T-spherical fuzzy power aggregation operators and their applications in multi-attribute decision making

An interaction and feedback mechanism-based group decision-making for emergency medical supplies supplier selection using T-spherical fuzzy information

Selecting a supplier for emergency medical supplies during disasters can be considered a typical multiple attribute group decision-making (MAGDM) problem. MAGDM is an intriguing common problem that is rife with ambiguity and uncertainty. It becomes much more challenging when governments and medical care enterprises adjust their priorities in response to the escalating problems and the effectiveness of the actions taken in different countries. As decision-making problems become increasingly complicated nowadays, a growing number of experts are likely to use T-spherical fuzzy sets (T-SFSs) rather than exact numbers. T-SFS is a novel extension of fuzzy sets that can fully convey ambiguous and complicated information in MAGDM. The objective of this paper is to propose a MAGDM methodology based on interaction and feedback mechanism (IFM) and T-SFS theory. In it, we first introduce T-SF partitioned Bonferroni mean (T-SFPBM) and T-SF weighted partitioned Bonferroni mean (T-SFWPBM) operators to fuse the evaluation information provided by experts. Then, an IFM is designed to achieve a consensus between multiple experts. In the meantime, we also find the weights of experts by using T-SF information. Furthermore, in light of the combination of IFM and T-SFWPBM operator, an MAGDM algorithm is designed. Finally, an example of supplier selection for emergency medical supplies is provided to demonstrate the viability of the suggested approach. The influence of parameters on decision results and comparative analysis with the existing methods confirmed the reliability and accuracy of the suggested approach.

Multiple criteria decision analytic methods in management with T-spherical fuzzy information

With a focus on T-spherical fuzzy (T-SF) sets, the aim of this paper is to create a split-new appraisal mechanism and an innovative decision analytic method for use with multiple-criteria assessment and selection in uncertain situations. The T-SF frame is the latest recent advancement in fuzzy settings and uses four facets (consisting of membership grades of positivity, neutrality, negativity, and refusal) to elucidate complex uncertainties, thereby evidently reducing information loss, in anticipation of fully manifesting indistinct and equivocal information. This paper adds to the body of knowledge regarding multiple criteria choice modeling by raising T-SF correlation-oriented measurements connected to the fixed and displaced ideal/anti-ideal benchmarks and by creating an approachable appraisal mechanism for advancing a T-SF decision analytic methodology. Consider, in particular, the performance ratings of available options in terms of judging criteria under the T-SF type of uncertainties. This research gives correlation-oriented measurements focusing on two varieties of maximum and square root functions in T-SF situations, which serve as a solid foundation for an efficacious appraisal mechanism from two views of anchored judgments corresponding to the fixed and displaced benchmarks. The T-SF Minkowski distance index is generated to integrate the outranking and outranked identifiers relying on correlation-oriented measurements for figuring out the local outranking and outranked indices. The T-SF decision analytic procedures are constructed using a new appraisal significance index that is founded on certain valuable insights of correlation-oriented maximizing and minimizing indices as well as global outranking and outranked indices. Additionally, a concrete location selection dilemma is dealt with in this research to showcase the applicability and efficiency of the suggested T-SF decision analytic methodology. Sensitivity analyses and comparative studies are carried out to investigate substantial modifications in pertinent parameters and to confirm the robustness of the predominance relationships among the available options. The suggested approaches are adaptable, flexible, and reliable, according to the application outcomes and comparison findings. This research provides four scientific contributions: (1) the utilization of T-SF correlation coefficients as the basis for prioritization analysis involving multiple criteria assessments, (2) the evolution of the T-SF Minkowski distance index to model outranking decision-making processes, (3) the creation of a reliable appraisal mechanism based on T-SF correlation-oriented measurements for intelligent decision support, and (4) the advancement of computational tools and procedures (e.g., correlation-oriented maximizing and minimizing indices, global outranking and outranked indices, and appraisal significance indices) to perform the decision analytic procedure in T-SF settings. In terms of managerial implications, the solution findings support the employment of the fixed ideal/anti-ideal benchmarking mechanism, as its measurements and indices are easy to operate and suitably sensitive. Next, in practical implementations of the T-SF decision analytic procedure, it is advised to utilize the T-SF Manhattan distance index for calculating convenience. Finally, the T-SF decision analytic techniques offer fundamental ideas and measurements appropriate for manipulating T-SF information in complex decision situations, thereby increasing the application potential in the area of decision-making with information uncertainty.

Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making

The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.

Spherical fuzzy hamacher power aggregation operators based on entropy for multiple attribute group decision making

As an improved form of fuzzy sets (FSs), spherical fuzzy sets (SFSs) could provide decision makers (DMs) with more free space to express their preference information. In this article, we first develop some Hamacher power aggregation operators under SFSs by power operators and Hamacher operators, including spherical fuzzy Hamacher power average (SFHPA) operator, spherical fuzzy Hamacher power geometric (SFHPG) operator, spherical fuzzy Hamacher power weighted average (SFHPWA) operator, spherical fuzzy Hamacher power weighted geometric (SFHPWG) operator, spherical fuzzy Hamacher power ordered weighted average (SFHPOWA) operator, spherical fuzzy Hamacher power ordered weighted geometric (SFHPOWG) operator, spherical fuzzy Hamacher power hybrid average (SFHPHA) operator and spherical fuzzy Hamacher power hybrid geometric (SFHPHG) operator. At the same time, some properties of the proposed operators are investigated, and the relationships between these operators and existing operators are discussed. Furthermore, a novel spherical fuzzy entropy measure is introduced to calculate unknown attribute weights. Then, some novel multiple attribute group decision making (MAGDM) methods are established by the proposed operators as well as entropy measure under SFSs. Lastly, the practicability of the presented methods is verified with a numerical case. Moreover, the robustness, availability and superiority for the developed methods are demonstrated via sensitivity analysis and further comparation with the existing methods.

Prioritization of thermal energy techniques by employing picture fuzzy soft power average and geometric aggregation operators

Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average [Formula: see text], weighted picture fuzzy soft power average [Formula: see text] and ordered weighted picture fuzzy soft power average [Formula: see text] aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric [Formula: see text], weighted picture fuzzy soft power geometric [Formula: see text] and ordered weighted picture fuzzy soft power geometric [Formula: see text] aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions.

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

In this article, a novel CoCoSo (Combined compromise solution) method based on Frank operational laws and softmax function is investigated to handle multiple attribute group decision-making problems for T-spherical fuzzy sets. We extend Frank operations in T-spherical fuzzy environment and develop a series of aggregation operators, including T-spherical fuzzy Frank softmax (T-SFFS) average and geometric operators, and their weighted forms, i.e., T-SFFS weighted averaging (T-SFFSWA) and T-SFFS weighted geometric (T-SFFSWG) operators. Some of their basic properties and particular cases are discussed. Meanwhile, the monotonicity of proposed operators is also analyzed, and it is discussed that how they indicate the decision-makers’ optimistic and pessimistic decision attitudes with risk preference. Furthermore, a novel CoCoSo method based on Hamming distance measure is proposed, which considers both decision-maker’s decision attitude and attribute priority, and a multiple attribute group decision-making framework with two independent and parallel T-spherical fuzzy information processing processes are designed. Lastly, a real case of spent power battery recycling technology (SPBRT) selection is presented to show the practicability of the proposed method. Also sensitivity and comparative analyses are carried out to prove the reliability, effectiveness, and superiority of our proposed method.

Analysis of the suitability of the solar panels for hospitals: A new fuzzy decision-making model proposal with the T-Spherical TOP-DEMATEL method

In this study, a new fuzzy decision-making model is created to evaluate whether the solar panels are efficient to minimize energy costs of the hospitals. The weights of the criteria are calculated by considering T-Spherical fuzzy decision-making trial and evaluation laboratory (DEMATEL) method. Moreover, for the purpose of measuring the coherency of the findings, analysis results are also calculated for different t values. Additionally, by making improvements to some criticisms to the classical DEMATEL method, a new technique is created by the name of TOP-DEMATEL while integrating some steps of technique for order preference by similarity to ideal solution (TOPSIS) to the DEMATEL technique. The main novelty of this study is that it is analyzed whether the solar panels are effective in reducing the costs of hospitals with an original decision-making model. It is concluded that generating own energy in the long run is the most crucial item according to both T-Spherical fuzzy DEMATEL and TOP-DEMATEL methods. The analysis results are quite similar for different t values. This situation gives information about the coherency and reliability of the findings. This situation gives information that the solar panels should be taken into consideration for the hospitals because they will minimize energy dependency of the hospitals. On the other side, the results of T-Spherical fuzzy TOP-DEMATEL indicate that the high initial investment cost is the second most critical factor in this respect. This finding is quite different by comparing with the results of T-Spherical fuzzy TOP-DEMATEL. Hence, it is seen that cost effectiveness should also be taken into consideration for the decision of generating the solar panels in the hospitals.

A Novel Approach Based on Power Aggregation Operator with the Hybrid-Indicator Information for Evaluating Regional Development Level of Rural Practical Talents

The development level evaluation of regional rural practical talents needs to comprehensively consider a variety of factors. The general development level of rural practical talents in different regions has little difference, but there are significant differences between different factors. This paper proposes a set of scientific indicators for evaluating rural practical talents, which can be used to understand the development status and level of rural practical talents in various regions and to further provide method support for the development level evaluation of rural practical talents in various regions of China. To avoid the overly subjective drawback of setting index weights in the Analytic Hierarchy Process (AHP), we set the indicator weights via the variation coefficient method and fuse the evaluation information based on an aggregation approach with a hybrid-indicator information power operator, which can lead to a more scientific and effective evaluation of the development level of rural practical talents. Finally, we apply the proposed approach to conducting the applied research on real cases, give relevant analysis and suggestions, and propose the training and introduction policies for the rural practical talents, to promote the development of rural revitalization and construction.

T-spherical uncertain linguistic MARCOS method based on generalized distance and Heronian mean for multi-attribute group decision-making with unknown weight information

The T-spherical uncertain linguistic (TSUL) sets (TSULSs) integrated by T-spherical fuzzy sets and uncertain linguistic variables are introduced in this article. This new concept is not only a generalized form but also can integrate decision-makers’ quantitative evaluation ideas and qualitative evaluation information. The TSULSs serve as a reliable and comprehensive tool for describing complex and uncertain decision information. This paper focuses on an extended MARCOS (Measurement of Alternatives and Ranking according to the Compromise Solution) method to handle the TSUL multi-attribute group decision-making problems where the weight information is completely unknown. First, we define, respectively, the operation rules and generalized distance measure of T-spherical uncertain linguistic numbers (TSULNs). Then, we develop two kinds of aggregation operators of TSULNs, one kind of operator with independent attributes is T-spherical uncertain linguistic weighted averaging and geometric (TSULWA and TSULWG) operators, and the other is T-spherical uncertain linguistic Heronian mean aggregation operators (TSULHM and TSULWHM) considering attributes interrelationship. Their related properties are discussed and a series of reduced forms are presented. Subsequently, a new TSUL-MARCOS-based multi-attribute group decision-making model combining the proposed aggregation operators and generalized distance is constructed. Finally, a real case of investment decision for a community group-buying platform is presented for illustration. We further test the rationality and superiorities of the proposed method through sensitivity analysis and comparative study.

Onsite/offsite social commerce adoption for SMEs using fuzzy linguistic decision making in complex framework

There has been a growing social commerce adoption trend among SMEs for few years. However, it is often a challenging strategic task for SMEs to choose the right type of social commerce. SMEs usually have a limited budget, technical skills and resources and want to maximise productivity with those limited resources. There is much literature that discusses the social commerce adoption strategy for SMEs. However, there is no work to enable SMEs to choose social commerce-onsite/offsite or hybrid strategy. Moreover, very few studies allow the decision-makers to handle uncertain, complex nonlinear relationships of social commerce adoption factors. The paper proposes a fuzzy linguistic multi-criteria group decision-making in a complex framework for onsite, offsite social commerce adoption to address the problem. The proposed approach uses a novel hybrid approach by combining FAHP, FOWA and selection criteria of the technological-organisation-environment (TOE) framework. Unlike previous methods, the proposed approach uses the decision maker's attitudinal characteristics and recommends intelligently using the OWA operator. The approach further demonstrates the decision behaviour of the decision-makers with Fuzzy Minimum (FMin), Fuzzy Maximum (FMax), Laplace criteria, Hurwicz criteria, FWA, FOWA and FPOWA. The framework enables the SMEs to choose the right type of social commerce considering TOE factors that help them build a stronger relationship with current and potential customers. The approach's applicability is demonstrated using a case study of three SMEs seeking to adopt a social commerce type. The analysis results indicate the proposed approach's effectiveness in handling uncertain, complex nonlinear decisions in social commerce adoption.

T-spherical fuzzy COPRAS method for multi-criteria decision-making problem

In this manuscript, we introduce a multi-criteria decision-making (MCDM) method under T-spherical fuzzy set environment. Firstly, we propose a method to use the correlation coefficient and standard deviation (CCSD) method to determine the attribute weight under T-spherical fuzzy environment, when the attribute weight information is completely unknown or partially unknown. Secondly, we introduce a T-spherical fuzzy complex proportional assessment (COPRAS) method. Finally, a numerical example is given to illustrate the application of the T-spherical fuzzy COPRAS method, and some comparative analysis is carried out to verify the feasibility and effectiveness of the proposed method.

T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made.

Waste Clothing Recycling Channel Selection Using a CoCoSo-D Method Based on Sine Trigonometric Interaction Operational Laws with Pythagorean Fuzzy Information

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

Interaction power Heronian mean aggregation operators for multiple attribute decision making with T-spherical fuzzy information

The interaction operation laws (IOLs) between membership functions can effectively avoid the emergence of counterintuitive situations. The power average (PA) operator can eliminate the negative effect of extremely or improperly assessments on the decision results. The Heronian mean (HM) operator is capable of examining the interrelationship between the two attributes. To synthesize the powers of the IOLs, PA and HM operators in this paper, the PA and HM operators are extended to process T-spherical fuzzy evaluation information perfectly based on the IOLs, and the T-spherical fuzzy interaction power Heronian mean (T-SFIPHM) operator and its weighted form are proposed. We further present some properties of these proposed AOs and discuss several special cases. Moreover, a novel method to T-spherical fuzzy multiple attribute decision making (MADM) problems applying the proposed AO is developed. Lastly, we present a numerical example to validate its feasibility and reasonableness, and the superiority of the developed method is further illustrated by sensitivity analysis of parameters and comparison with existing methods. The results show that proposed AOs not only can capture the interactivity among membership degree (MD), abstinence degree (AD) and non-membership degree (NMD) of T-spherical fuzzy numbers (T-SFNs), bust also ensure the overall balance of variable values in the process of information fusion and realize the interrelationship between attribute variables, so the decision results can be closer to reality and more reliable.

Approach to multi-attribute decision-making problems based on neutrality aggregation operators of T-spherical fuzzy information

In the process of decision-making, uncertain information is always challenging to deal with. T-spherical fuzzy set (TSFS) operates vagueness of data by analysing three independent functions, namely membership, non-membership, and abstinence function. The TSFS provides us robust scheme with parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q\ge 1$$\end{document} q ≥ 1 to handle the countless opportunities. Hence, this set proves its superiority over the existing picture fuzzy set (PFS) and spherical fuzzy set (SFS). Now a day, decision-makers usually assign impartial values throughout the assessment. This manuscript demonstrates some new operational laws by fusing the neutral characteristics of the degrees of membership and using the probability sum (PS) function. Meanwhile, we determine several aggregation operators (AOs) including weighted averaging neutral, ordered weighed neutral, and hybrid averaging neutral AOs to aggregate the data under T-spherical fuzzy (TSF) environment. As it came to the notice that weighted neutral averaging aggregation operators of the Pythagorean fuzzy set (PyFS), single-valued neutrosophic fuzzy set (SVNFS), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document} q -rung orthopair fuzzy set (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document} q -ROFS) have some restrictions during the decision-making problems. So, to overcome this, we introduce a new multi-attribute group decision-making method (MAGDM) based on proposed AOs. Lastly, we provide various numerical instances to explain the method and exhibit its supremacy. Furthermore, a comparative analysis is conducted to compare the potential of proposed AOs with some other existing methods.

Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment

In this article, we have introduced a new linguistic generalized spherical fuzzy set by combining the idea of generalized spherical fuzzy set and linguistic fuzzy set. Linguistic generalized spherical fuzzy set is described by linguistic positive, linguistic neutral and linguistic negative membership degrees with the condition that the square sum of its linguistic membership degrees is less than or equal to 3 which deal with the uncertain and imprecise information in decision making in a much more suitable way. We have discussed some basic operations of linguistic generalized spherical fuzzy sets and introduced new score and accuracy functions to compare any two linguistic generalized spherical fuzzy numbers. We have developed various types of aggregation operators based on the newly defined linguistic generalized spherical fuzzy set, which have been manifested to construct a new multi-criteria group decision-making technique. Numerical example has been presented to demonstrate the proposed model. Finally, sensitivity and comparative analysis is performed to show the reliability and efficiency of the new multi-criteria group decision-making technique.

Performance Evaluation of Solar Energy Cells Using the Interval-Valued T-Spherical Fuzzy Bonferroni Mean Operators

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

T-Spherical Fuzzy Rough Interactive Power Heronian Mean Aggregation Operators for Multiple Attribute Group Decision-Making

In this article, to synthesize the merits of interaction operational laws (IOLs), rough numbers (RNs), power average (PA) and Heronian mean (HM), a new notion of T-spherical fuzzy rough numbers (T-SFRNs) is first introduced to describe the intention of group experts accurately and take the interaction between individual experts into account with complete and symmetric information. The distance measure and ordering rules of T-SFRNs are proposed, and the IOLs of T-SFRNs are extended. Next, the PA and HM are combined based on the IOLs of T-SFRNs, and the T-Spherical fuzzy rough interaction power Heronian mean operator and its weighted form are proposed. These aggregation operators can accurately express both individual and group uncertainty using T-SFRNs, capture the interaction among membership degree, abstinence degree and non-membership degree of T-SFRNs by employing IOLs, ensure the overall balance of variable values by the PA in the process of information fusion, and realize the interrelationship between attribute variables by the HM. Several properties and special cases of these aggregation operators are further presented and discussed. Subsequently, a new approach for dealing with T-spherical fuzzy multiple attribute group decision-making problems based on proposed aggregation operator is developed. Lastly, in order to validate the feasibility and reasonableness of the proposed approach, a numerical example is presented, and the superiorities of the proposed method are illustrated by describing a sensitivity analysis and a comparative analysis.

Vague data analysis using neutrosophic Jarque-Bera test

In decision-making problems, the researchers’ application of parametric tests is the first choice due to their wide applicability, reliability, and validity. The common parametric tests require the validation of the normality assumption even for large sample sizes in some cases. Jarque-Bera test is among one of the methods available in the literature used to serve the purpose. One of the Jarque-Bera test restrictions is the computational limitations available only for the data in exact form. The operational procedure of the test is helpless for the interval-valued data. The interval-valued data generally occurs in situations under fuzzy logic or indeterminate state of the outcome variable and is often called neutrosophic form. The present research modifies the existing statistic of the Jarque-Bera test for the interval-valued data. The modified design and operational procedure of the newly proposed Jarque-Bera test will be useful to assess the normality of a data set under the neutrosophic environment. The proposed neutrosophic Jarque-Bera test is applied and compared with its existing form with the help of a numerical example of real gold mines data generated under the fuzzy environment. The study’s findings suggested that the proposed test is effective, informative, and suitable to be applied in indeterminacy compared to the existing Jarque–Bera test.

A T-spherical fuzzy ELECTRE approach for multiple criteria assessment problem from a comparative perspective of score functions

The theory involving T-spherical fuzziness provides an exceptionally good tool to efficiently manipulate the impreciseness, equivocation, and vagueness inherent in multiple criteria assessment and decision-making processes. By exploiting the notions of score functions and distance measures for complex T-spherical fuzzy information, this paper aims to propound an innovational T-spherical fuzzy ELECTRE (ELimination Et Choice Translating REality) approach to handling intricate and convoluted evaluation problems. Several newly-created score functions are employed from the comparative perspective to constitute a core procedure concerning concordance and discordance determination in the current T-spherical fuzzy ELECTRE method. By the agency of a realistic application, this paper appraises the usefulness and efficacy of available score functions in the advanced ELECTRE mechanism under T-spherical fuzzy uncertainties. This paper incorporates two forms of Minkowski distance measures into the core procedure; moreover, the effectuality of the advocated measure in differentiating T-spherical fuzzy information is validated. The effectiveness outcomes of the evolved method have been investigated through the medium of an investment decision regarding potential company options for extending the business scope. The real-world application also explores the comparative advantages of distinct score functions in tackling multiple criteria decision-making tasks. Finally, this paper puts forward a conclusion and future research directions.

Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

A Novel Approached Based on T-Spherical Fuzzy Schweizer-Sklar Power Heronian Mean Operator for Evaluating Water Reuse Applications under Uncertainty

The T-Spherical Fuzzy set (T-SPHFS) is one of the core simplifications of quite a lot of fuzzy concepts such as fuzzy set (FS), intuitionistic fuzzy set (ITFS), picture fuzzy set (PIFS), Q-rung orthopair fuzzy set (Q-RUOFS), etc. T-SPHFS reveals fuzzy judgment by the degree of positive membership, degree of abstinence, degree of negative membership, and degree of refusal with relaxed conditions, and this is a more powerful mathematical tool to pair with inconsistent, indecisive, and indistinguishable information. In this article, several novel operational laws for T-SPFNs based on the Schweizer–Sklar t-norm (SSTN) and the Schweizer–Sklar t-conorm (SSTCN) are initiated, and some desirable characteristics of these operational laws are investigated. Further, maintaining the dominance of the power aggregation (POA) operators that confiscate the ramifications of the inappropriate data and Heronian mean (HEM) operators that consider the interrelationship among the input information being aggregated, we intend to focus on the T-Spherical fuzzy Schweizer–Sklar power Heronian mean (T-SPHFSSPHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power geometric Heronian mean (T-SPHFSSPGHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted Heronian mean (T-SPHFSSPWHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted geometric Heronian mean (T-SPHFSSPWGHEM) operator, and their core properties and exceptional cases in connection with the parameters. Additionally, deployed on these newly initiated aggregation operators (AOs), a novel multiple attribute decision making (MADM) model is proposed. Then, the initiated model is applied to the City of Penticton (British Columbia, Canada) to select the best choice among the accessible seven water reuse choices to manifest the practicality and potency of the preferred model and a comparison with the proffered models is also particularized.