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Supplier selection is a very crucial process within a business or commercial enterprise because it depends upon different components like reliability, customer need, services, cost and reputation. A suitable supplier is familiar with developing a relationship between customer needs and business. To serve this purpose, the multiple attribute group decision-making (MAGDM) technique is a well-known and efficient aggregation model used to evaluate flexible optimal options by considering some appropriate criteria or attributes. Experts face some sophisticated challenges during the decision-making process due to uncertain and ambiguous information about human opinions. To address such conditions, we explore the notion of spherical fuzzy sets (SFS) and their reliable operations. Some flexible operational laws of Dombi t-norms are also developed in light of spherical fuzzy (SF) information. Combining the theory of Hamy mean (HM) models and Dombi aggregation tools, some robust strategies are also studied in this research work. The main objectives of this article are to propose some dominant strategies in the presence of SF information including spherical fuzzy Dombi Hamy mean (SFDHM), spherical fuzzy Dombi weighted Hamy mean (SFDWHM), spherical fuzzy Dombi Dual Hamy mean (SFDDHM) and spherical fuzzy Dombi weighted Dual Hamy mean (SFDWDHM) operators. The MAGDM techniques are utilized to evaluate the flexibility of our derived methodologies under considering SF information. An experimental case study is utilized to evaluate a notable supplier enterprise under consideration of our developed methodologies. Finally, a comprehensive overview of our research work is also presented. [ABSTRACT FROM AUTHOR]

A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM's behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods. [ABSTRACT FROM AUTHOR]

A picture fuzzy set (PFS) is the extended version of an intuitionistic fuzzy set (IFS) and can deal with dubious and imprecision information. Dombi aggregation models are powerful mathematical tools utilized to aggregate human opinions and information in different fields, including social networking, data analysis, architecture, and neurosciences. Bonferroni means (BM) and geometric Bonferroni means (GBM) operators are allowed to define interrelationships among input arguments and play an extensive role in multi-attribute group decision-making (MAGDM) problems. In this article, we anticipated some robust aggregation operators (AOs) of PFSs based on Dombi aggregation models, namely "picture fuzzy Dombi Bonferroni mean" (PFDBM), "picture fuzzy Dombi weighted Bonferroni mean" (PFDWBM), "picture fuzzy Dombi geometric Bonferroni mean" (PFDGBM), and picture fuzzy Dombi weighted geometric Bonferroni mean" (PFDWGBM) operators. Some appropriate characteristics and special cases of our proposed methodologies are also presented. An algorithm of the MAGDM problem is also characterized to resolve complex real-life situations. Moreover, we also determined a practical example of the waste materials to evaluate a suitable recycling machine using our developed methodologies. To ratify the reliability and versatility of our current approaches, by contrasting the findings of existing approaches with the results of developed techniques. [ABSTRACT FROM AUTHOR]

Multiple-attribute group decision-making (MAGDM) technique is often used to make decisions when several optimal options are under consideration. It can be difficult to select a reasonable optimal option for the decision maker under consideration of insufficient information. The theory of Hamy mean (HM) operators are used to express correlation among different input arguments and provide a smooth approximation during the decision-making process. Recently, Aczel Alsina aggregating expressions gained a lot of attention from numerous mathematicians under different fuzzy circumstances. This article aims to illustrate the notion of a Pythagorean fuzzy (PyF) set (PyFS) with some restricted constraints, such as a sum of the square of truth membership value and falsity membership value. We developed a series of new approaches under consideration of the HM tools, including PyF Aczel Alsina Hamy mean (PyFAAHM), and PyF Aczel Alsina weighted Hamy mean (PyFAAWHM) operators. Further, we also extend the theory of Dual Hamy mean (DHM) operators and derived a series of new methodologies such as PyF Aczel Alsina Dual Hamy mean (PyFAADHM) and PyF Aczel Alsina weighted Dual Hamy mean (PyFAAWDHM) operators. To demonstrate the flexibility of our derived approaches, we illustrate an application of a multinational company considering the MAGDM technique. An experimental case study is also illustrated to evaluate a reasonable option from a group of options. We see the advantages and compatibility of our findings by comparing the results of existing approaches with the results of currently discussed methodologies. [ABSTRACT FROM AUTHOR]

Renewable energy sources play an influential role in the world's climate and reduce the rate of harmful gasses such as carbon dioxide, methane, nitrous oxide, and many other greenhouse gasses that contribute to global warming. The theoretical concept of the T-spherical fuzzy (T-SF) set (T-SFS) is the most suitable model to evaluate energy resources under uncertainty. This article illustrates appropriate operations based on Dombi triangular norm and t-conorm. We derived a series of new aggregation approaches, such as T-SF Dombi Hamy mean (T-SFDHM) and T-SF weighted Dombi Hamy Mean (T-SFDWHM) operators. Further authors illustrated a list of new approaches such as T-SF Dual Dombi Hamy mean (T-SFDDHM), and T-SF Dombi weighted Dual Hamy mean (T-SFDWDHM) operators. Some exceptional cases and desirable properties of our derived approaches are also studied. We illustrate an application of renewable energy resources to be evaluated using a multi-attribute group decision-making (MAGDM) method. A case study was also studied to choose appropriate energy resources using our proposed methodology of the T-SFDWHM and T-SFDWDHM operators. To show the effectiveness and validity of our current methods, we compared the existing results with currently developed aggregation operators (AOs). [ABSTRACT FROM AUTHOR]

Prioritization is usually required in problems involving multi-attribute group decision-making (MAGDM). Several strategies and procedures have been introduced in fuzzy systems to apply prioritization. This study examines the MAGDM problem in a Pythagorean fuzzy (PF) setting with varying amounts of demand for specialists and attributes. We regard the novel Aczel Alsina aggregation operators (AOs) as the most addition to fuzzy mathematics that can deal with uncertainties significantly. We suggest a few PF AOs based on Aczel Alsina t-norm and t-conorm, including the PF-prioritized Aczel Alsina averaging (PFPAAA) and PF-prioritized Aczel Alsina geometric (PFPAAG) operators. It is proven that these AOs fulfil the aggregation criteria by investigating the properties of monotonicity, boundedness, and idempotency. The weights for prioritization are derived from the knowledge of experts, and the proposed operators can capture the phenomenon of prioritization among the aggregated arguments. The proposed AOs are then applied to assess fire extinguishers using a MAGDM technique. The importance of PFPAAA and PFPAAG operators is verified by comparing the proposed AOs with other well-known AOs. [ABSTRACT FROM AUTHOR]

The Aczel-Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982. They are modified forms of the algebraic t-norm and t-conorm. Furthermore, the theory of picture fuzzy values is a very valuable and appropriate technique for describing awkward and unreliable information in a real-life scenario. In this research, we analyze the theory of averaging and geometric aggregation operators (AOs) in the presence of the Aczel-Alsina operational laws and prioritization degree based on picture fuzzy (PF) information, such as the prioritized PF Aczel-Alsina average operator and prioritized PF Aczel-Alsina geometric operator. Moreover, we examine properties such as idempotency, monotonicity and boundedness for the derived operators and also evaluated some important results. Furthermore, we use the derived operators to create a system for controlling the multi-attribute decision-making problem using PF information. To show the approach's effectiveness and the developed operators' validity, a numerical example is given. Also, a comparative analysis is presented. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision-making (MAGDM) is an interesting technique to find the most optimal alternative among comparative alternatives. Several authors put forward to MAGDM by introducing different fuzzy frameworks and also different tools to deal with fuzzy information. Intuitionistic fuzzy set (IFS) is the fuzzy framework that deals with the uncertainty in MAGDM. Due to their flexibility and generality, Frank t-norm (FTNM) and t-conorm (FTCNM) play an essential role in information fusion. Moreover, as the generalization of some mean operators, the Maclaurin symmetric mean (MSM) operator considers the relationship between multi-criteria arguments, especially in MAGDM. This article aims to develop some MSM aggregation operators (AOs) for the intuitionistic fuzzy set (IFS) based on FTNM and FTCNM and to apply newly developed AOs in the MAGDM. To utilize the MAGDM algorithm, first, we defined the MSM by using the FTNM and FTCNM in the environment of IFS. Then we proposed intuitionistic fuzzy (IF) Frank MSM (IFFMSM) and IF Frank weighted MSM (IFFWMSM) operators. Then, the fundamental properties of these AOs are stated and proved. Then, the strategy is given that accounts for the application of the newly developed family of AOs. Further, freshly defined operators are applied to the MAGDM problem with the help of an example where the risk factors of the construction industry are assessed. To cope with the significance, the proposed AOs are compared with some existing AOs. This study also addresses the variation of these AOs' behavior based on the interpretation of sensitive parameters. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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

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

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

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 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 q -rung orthopair fuzzy set (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. [ABSTRACT FROM AUTHOR]

The novel concept of the complex interval-valued T-spherical fuzzy set (CIVTSFS) is presented to handle the vagueness in the data. The proposed set takes the advantages of interval-valued spherical fuzzy sets and complex numbers to represent the information in terms of the interval-valued number of the truth, abstinence and falsity degrees. Various operation laws are stated to enrich the features of CIVTSFS. By utilising the proposed laws, several weighted operators are stated to aggregate the different preference of the experts towards the evaluation of the alternatives. Furthermore, a group decision-making algorithm is stated to solve the decision-making problems by utilising the uncertain data under CIVTSFS information. The presented algorithm is demonstrated through a numerical example and their advantages are indicated. [ABSTRACT FROM AUTHOR]

An interval-valued T-spherical fuzzy set (IVTSFS) is an efficient framework to treat ambiguous and vague information more efficiently. It has four functions consisting of the information in intervals. With the help of these functions, IVTSFS is a more reliable framework than the other existing frameworks. This article aims to establish algebraic operations of IVTSFSs named Frank sum, Frank multiplication, and Frank scalar multiplication stranded on Frank t-norm and t-conorm. Further, some averaging and geometric aggregation operators (AOs), i.e., interval-valued T-spherical fuzzy Frank weighted averaging (IVTSFFWA) and interval-valued T-spherical fuzzy Frank weighted geometric (IVTSFFWG) operators are established based on the defined operations, and then the properties of these operators are observed. The proposed approach is supported by an illustrative example, in which we have applied our proposed approach to a multiattribute group decision-making (MAGDM) problem. For the significance of the proposed approach, a comparative study is done. The various effects of the variation of parameters are also investigated which plays an important role in the final results. [ABSTRACT FROM AUTHOR]

This manuscript is aimed at developing some novel operational laws named scalar neutrality operation and neutrality addition on picture fuzzy numbers (PFNs). The main focus of this work is to involve the neutral behaviour of the experts towards the priorities of entities where it presents equal degrees to independent membership functions. Moreover, based on these operations, some novel aggregation operators are established to aggregate the different priorities of experts. Some useful relations and characteristics are examined thoroughly. Lastly, the multiattribute group decision-making algorithm in accordance with the suggested operation is illustrated and examined a case study in order to choose a suitable mining company for a mining project along with several numerical examples. The advantages, as well as the superiority of the suggested approach, are exhibited by comparing the results with a few existing methods. [ABSTRACT FROM AUTHOR]

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

The novel concept of the complex interval-valued T-spherical fuzzy set (CIVTSFS) is presented to handle the vagueness in the data. The proposed set takes the advantages of interval-valued spherical fuzzy sets and complex numbers to represent the information in terms of the interval-valued number of the truth, abstinence and falsity degrees. Various operation laws are stated to enrich the features of CIVTSFS. By utilising the proposed laws, several weighted operators are stated to aggregate the different preference of the experts towards the evaluation of the alternatives. Furthermore, a group decision-making algorithm is stated to solve the decision-making problems by utilising the uncertain data under CIVTSFS information. The presented algorithm is demonstrated through a numerical example and their advantages are indicated. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets are an extension of various fuzzy concepts and demonstrate fuzzy opinion using membership, abstinence, nonmembership and refusal degrees with relaxed conditions, and it is a better mathematical tool to deal with uncertain and vague information. Recently, Dombi operational laws for spherical fuzzy numbers (SPFNs) are developed for multi-attribute decision-making purpose. In this article, some limitations of the said Dombi operational laws for SPFNs are investigated as the aggregated information that came out using existing aggregation operators deviate from the range. Therefore, in this paper, we aim to present some improved Dombi operational laws for SPFNs. Further, keeping the advantages of the power aggregation operators that it takes into account the relationship of the information being aggregated, we aim to develop the spherical fuzzy Dombi power average operator, the spherical fuzzy Dombi weighted power average operator, spherical fuzzy Dombi power geometric operator, and spherical fuzzy Dombi weighted power geometric operator and their desirable properties are discussed. The main advantage of these developed Dombi power aggregation operators is that they eliminate the effect of awkward data and are more flexible due to general parameters involved in aggregation process. Moreover, based on these Dombi power aggregation operators, a novel multi-attribute group decision-making approach is instituted followed by a numerical example to show the practicality and effectiveness of the proposed approach and comparison with the existing approaches is also given. [ABSTRACT FROM AUTHOR]

This article aims to develop the Aczel–Alsina operational laws based on power aggregation operators (PAOs) for the q-Rung orthopair fuzzy set (FS) (q-ROFS) framework. Changing the parameter can alter these sets according to the degree of fluctuation, providing a range of options. The decision-making sciences use "q-ROFS" to describe the family of the most distinct fuzzy information thoughts. In response to the degree of variation, the q-ROFSs can increasingly adjust the information region by fluctuating the restriction q ≥ 1 , making numerous options. But on the other hand, PAOs have the advantage of vanishing the influence of awkward data from the final results. To take advantages of POAs, based on Aczel- Alsina (AA) operational laws, q-Rung orthopair fuzzy (q-ROF) AA power-weighted averaging (q-ROFAAPWA) and q-ROF AA power-weighted geometric (q-ROFAAPWG) operators are stated. Also, it studied that the proposed AOs fulfilled the conditions of boundedness, monotonicity, and idempotency. Based on these newly constructed AOs, a technique for dealing the multi-attribute group decision-making (MAGDM) problems is suggested. Numerous research, correlations with another modern approach and a numerical example of selecting stock market companies have been used to show the suggested system's applicability. The sensitivity analysis of the developed method is examined. A comparative study with other prevailing methods is also providing for superiority analysis. Finally, we demonstrated that in the results and discussion section, the proposed AOs in the q-ROPFS framework are more reliable in aggregating information than intuitionistic fuzzy (IF) set (IFS) and Pythagorean FS (PyFS) frameworks. [ABSTRACT FROM AUTHOR]

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

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

• A CODAS-based group decision model is designed for the T-spherical fuzzy context. • A T-spherical fuzzy Minkowski distance operator based on Heronian mean is proposed. • A novel ordered weighted Heronian Minkowski distance (TSFOWHMD) operator is advanced. • The TSFOWHMD operator is utilized to improve the CODAS method. • The applicability of the developed methodology is verified through a case study. T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology. [ABSTRACT FROM AUTHOR]