comparative investigation determined that the suggested method for detecting water-borne infectious disease due to floods is more effective and productive than conventional methods because of its logical structure. [ABSTRACT FROM AUTHOR]

Green supplier selection is an important debate in green supply chain management (GSCM), attracting global attention from scholars, especially companies and policymakers. Companies frequently search for new ideas and strategies to assist them in realizing sustainable development. Because of the speculative character of human opinions, supplier selection frequently includes unreliable data, and the interval-valued Pythagorean fuzzy soft set (IVPFSS) provides an exceptional capacity to cope with excessive fuzziness, inconsistency, and inexactness through the decision-making procedure. The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers (IVPFSNs) and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average (IVPFSIWA) and the interval-valued Pythagorean fuzzy soft interaction weighted geometric (IVPFSIWG) operators, and analyze their properties. These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals, providing a superior solution to othermethods. Moreover, specialist judgments were calculated by the MCGDM technique, supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects. Lastly, a statistical clarification of the planned method for green supplier selection is presented. [ABSTRACT FROM AUTHOR]

Traditional fossil fuels and has become an important component of clean energy. Vigorously investing in and developing renewable energy projects is of great strategic significance for enhancing sustainable energy development. Due to the unique nature of energy project investment, evaluating the investment risks of renewable energy projects is crucial for enhancing project feasibility. Therefore, this study propounds a novel multiple-criteria group decision framework based on the extended TODIM method (an acronym in Portuguese for Interactive and Multi-criteria Decision Making) under q-rung orthopair fuzzy (q-ROF) set for the application of renewable energy project investment risk assessment. To begin with, a novel q-ROF Lance distance measure is propounded for conquering the deficiencies caused by the prior distances. Then, an improved weight model by the defined q-ROF Lance distance is applied for determining the weight of experts, and an integration model that incorporates the group individual best and worst (GIBWM) and criteria importance through inter-criteria correlation (CRITIC) is presented for ascertaining the synthetics weight of criteria. Afterward, an extended TODIM method based upon the prospect theory using the proposed Lance distance measure is developed to rank alternatives. Furthermore, a hybrid decision framework is constructed to assess the investment risk of renewable energy projects. The sensitivity analysis regarding the risk avoidance coefficient is conducted to explore the stability and robustness of the propounded assessment framework. Further, the extant methodologies are utilized to compare with the designed decision framework to highlight its strengths and superiorities. The outcomes exhibit that the propounded framework can provide efficient decision support for assessing renewable energy project investment risk by modeling the uncertainty and psychological behavior of the assessment procedure. [ABSTRACT FROM AUTHOR]

In the complex landscape of financial accounting, selecting an optimal accounting system is crucial for organizations aiming to enhance compliance, financial reporting accuracy, and operational efficiency. To address these challenges, this study introduces a novel decision-making approach, integrating Measurement Alternatives and Ranking according to the Compromise Solution (MARCOS) with Picture Fuzzy Sets (PFS), known as the Picture Fuzzy MARCOS (PF-MARCOS) approach. PF-MARCOS provides a more accurate and comprehensive evaluation of financial accounting systems by incorporating vagueness and ambiguity in decision-making. Applying this approach to assess ten accounting platforms, the study evaluates key parameters, including compliance with international standards, cost, scalability, security, ease of implementation, accuracy, and user-friendliness. Decision-makers can efficiently rank alternatives using this systematic approach, determining which choices are most suited to long-term budgetary constraints. The results highlight the potential of PF-MARCOS for handling complex and uncertain financial scenarios, offering an effective tool to improve managerial financial accounting decision-making.

In the last few decades, there has been a significant increase in the importance of assessing social and ecological implications within industrial product supply chains. This tendency has given rise to the notion of supplier sustainability, which entails meeting the economic, environmental, and social demands of all suppliers. The supplier selections are typically based on experts’ opinion, which are then reflected in supplier ratings. When examining sustainability indicators, experts may not be fully aware of all aspects of suppliers’ economic, social, and environmental qualities. In the Decision Making (DM) approaches such as Pythagorean Fuzzy (PF) and q-Rung Orthopair Fuzzy (q-ROF) sets, experts are unable to use different powers for membership and non-membership grades simultaneously. In real-life DM problems, experts may require different power levels for membership and non-membership grades. In this paper, we propose a new extension of the COPRAS method under p, q-Quasirung orthopair fuzzy ( $p,q-$ QOF) sets, which allow decision-makers to use different power levels for membership and non-membership grades by incorporating parameters p and q. In the proposed approach, it is assumed that in addition to compiling the expert scores for suppliers, the issue analyst evaluates each expert’s degree of expertise for each criterion. The best choice is then determined by combining the data using the COPRAS method. The Inter-Criteria Correlation (CRITIC) method is employed to determine the unknown criteria weights. To demonstrate the effectiveness of our proposed approach, we apply it to a Multi-Criteria Group Decision-Making (MCGDM) problem that is focused on green supplier selection. Finally, we conduct a comparative study with existing approaches to demonstrate the practicality and applicability of the proposed DM method.

In this paper, we introduce the neutrosophic vague soft set, a combination of vague and neutrosophic soft sets. With the help of aggregated operations, we discuss neutrosophic vague soft sets. Multi-criteria group decision making can be evaluated effectively using the VIKOR approach. In this approach, the score function is generated by aggregating the VIKOR method to a neutrosophic vague soft approach. With the help of closeness values, alternative solutions are presented as optimal ones. To invest some money into the top five companies on the stock exchange, an investment company intends to purchase shares of the companies. Their investment strategy was to allocate some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars, and 10 dollars according to the top five ranked companies to minimize this effect. [ABSTRACT FROM AUTHOR]

With the development of digital creative industry and the use of more emerging digital technologies, the forms of digital cultural and creative design products are also increasingly diversified. Unlike traditional cultural and creative design products, digital cultural and creative design products are no longer limited to physical products, but appear more in the field of exhibition, virtual reality and product visualization. At the initial stage of the combination of digital information technology and cultural and creative content, digital cultural and creative design products, unlike ordinary cultural and creative design products, opened a new vision for users. The design quality evaluation of digital cultural and creative design products is viewed as a multi-criteria group decision-making (MCGDM). The single-value neutrosophic sets (SVNSs) concept and its interval-valued version (Interval-valued neutrosophic sets, IVNSs) are within the recent rapid developments for managing the uncertain representation problem in MCGDM. In SVNSs, decision makers (DMs) could portray membership, non-membership and hesitancy. IVNSs expands this useful feature through portraying intervals to these three information decision degrees. In this manner, the uncertainty, ambiguity and vagueness hidden in human judgements could be quantified more efficiently. IVNSs have been widely employed and researched in MCGDM. The main purpose of this paper is to proposed the Interval-valued neutrosophic number MABAC (IVNN-MABAC) technique based on prospect theory (PT) to address the MCGDM. Eventually, an example for design quality evaluation of digital cultural and creative design products and some comparative analysis was employed to demonstrate the superiority of the designed technique. [ABSTRACT FROM AUTHOR]

The aim of the paper is to extend the ARAS (Additive Ratio ASsessment) strategy to the single-valued pentapartitioned neutrosophic number environment which we call the SVPNN-ARAS strategy. The single-valued pentapartitioned neutrosophic number is the extension of fuzzy number and neutrosophic number. It comprehensively deals with uncertainty as it replaces indeterminacy with three independent entities, namely, contradiction, ignorance, and unknown. To develop a decision-making strategy, the arithmetic averaging operator for pentapartitioned numbers is defined and its basic properties are established. Single valued pentapartitioned number is a suitable mathematical tool to deal with uncertainty comprehensively. The SVPNN-ARAS strategy effectively evaluates and ranks feasible alternatives. In this paper, the ARAS strategy for multi-criteria group decision-making in a pentapartitioned neutrosophic number environment is developed. To demonstrate the applicability of the proposed strategy, a green supplier selection problem is solved and sensitivity analysis is performed to reflect the impacts of weighting of the decision makers and criteria on ranking the alternatives.

The theory of cubic bipolar fuzzy sets (CBFSs) is a robust approach for dealing with vagueness and bipolarity in real-life circumstances. This theory provides a hybrid machine learning paradigm that can accurately describe two-sided contrasting features for medical diagnosis. The ELECTRE-II model, which is extensively used, is expanded in this article to include the cubic bipolar fuzzy (CBF) context. In order to produce a comprehensive preference ordering of actions, ELECTRE-II establishes two different forms of embedded outranking relations while taking into account the subjective human judgments. A huge number of applications have been created by its variations under various models, considering the CBF model's greater capacity to deal. For opinions in the adaptive CBF structure with unknown information, the CBF-ELECTRE-II group decision support method is described. With the use of proper CBF aggregation operations, the expert CBF views on each alternative and criterion are compiled in the first step. The approach then constructs weak and strong outranking relations and offers three distinct CBF outranking set kinds ("concordance", "indifferent" and "discordance" sets). Strong and weak outranking graphs serve as a visual depiction of the latter, which is finally studied by a rigorous iterative procedure that yields a preferred system. For these objectives, integrated CBF-VIKOR and CBF-ELECTRE-II techniques are developed for multi-criteria group decision making (MCDGM). Finally, suggested techniques are recommended to determine ranking index of efficient road freight transportation (FRT) in Industry 4.0. The ranking index and optimal decision are also computed with other techniques to demonstrate robustness of proposed MCDGM approach.

Abstract Digital marketing technology can not only help enterprises effectively control marketing costs but also accurately identify target customers and determine customer needs to improve marketing conversion rates. Multiple conflicting and asymmetric criteria need to be taken simultaneously into account to effectively assess digital marketing technology. Accordingly, the target of our paper is to propound an enhanced additive ratio assessment (ARAS) methodology to aid experts in evaluating digital marketing technology in a complex uncertain setting. The spherical fuzzy (SF) set is an expansion of the picture fuzzy set (PFS) that has been recognized as a powerful model to portray indeterminacy and vagueness. A fresh score function is proffered to compare the SF numbers and its merits are also analyzed. Then, some novel operations for SF numbers are defined and several aggregation operators based on them are propounded. Further, a mixed multi-criteria group decision-making (MCGDM) method is developed by incorporating the method based on the removal effects of criteria (MEREC), step-wise weight assessment ratio analysis (SWARA), and enhanced ARAS approach under SF information. Also, a case concerning digital marketing technology evaluation is executed to prove the efficiency and practicability of the presented SF-MEREC–SWARA–ARAS method. Finally, contrast and sensitivity investigations are also implemented to highlight the strengths and robustness of the proffered methodology, respectively.

Abstract The distribution of emergency shelter materials in emergency cases around the world is a hard task, the goal of this research is to offer a Complex Non-linear Diophantine Fuzzy (C-NLDF) decision-making model for earthquake shelter construction. Essentially, the article is divided into three sections to acquire acceptable and precise measures in emergency decision-making situations. First, we present the Complex Non-Linear Diophantine Fuzzy Set (CN-LDFS), a new generalization of the complex linear Diophantine fuzzy set (CLDFS) and q-linear Diophantine fuzzy set (q-LDFS), as well as explore its key aspects. Furthermore, aggregation operators are useful for aggregating uncertainty in decision-making issues. As a result, algebraic norms for CN-LDFSs are produced based on certain operational laws. In the second section of the work, we offer a series of averaging and geometric aggregation operators under CN-LDFS that are based on defined operating laws. In the final section of the work, under complex Non-linear Diophantine fuzzy information, the ranking algorithms based on suggested aggregation operators are present to address the case study regarding emergency situation of earthquakes. In comparison section, results of existing and proposed operators explore the effectiveness of proposed methodologies and provide accurate emergency measures to address the global uncertainty about the construction of emergency shelters in earthquakes.

A crucial step for agricultural product merchants to achieve profitable and sustainable development in the live-streaming e-commerce age is evaluating the risk of the agricultural products live-streaming e-commerce platform. However, there isn't much reliable research available right now on the risk evaluation of platforms. Therefore, this study suggests an improved risk evaluation method based on interval-valued intuitionistic fuzzy multi-criteria group decision-making (MCGDM). This method determines the decision-maker weight for the risk criterion according to the levels of professionalism of the decision-makers in the risk criterion and uses the VIse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to rate the risk of the alternative agricultural products live-streaming e-commerce platforms. The viability and dependability of the approach described in this work are demonstrated using a case study. The strengths and weaknesses of this approach are illustrated by a comparative analysis. With the help of this paper, agricultural product merchants will be able to identify the live-streaming e-commerce platform that carries the least amount of overall risk and work toward the paper's stated objectives of sustainable development in addition to developing and enhancing theoretical research findings in the field. [ABSTRACT FROM AUTHOR]

An interval-valued q-rung orthopair fuzzy set ( I V q r O F S ) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q ≥ 1 . Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted I V p , q r O F S . This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the I V p , q r O F S and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy ( I V p , q r O F ) numbers, a novel score function is put forward and compared to the known I V q r O F S -based score functions to determine its viability. Moreover, we present I V p , q r O F aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of I V p , q r O F criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method's stability, and a comparative analysis is performed to elucidate its strengths and advantages. [ABSTRACT FROM AUTHOR]

The q-rung neutrosophic vague soft set (q-rung NVSS) is a generalization of the neutrosophic vague soft set (NVSS) and the vague soft set (VSS). The TOPSIS aggregated operation (AO) was used to discuss the q-rung NVSS. As an extension of VSS, the TOPSIS method effectively makes multi-criteria group decision making (MCGDM). With a score function, the goal is to find a positive and negative ideal solution based on q-rung NVSS. Closeness values are determined by presenting optimal alternatives. We provide practical examples to support our conclusions. This results in the outcome of the models for which q is provided. Considering the validity and usefulness of the models under consideration can be achieved by comparing them with those that have been proposed. Recent discoveries have generated quite a bit of interest and fascination. [ABSTRACT FROM AUTHOR]

The distribution of emergency shelter materials in emergency cases around the world is a hard task, the goal of this research is to offer a Complex Non-linear Diophantine Fuzzy (C-NLDF) decision-making model for earthquake shelter construction. Essentially, the article is divided into three sections to acquire acceptable and precise measures in emergency decision-making situations. First, we present the Complex Non-Linear Diophantine Fuzzy Set (CN-LDFS), a new generalization of the complex linear Diophantine fuzzy set (CLDFS) and q-linear Diophantine fuzzy set (q-LDFS), as well as explore its key aspects. Furthermore, aggregation operators are useful for aggregating uncertainty in decision-making issues. As a result, algebraic norms for CN-LDFSs are produced based on certain operational laws. In the second section of the work, we offer a series of averaging and geometric aggregation operators under CN-LDFS that are based on defined operating laws. In the final section of the work, under complex Non-linear Diophantine fuzzy information, the ranking algorithms based on suggested aggregation operators are present to address the case study regarding emergency situation of earthquakes. In comparison section, results of existing and proposed operators explore the effectiveness of proposed methodologies and provide accurate emergency measures to address the global uncertainty about the construction of emergency shelters in earthquakes. [ABSTRACT FROM AUTHOR]

The theory of cubic bipolar fuzzy sets (CBFSs) is a robust approach for dealing with vagueness and bipolarity in real-life circumstances. This theory provides a hybrid machine learning paradigm that can accurately describe two-sided contrasting features for medical diagnosis. The ELECTRE-II model, which is extensively used, is expanded in this article to include the cubic bipolar fuzzy (CBF) context. In order to produce a comprehensive preference ordering of actions, ELECTREII establishes two different forms of embedded outranking relations while taking into account the subjective human judgments. A huge number of applications have been created by its variations under various models, considering the CBF model's greater capacity to deal. For opinions in the adaptive CBF structure with unknown information, the CBF-ELECTRE-II group decision support method is described. With the use of proper CBF aggregation operations, the expert CBF views on each alternative and criterion are compiled in the first step. The approach then constructs weak and strong outranking relations and offers three distinct CBF outranking set kinds ("concordance", "indifferent" and "discordance" sets). Strong and weak outranking graphs serve as a visual depiction of the latter, which is finally studied by a rigorous iterative procedure that yields a preferred system. For these objectives, integrated CBF-VIKOR and CBF-ELECTRE-II techniques are developed for multi-criteria group decision making (MCDGM). Finally, suggested techniques are recommended to determine ranking index of efficient road freight transportation (FRT) in Industry 4.0. The ranking index and optimal decision are also computed with other techniques to demonstrate robustness of proposed MCDGM approach. [ABSTRACT FROM AUTHOR]

A cubic bipolar fuzzy set (CBFS) is by far the most efficient model for handling bipolar fuzziness because it carries both single-valued (SV) and interval-valued (Ⅳ) bipolar fuzzy numbers at the same time. The sine trigonometric function possesses two consequential qualities, namely, periodicity and symmetry, both of which are helpful tools for matching decision makers' conjectures. This article aims to integrate the sine function and cubic bipolar fuzzy data. As a result, sine trigonometric operational laws (STOLs) for cubic bipolar fuzzy numbers (CBFNs) are defined in this article. Premised on these laws, a substantial range of aggregation operators (AOs) are introduced. Certain features of these operators, including monotonicity, idempotency, and boundedness, are explored as well. Using the proffered AOs, a novel multi-criteria group decision-making (MCGDM) strategy is developed. An extensive case study of carbon capture and storage (CCS) technology has been provided to show the viability of the suggested method. A numerical example is provided to manifest the feasibility of the developed approach. Finally, a comparison study is executed to discuss the efficacy of the novel MCGDM framework.

Optimization techniques can be used to find the optimal combination of inputs and parameters and help identify the most efficient solution. Aggregation operators (AOs) play a prominent role in discernment between two circulations of prospect and pull out anxieties from that insight. The most fundamental objective of this research is to extend the interaction AOs to the interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS), the comprehensive system of the interval-valued Pythagorean fuzzy soft set (IVPFSS). The IVPFHSS adroitly contracts with defective and ambagious facts compared to the prevalent Pythagorean fuzzy soft set and interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS). It is the dominant technique for enlarging imprecise information in decision-making (DM). The most important intention of this exploration is to intend interactional operational laws for IVPFHSNs. We extend the AOs to interaction AOs under IVPFHSS setting such as interval-valued Pythagorean fuzzy hypersoft interactive weighted average (IVPFHSIWA) and interval-valued Pythagorean fuzzy hypersoft interactive weighted geometric (IVPFHSIWG) operators. Also, we study the significant properties of the proposed operators, such as Idempotency, Boundedness, and Homogeneity. Still, the prevalent multi-criteria group decision-making (MCGDM) approaches consistently carry irreconcilable consequences. Meanwhile, our proposed MCGDM model is deliberate to accommodate these shortcomings. By utilizing a developed mathematical model and optimization technique, Industry 5.0 can achieve digital green innovation, enabling the development of sustainable processes that significantly decrease environmental impact. The impacts show that the intentional model is more operative and consistent in conducting inaccurate data based on IVPFHSS.

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In this paper, we present the Pythagorean neutrosophic interval valued fuzzy soft set. This is a generalization of the Pythagorean interval valued fuzzy soft set as well as the neutrosophic interval valued fuzzy soft set. It is discussed in this paper how an aggregated operation is used to aggregate the decision matrix of PNIVS. There are a number of extensions to the normosophic fuzzy soft sets that involve the use of multi-criteria decisionmaking. The aim of this study is to develop a score function based on aggregating TOPSIS methods in order to find ideal solutions for PNIVS that have both positive and negative values. The purpose of this study is to identify the optimal alternative under closeness conditions. It gives us the opportunity to interact with two real life problems, such as the production of ten different types of motorbikes by an automobile company. According to this set of parameters, a motorbike is determined by the fuel tank capacity, better styling, a better price, more mileage, durable, and other factors that determine how a customer can choose which bike to buy. [ABSTRACT FROM AUTHOR]

In contrast to the Pythagorean interval valued fuzzy soft set and the neutrosophic interval valued fuzzy soft set, the Pythagorean neutrosophic interval valued fuzzy soft set is a generalization of these sets. We discuss aggregating PyNIVFS decision matrixes by using aggregated operations. The VIKOR method, which is an extension of neutrosophic fuzzy soft sets, is a powerful method for evaluating multi-criteria group decision making. The score function in this approach is based on the aggregation of the VIKOR method to a PyNIVFSpositive and negative solution. Optimal alternatives are introduced under closeness. An investment company plans to purchase some shares of the top five companies in the stock exchange to invest some money on. In order to minimize this factor, they decided to invest some of their cash in percentages of 30 dollars, 25 dollars, 20 dollars, 15 dollars and 10 dollars in accordance with the top five ranked companies in order to minimize the effect of this factor. [ABSTRACT FROM AUTHOR]

As a generalized fuzzy set, the dual hesitant bipolar fuzzy set (DHBFS) has received considerable attention and has recently become a widespread topic. The DHBFSs can reflect the disagreement and hesitancy of decision-makers flexibly and conveniently. However, we find that in DHBFS, all elements are endowed with the same importance, which indicates that multiple occurrence and appearance of some elements is neglected, which is evidently impractical. To circumvent this issue, this article aims to originate a new fuzzy tool, namely the probabilistic hesitant bipolar fuzzy set (PHBFS), which takes into account not only different grades of membership and negative membership but also their probabilistic data. Further, we outline some basic concepts, including score function, accuracy degree, normalization, comparison rule, and basic operations for PHBFS. Besides, we formulate some aggregation operators for aggregating probabilistic hesitant bipolar fuzzy information, including probabilistic hesitant bipolar fuzzy Hamacher prioritized average operator, probabilistic hesitant bipolar fuzzy Hamacher prioritized geometric operator and their weighted forms. Several special cases of these propound operators are also outlined. Based on these foundations, we develop a multi-criteria group decision-making method to cope with probabilistic hesitant bipolar fuzzy information-based problems. The proposed methodology is more reasonable for getting a better selection result and can overcome the disadvantage of information loss. At last, the proposed method is employed in the decision-making case related to recruiting foreign faculty members, and its practicality and effectiveness are verified. [ABSTRACT FROM AUTHOR]

Generalized spherical fuzzy number (GSFN) is an extension of spherical fuzzy number (SFN) which deals the uncertainties involved in the real-life problems in much better way than other fuzzy numbers. So far, some fundamental operational laws of GSFNs are characterized, yet excluding the logarithmic operation. In this manuscript, we have defined and discussed various algebraic properties of logarithmic operational law (LOL) for GSFN where the logarithmic base δ is a positive real number. Moreover, we have developed weighted averaging and weighted geometric aggregation operators and utilize these aggregation operators to initiate a multi-criteria group decision making (MCGDM) technique in the generalized spherical fuzzy (GSF) environment, which has been used to solve a problem of cloud service management. We have indicated the utility and reliability of the proposed MCGDM technique through sensitivity analysis. Finally, a comparative study has been presented with the help of a real data set to justify the rationality and efficiency of our proposed method with the existing methods. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to optimize the performance and emission characteristics of a single cylinder compression ignition engine using diesel-hydrogen dual fuel. A TMI (timed manifold injection) system was designed employing an ECU (electronic control unit) for hydrogen induction into the engine manifold. The results showed a significant enhancement in BTHE (12.44% Max. enhancement at 85% full load condition under DH4 strategy) compared to base-diesel operation. The NOx emissions were enhanced to a maximum of 10.33 g/kw-hr at full load under the DH4 strategy. The emissions of UHC were found to be higher at lower loads and get significantly reduced to a maximum of 3.98 g/kw-hr at full load under the DH2 strategy. In comparison, soot emissions decrease substantially and are reduced to a maximum of 0.02 g/kw-hr at 85% full load condition under the DH5 strategy. The proposed method utilizes a Spherical Fuzzy MARCOS MCGDM-based Type-3 Fuzzy Logic approach, which integrates several criteria and uncertain inputs to improve decision-making. The paper outlines the theoretical framework of the approach and the experimental setup used for validation. The results demonstrate that the proposed method significantly reduces emissions while simultaneously improving the engine's performance. Overall, this study offers an innovative and effective solution for optimizing the performance and emissions of diesel-hydrogen dual fuel engines. • Pure diesel and diesel–H 2 blends are expermented. • Diesel–H 2 blends enhanced BTHE than pure diesel in all part loads. • Diesel–H 2 blends reduced the overall emission spectrum for the existing engine. • The performance-emission trade-off prediction studied using Type-3 Fuzzy Logic. • Spherical Fuzzy MARCOS was used to select the most effective predictive logic scheme. [ABSTRACT FROM AUTHOR]

Over the past century, there has been a dramatic increasing interest in the multi-criteria group decision-making (MCGDM) technique, with a considerable amount of studies published regarding it. One of the well-known approaches in the MCGDM paradigm is Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The integration of the TOPSIS method with fuzzy set theory has proven to be successful in various applications. Recently, a wide array of publications has proposed implementing a type-2 fuzzy set with TOPSIS. However, the additional degree of uncertainty represented by type 2 has largely been ignored, especially in a few specific mathematical operations in the model. We propose constructing interval type-2 fuzzy membership functions (IT2 MFs) using interval-based data gathered from a survey, where this is used to generate a new scale to represent ratings for each alternative. This procedure utilized all information gathered from decision makers. In addition, we present a complete algorithm for TOPSIS based on IT2 fuzzy sets (IT2 FSs) which preserve the interval-based form output. The output in the form of intervals offers decision makers (DMs) with more detailed information, enabling them to make more nuanced decisions. This can include cautious decisions when intervals are wider and overlapping. Although understanding the exact meaning of these intervals and their widths in a decision-making context is challenging, this paper introduces a systematic method for connecting input uncertainty to output uncertainty in the TOPSIS technique. This approach establishes a solid foundation for future research. Thus far, no other researchers have suggested a data-driven method that combines TOPSIS with fuzzification and provides intervals as the final output. [ABSTRACT FROM AUTHOR]

• A novel group decision methods classification framework has been presented. • A review of existing multiple-source aggregation methods has been carried out. • Existing methods have been compared with current needs in the scientific field. • Future research pathways are provided to enhance upcoming techniques. • A multiple-source aggregation methods guide is provided. Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts' weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts' weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts' weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions. [ABSTRACT FROM AUTHOR]

A cubic bipolar fuzzy set (CBFS) is by far the most efficient model for handling bipolar fuzziness because it carries both single-valued (SV) and interval-valued (Ⅳ) bipolar fuzzy numbers at the same time. The sine trigonometric function possesses two consequential qualities, namely, periodicity and symmetry, both of which are helpful tools for matching decision makers' conjectures. This article aims to integrate the sine function and cubic bipolar fuzzy data. As a result, sine trigonometric operational laws (STOLs) for cubic bipolar fuzzy numbers (CBFNs) are defined in this article. Premised on these laws, a substantial range of aggregation operators (AOs) are introduced. Certain features of these operators, including monotonicity, idempotency, and boundedness, are explored as well. Using the proffered AOs, a novel multi-criteria group decision-making (MCGDM) strategy is developed. An extensive case study of carbon capture and storage (CCS) technology has been provided to show the viability of the suggested method. A numerical example is provided to manifest the feasibility of the developed approach. Finally, a comparison study is executed to discuss the efficacy of the novel MCGDM framework. [ABSTRACT FROM AUTHOR]

Complex fuzzy (CF) sets (CFSs) play an important role in modeling two-dimensional information challenges. Researchers exploring decision-making systems have recently become interested in CFS extensions. The complex T-spherical fuzzy (CT-SF) set (CT-SFS) is a recent extension of the CFSs. The present study aims to devise the Frank operational laws for the CT-SF environment and to verify their required properties. Subsequently, some CT-SF Frank aggregation operators are explored, such as CT-SF Frank weighted averaging (CT-SFFWA) operator, CT-SF Frank weighted geometric (CT-SFFWG) operator, CT-SF Frank ordered weighted averaging (CT-SFFOWA) operator, and CT-SF Frank ordered weighted geometric (CT-SFFOWG) operator, CT-SF Frank hybrid averaging (CT-SFFHA) operator, CT-SF Frank hybrid geometric (CT-SFFHG) operator, and their peculiar cases are examined. Based on the devised operators, a novel multi-criteria group decision-making (MCGDM) methodology is investigated to tackle MCGDM problems under the CT-SF environment. Lastly, the practicality and effectiveness of the presented methodology are conducted by parameter analysis and comparative exploration.

This study intends to significantly enhance the capacity of decision experts (DEs) to capture their judgment in a larger area. In order to accomplish this, we propound the $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy set ( $\textsf {r},\textsf {s},\textsf {t}$ -SFS), an expansion of the t-spherical fuzzy set. In $\textsf {r},\textsf {s},\textsf {t}$ -SFS the sum of the $\textsf {r}$ th power of membership grade, $\textsf {s}$ th power of neutral grade and the $\textsf {t}$ th power of non-membership grade is less than or equal to 1, where $\textsf {r}$ , $\textsf {s}$ and $\textsf {t}$ are natural numbers. Due to the inclusion of the extra parameters $\textsf {r}$ and $\textsf {s}$ , the $\textsf {r},\textsf {s},\textsf {t}$ -SFS is able to describe assessment information in a more flexible and comprehensive manner. This work begins by defining $\textsf {r},\textsf {s},\textsf {t}$ -SFS and demonstrating that it is an extension of various existing fuzzy sets. The fundamental operations, score, and accuracy functions of $\textsf {r},\textsf {s},\textsf {t}$ -SFS are then introduced, and their mathematical features are examined. Also, we study some distance measures between $\textsf {r},\textsf {s},\textsf {t}$ -SFSs and their required properties. Next, to aggregate $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy data, $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy weighted averaging ( $\textsf {r},\textsf {s},\textsf {t}$ -SFWA) and $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy weighted geometric ( $\textsf {r},\textsf {s},\textsf {t}$ -SFWG) operators are bring forward along with some of their essential properties. Based on the proposed distance measure, maximizing deviation method is combined with $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy information to establish the criteria weight determination method. Following this, we present $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method using the grounds of classical VIKOR method depending upon two focal properties, namely, group utility and individual regret of opponent. To demonstrate the use of the framed approach and exhibit its validity, we present a case study of arc welding robot selection. Besides, the effectiveness and accuracy of the proposed VIKOR are proved by parameter analysis and comparison analysis findings.

In this paper, we firstly put forward a new linguistic set called Z-probabilistic double hierarchy linguistic term set (Z-PDHLTS) based on Z-number, which considers both the complexity of linguistic variables and the credibility of evaluation information. Then, a new comparison method of Z-PDHLTS based on possibility degree is put forward to compare the size of two sets. In addition, a possibility degree matrix method and ZPDHL -VIKOR method for multi-criteria group decision making problem with Z-PDHLTS are proposed to rank alternatives. Finally, an example of green mine selection is used and some comparative analyses are made to explain its effectiveness. [ABSTRACT FROM AUTHOR]

Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model. [ABSTRACT FROM AUTHOR]