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Fuzzy multi-criteria decision making (FMCDM) is a critical field that addresses the inherent uncertainty and imprecision in complex decision scenarios. This study tackles the significant challenge of evaluating energy storage technologies (ESTs) in Vietnam's offshore wind sector, where traditional decision-making models often fall short due to their inability to handle fuzzy data and complex criteria interactions effectively. To overcome these limitations, the novel T-spherical fuzzy Einstein interaction operation matrix energy decision-making approach is introduced. This methodology integrates T-spherical fuzzy sets with matrix energy concepts and Einstein interaction operations, thereby eliminating the need for traditional aggregation processes and criteria weight determinations. My approach provides a structured evaluation of ESTs, highlighting that hydrogen storage, among others, demonstrates significant potential for high energy capacity and long-term storage. The findings not only underscore the robustness of this new method in managing the complexities of renewable energy assessment but also offer a comprehensive tool for selecting the most suitable ESTs to support Vietnam's energy transition strategies. This study recognizes limitations related to data dependency, which could affect the generalizability of the results. Future research is suggested to expand the ESTs considered and integrate extensive real-world operational data, aiming to deepen the exploration of economic impacts and long-term viability of these technologies. This revised approach emphasizes both the challenge of evaluating ESTs under uncertain conditions and my innovative solution, enhancing the relevance and applicability of the findings. [ABSTRACT FROM AUTHOR]

This paper presents a thorough review of our state-of-the-art technique for enhancing dynamic grid partitioning and scheduling in multi-energy source systems. We use a hybrid approach to T-spherical fuzzy sets, combining the alternative ranking order method accounting for the two-step normalization (AROMAN) method for alternating ranking order to enable two-step normalisation with the method based on removal effects of criteria (MEREC) for eliminating criteria effects. This enables us to obtain the highest level of accuracy from our findings. To ascertain the relative importance of these criteria, we use MEREC to perform a rigorous examination of the influence that each evaluation criterion has on the outcomes of the decision-making process. In addition, we use AROMAN to provide a strong foundation for assessing potential solutions by accounting for spherical fuzzy sets to account for any ambiguity. We illustrate how our approach successfully considers several factors, such as social acceptability, technical feasibility, environmental sustainability, and economic feasibility, through the analysis of an extensive case study. Our approach provides decision-makers (DMs) with a rigorous and rational framework for assessing and choosing the best grid division and scheduling options. This is done in an effort to support the administration and design of resilient and sustainable multi-energy systems. This research contributes to the growing body of knowledge in this area by offering insights that help to direct policy, planning, and investment decisions in the shift towards more sustainable energy infrastructures. Moreover, it adds to the growing body of information on multi-criteria decision-making (MCDM) in energy system optimization. [ABSTRACT FROM AUTHOR]

By implementing new technologies, university technology transfer (UTT) is crucial for economic advancement. However, developing countries face numerous challenges regarding UTT. This study proposes a unique approach by combining Multi-Criteria Decision Making (MCDM) methods such as Delphi and Decision-Making Trial And Evaluation Laboratory (DEMATEL) with Fuzzy Theories, specifically Spherical Fuzzy Sets (SFSs) and T – Spherical Fuzzy Sets (T-SFSs), to examine the barriers in UTT. The distinctive aspect of this study lies in addressing the limitations of SFSs and upgrading them to T-SFSs by incorporating them with the DEMATEL approach. Initially, SFS Delphi is employed to identify and eliminate nonimportant barriers. Subsequently, SF DEMATEL is utilized to classify barriers into cause-effect groups and determine their interactive relationships. However, SFSs have revealed specific weaknesses during this step, prompting the adoption of T-SF DEMATEL as a replacement. The findings highlight the perfect compatibility of T-SFSs with the research model and identify several primary barriers that hinder UTT, including C14, inconsistent rules and regulations, C9, misalignment between research and commercialization objectives, C3- lack of recognition for university-industry linkages, and C5- lack of resources. This study not only improves the understanding of UTT for decision makers, entrepreneurs, and policymakers, facilitating the creation of solutions, but also serves as a reference for researchers in the application of T-SFSs in other research domains.

During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models.

In response to the transportation industry’s immediate need for more proactive and foresighted management, cooperative intelligent transportation systems (C-ITS) use wireless technology to foster real-time communication between vehicles and infrastructure, with the goal of increasing road safety and streamlining traffic flow. The introduction of self-powered sensors, which have the clever capacity to produce their own electricity, is critical for the reliability of transport operations across a wide range of C-ITS applications. Our analytical technique, which employs the criteria importance through intercriteria correlation (CRITIC) methodology and the weighted aggregated sum product assessment (WASPAS) approach, does not end there. We have taken it a step further by using the T-spherical fuzzy (T-SF) form of CRITIC-WASPAS, which adds a more subtle layer to our evaluation. We embark on an in-depth case study, methodically evaluating five choices against eight criteria. In the context of the CRITIC-WASPAS framework, the application of the T-SF logic enhances analytical precision by taking into account uncertainty throughout the decision-making process. This is particularly beneficial in the context of complex systems like C-ITS. The incorporation of CRITIC also makes it possible to evaluate the correlations between different criteria, which ultimately results in decision outcomes that are more nuanced and robust. This is accomplished by aggregating all of the criteria and options. This rigorous and intelligent strategy goes beyond simply meeting urgent system needs. It tactically impacts decision-making, moving the transport industry forward significantly.

The T-spherical fuzzy set (T-SFS) has been widely used in multi-attribute decision-making (MADM) problems due to its powerful expression ability for uncertain information. The evidential reasoning (ER) method can avoid the information loss when aggregating the evaluation values of an alternative with regard to all attributes, which can prevent the decision result from being dominated by extreme evaluation values. Considering the significant advantage of the ER method in information aggregation, this paper develops a new aggregation model assimilating the T-SFSs and the ER method, which is called evidential T-spherical fuzzy MADM (ET-SFMADM). The ET-SFMADM can prevent information loss in the decision process, so as to obtain a correct ranking of the alternatives. Furthermore, this paper also proposes a T-spherical fuzzy cross entropy (T-SFCE) to determine the weights of attributes, which can reduce dependence on decision-makers. Finally, the viability of the ET-SFMADM is illustrated through a numerical example for the implementation effect of the hierarchical medical treatment system in different regions, and further the sensitivity analysis and comparison analysis with existing MADM methods are carried out to demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples.. [ABSTRACT FROM AUTHOR]

During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models. [ABSTRACT FROM AUTHOR]

This study introduces the integrated T-spherical fuzzy Einstein interaction aggregator group decision-making approach, a novel framework designed to enhance multi-criteria decision-making (MCDM). Implementing the case study of concrete 3D printing technology in Vietnam, this approach integrates T-spherical fuzzy sets with Einstein aggregation operators to handle the complexities of uncertain and subjective expert judgments effectively. The methodology provides a robust mechanism for evaluating and prioritizing the barriers and strategies associated with the implementation of concrete 3D printing. Findings from this study underline the significance of technological advancements and strategic financial incentives, with R&D strategy emerging as the top priority. This research contributes to both theoretical advancements in decision-making frameworks and offers practical insights for industries looking to integrate emerging technologies. Moreover, it demonstrates the application of advanced fuzzy set theories in real-world settings, providing a valuable tool for decision-makers facing similar technological adoption challenges.

Traditional Chinese art is vast and profound, with various colors having rich meanings. The combination of colors can vividly and intuitively represent various characteristics of things. Fully reflecting the characteristics of traditional Chinese folk art in graphic design can achieve extremely strong expressive effects. In current graphic design, the artistic colors of traditional Chinese folk art have not yet been fully displayed, and there is a lack of understanding of the profound connotation of traditional Chinese art. The graphic design industry has a very broad development space. The comprehensive evaluation of graphic design effects based on color psychology is a classical multiple attribute group decision making (MAGDM) problems. In this work, we shall present some novel Dice similarity measures (DSM) of T-spherical fuzzy sets(T-SFSs) and the generalized Dice similarity measures (GDSM) of and indicates that the DSM and asymmetric measures (projection measures) are the special cases of the GDSM in some parameter values. Then, we propose the GDSM-based MAGDM models with T-SFSs. Then, we apply the GDSMs between T-SFSs to MAGDM. Finally, an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the GDSMs. The main contributions of this paper are summarized: (1) some novel Dice similarity measures (DSM) and the generalized Dice similarity measures (GDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed; (2) The weighted Dice similarity measures (WDSM) and the weighted generalized Dice similarity measures (WGDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed to solve the MAGDM; (3) an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the WGDSM; (4) Some comparative analysis are used to show the effectiveness of the proposed Dice similarity measures. [ABSTRACT FROM AUTHOR]

The basic aim of this study is to introduce an innovative concept of bipolar T-spherical fuzzy set (BTSFS) which is a hybrid structure of bipolar fuzzy set (BFS) and T-spherical fuzzy Set (TSFS). BTSFS is a unique type of fuzzy set that works with bipolarity of all membership grades (MGs), that is, truth MG, abstained MG and non-membership grade (NMG). This paper scrutinizes a few basic characteristics and essential operations of BTSFSs. The proposed results are compared with the existing fuzzy structures and also the importance of the proposed work is discussed. Further, the idea of new distance measures of BTSFSs has been presented to investigate the geometrical properties of BPFSs. An example related to pattern recognition (PR) based on new distance measures have been examined in the article. Furthermore, some new similarity measures (SMs) based on BTSFSs such as Dice SM and weighted Dice SM have been initiated. We have also studied the propositions related to proposed SMs. A multi-criteria decision-making (MCDM) method based on proposed SMs for BSTSFSs has also been presented in this article. Then, in the end, to check capability and viability, a practical demonstration of the planned approach has also been explained. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy (TSF) set is a suitable technique for depicting uncertain and vague information in real-life problems because it covered the truth, abstinence, falsity, and refusal grade with a suitable characteristic that is the sum of the q-power of the truth, abstinence, and falsity grades will be contained in the unit interval. The major objective of this article is to evaluate the novel theory of interaction operational laws for TSF information. Additionally, power Bonferroni mean (PBM) operators are the combination of two existing ideas such as Bonferroni and power aggregation operator and because of this reason, they are more general than the bundle of existing ideas. Inspired by the above valuable knowledge, we derive the PBM operators based on interaction operation laws for TSF values such as the TSF interaction PBM (TSFIPBM) operator and TSF weighted interaction PBM (TSFWIPBM) operator. Some special cases and the properties of the invented techniques are also examined. Furthermore, for addressing some real-life problems, we derive the multi-attribute decision-making (MADM) method in the consideration of the presented technique to enhance the stability and supremacy of the evaluated techniques. Finally, for comparing the proposed techniques with prevailing methods, we illustrate some numerical examples to show the supremacy and effectiveness of the derived theory. [ABSTRACT FROM AUTHOR]

This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (T-SLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (T-SLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (T-SLDFNs), different types of score and accuracy functions are defined. On the basis of the T-SLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted.

Vocal music is a relatively complex skill and skill course, which not only plays an important role in music education in universities, but also cultivates students' musical level and artistic cultivation. In the process of teaching vocal music in universities, how to improve the quality of teaching has become an important task and goal for teachers. The vocal music classroom teaching quality evaluation is a classical multiple-attribute group decision-making (MAGDM) problem. In this paper, some novel Dice similarity measures (DSM) and some generalized Dice similarity measures (GDSM) are proposed under T-spherical fuzzy sets (T-SFSs). Then, the weighted generalized Dice similarity measures (WGDSM) is used to solve the MAGDM with T-SFSs. Finally, an illustrative example for vocal music classroom teaching quality evaluation is given to demonstrate the efficiency of the GDSMs. [ABSTRACT FROM AUTHOR]

This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (TSLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (TSLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (TSLDFNs), different types of score and accuracy functions are defined. On the basis of the TSLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted. [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]

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. [ABSTRACT FROM AUTHOR]

Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel and Alsina in 1982 are more flexible than the other TN and TCN. Since Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, they have good applications in multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati et al. (2022) developed Aczel-Alsina aggregation operators (AOs) under intuitionistic FSs (IFSs) and interval-valued IFSs (IVIFSs) with their applications in solving IFS and IVIFS MADM problems. We know that T-spherical FSs (TSFSs) are a recently developed approach to uncertain information with less information loss and more reliability than IFSs and IVIFSs. In this paper, we develop these AOs on TSFSs as a new approach to solve MADM problems by using Aczel-Alsina TN and Aczel-Alsina TCN under T-spherical fuzzy (TSF) information. Furthermore, the basic operations of TSF numbers (TSFNs) are developed and exemplified. Based on these operations, two types of AOs, i.e., TSF Aczel-Alsina weighted average (TSFAAWA), and TSF Aczel-Alsina weighted geometric (TSFAAWG) operators, are introduced and investigated. The reliability and accuracy of the newly developed AOs are tested numerically and theoretically by the induction methods. To further give applications and also study the sensitivity of these TSF Aczel-Alsina operators, the problem of project evaluation using these proposed operators is comprehensively observed. The results obtained by using these TSF Aczel-Alsina operators are compared with some previously existing AOs of TSFSs. According to comparison results, we observe the reliability and efficiency of the proposed methods.

T-spherical fuzzy sets, the direct extension of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets are examined in this composition, and a mathematical examination among them is set up. A T-spherical fuzzy set can demonstrate phenomenon like choice utilizing four trademark capacities indicating the level of choice of inclusion, restraint, resistance, and exclusion, another example of such situation is that human opinion cannot be restricted to yes or no but it can be yes, abstain, no and refusal. T-spherical fuzzy set can deal the said situation with a boundless space. With the assistance of some mathematical outcomes, it is talked about that current similarity measures have a few drawbacks and could not be implemented where the data is in T-spherical fuzzy mode. Thus, some new similarity measures in T-spherical fuzzy environment are proposed, with the assistance of certain outcomes, it is demonstrated that the suggested similarity measures are generalization of current ones. Further the proposed similarity measures are applied in pattern recognition with numerical supportive examples. The maximum spanning tree clustering algorithm has been extended into T-spherical fuzzy context and supports our theory with numerical examples. A parallel investigation of fresh and existing similarity measures have been made and some of the benefits of designated work have been discussed. [ABSTRACT FROM AUTHOR]

The problem complexity of multi-criteria decision-making (MCDM) has been raised in the distribution of coronavirus disease 2019 (COVID-19) vaccines, which required solid and robust MCDM methods. Compared with other MCDM methods, the fuzzy-weighted zero-inconsistency (FWZIC) method and fuzzy decision by opinion score method (FDOSM) have demonstrated their solidity in solving different MCDM challenges. However, the fuzzy sets used in these methods have neglected the refusal concept and limited the restrictions on their constants. To end this, considering the advantage of the T-spherical fuzzy sets (T-SFSs) in handling the uncertainty in the data and obtaining information with more degree of freedom, this study has extended FWZIC and FDOSM methods into the T-SFSs environment (called T-SFWZIC and T-SFDOSM) to be used in the distribution of COVID-19 vaccines. The methodology was formulated on the basis of decision matrix adoption and development phases. The first phase described the adopted decision matrix used in the COVID-19 vaccine distribution. The second phase presented the sequential formulation steps of T-SFWZIC used for weighting the distribution criteria followed by T-SFDOSM utilised for prioritising the vaccine recipients. Results revealed the following: (1) T-SFWZIC effectively weighted the vaccine distribution criteria based on several parameters including T = 2, T = 4, T = 6, T = 8, and T = 10. Amongst all parameters, the age criterion received the highest weight, whereas the geographic locations severity criterion has the lowest weight. (2) According to the T parameters, a considerable variance has occurred on the vaccine recipient orders, indicating that the existence of T values affected the vaccine distribution. (3) In the individual context of T-SFDOSM, no unique prioritisation was observed based on the obtained opinions of each expert. (4) The group context of T-SFDOSM used in the prioritisation of vaccine recipients was considered the final distribution result as it unified the differences found in an individual context. The evaluation was performed based on systematic ranking assessment and sensitivity analysis. This evaluation showed that the prioritisation results based on each T parameter were subject to a systematic ranking that is supported by high correlation results over all discussed scenarios of changing criteria weights values.

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. [ABSTRACT FROM AUTHOR]

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them must be in the closed unit interval of [0, 1]. The sum condition seriously restricts the eligible values for grades. q-rung orthopair and T-spherical fuzzy sets have been introduced to establish a framework to tackle the mentioned problem for two-grade and three-grade fuzzy sets, respectively. Reducing the value of grades by means of power operator is the backbone idea of the both sets. However, these fuzzy sets are suffering from two drawbacks. The first one arises from the fact that there is no automatic structure to identify a proper power. Also, information loss is the other one which affects the accuracy of the decision-making process. This problem is a damaging consequence of changing the values of the grades. This paper introduces a novel reducing strategy to improve q-rung orthopair and T-spherical fuzzy sets by tackling the mentioned drawbacks. The proposed strategy solves out the former problem by establishing an automatic framework for finding a proper power which guarantee enough reduction of the values. The automatic framework is used for reducing the value of the maximum grade. Besides, the novel strategy reduces the rest of the grades according to their distance with the the maximum grade and its reduction rate. This paper proves mathematically that the ratio between the grades before and after of the reduction process will be intact, which results in solving information loss problem. Moreover, the higher accuracy level of the novel reduction strategy in comparison with the preceding methods, q-rung orthopair and T-sipherical fuzzy sets, is shown via different examples. [ABSTRACT FROM AUTHOR]

Fuzzy c‐means (FCM) is a time‐honored method for its simplicity of calculation and ease of understanding. However, the previous image segmentation work exploiting FCM could not achieve the ideal effect in image edge recognition of the fuzzy information or antinoise of the pixel. This paper exploits the spatial T‐spherical fuzzy c‐means model with bias correction (EM‐sTSFCMpq) to improves the effect of antinoise and image edge recognition. First, the image is transformed into a T‐spherical fuzzy set by a novel T‐spherical fuzzification technology with the processing of the bias fields. Second, the membership degree of the image is updated through the proposed T‐spherical FCM algorithm. Third, a novel calculation method of weighted combination is exploited to integrate spatial information to overcome the noise. The proposed method is applied to three‐dimensional MR image segmentation and the Berkeley segmentation datasets to illustrate the accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The purpose of writing this manuscript is to point out some limitations of existing associated immediate probability intuitionistic fuzzy geometric aggregation operators as these existing operators fail under some conditions such as the existing operators cannot handle the information given in Pythagorean fuzzy sets, picture fuzzy sets, spherical fuzzy sets, and T-spherical fuzzy sets and the existing aggregation operators also cannot aggregate the membership value when membership value of anyone intuitionistic fuzzy number become zero. To overcome these shortcomings associated immediate probability geometric aggregation operators have been developed for T-spherical fuzzy sets and associated immediate probability interactive geometric aggregation operators are proposed. Then a comparison between these operators is developed with the help of an example. The existing score function for T-spherical fuzzy sets does not involve abstinence so a new score function is developed which provides a better comparison between any two T-spherical fuzzy numbers. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. The advantages of the proposed work are also discussed in which it is shown that under some conditions the proposed operators can be reduced to other tools of uncertainty. The comparison between existing and proposed work is also developed with the help of an example. [ABSTRACT FROM AUTHOR]

The problem complexity of multi-criteria decision-making (MCDM) has been raised in the distribution of coronavirus disease 2019 (COVID-19) vaccines, which required solid and robust MCDM methods. Compared with other MCDM methods, the fuzzy-weighted zero-inconsistency (FWZIC) method and fuzzy decision by opinion score method (FDOSM) have demonstrated their solidity in solving different MCDM challenges. However, the fuzzy sets used in these methods have neglected the refusal concept and limited the restrictions on their constants. To end this, considering the advantage of the T-spherical fuzzy sets (T-SFSs) in handling the uncertainty in the data and obtaining information with more degree of freedom, this study has extended FWZIC and FDOSM methods into the T-SFSs environment (called T-SFWZIC and T-SFDOSM) to be used in the distribution of COVID-19 vaccines. The methodology was formulated on the basis of decision matrix adoption and development phases. The first phase described the adopted decision matrix used in the COVID-19 vaccine distribution. The second phase presented the sequential formulation steps of T-SFWZIC used for weighting the distribution criteria followed by T-SFDOSM utilised for prioritising the vaccine recipients. Results revealed the following: (1) T-SFWZIC effectively weighted the vaccine distribution criteria based on several parameters including T = 2, T = 4, T = 6, T = 8, and T = 10. Amongst all parameters, the age criterion received the highest weight, whereas the geographic locations severity criterion has the lowest weight. (2) According to the T parameters, a considerable variance has occurred on the vaccine recipient orders, indicating that the existence of T values affected the vaccine distribution. (3) In the individual context of T-SFDOSM, no unique prioritisation was observed based on the obtained opinions of each expert. (4) The group context of T-SFDOSM used in the prioritisation of vaccine recipients was considered the final distribution result as it unified the differences found in an individual context. The evaluation was performed based on systematic ranking assessment and sensitivity analysis. This evaluation showed that the prioritisation results based on each T parameter were subject to a systematic ranking that is supported by high correlation results over all discussed scenarios of changing criteria weights values. [ABSTRACT FROM AUTHOR]

The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach. [ABSTRACT FROM AUTHOR]

In this manuscript, the technique of the generalized MULTIMOORA method is investigated by using the concept of a T‐spherical fuzzy set (T‐SFS), which is the modified idea of a picture fuzzy set to handle awkward and vague information in daily life problems. T‐SFS covers the degree of truth, abstinence, and falsity with a rule that the sum of the qth‐powers of all degrees is restricted to the unit interval. Moreover, for examining the interrelationships among any number of T‐SFSs, we construct the idea of T‐spherical fuzzy Dombi prioritized weighted arithmetic (T‐SFDPWA) aggregation operators, T‐spherical fuzzy Dombi prioritized arithmetic, T‐spherical fuzzy Dombi prioritized geometric, and T‐spherical fuzzy Dombi prioritized weighted geometric (T‐SFDPWG) aggregation operators are given. Then, the basic properties of T‐SFDPWA and T‐SFDPWG aggregation operators are investigated and discussed in some of their cases. The investigated operators based on T‐SFS are utilized in the environment of multiattribute decision‐making problems to find the consistency and proficiency of the developed operators. In last, we illustrated some numerical examples based on explored operators is to examine the reliability and validity of the investigated operators with the help of comparative analysis and graphical representations with some existing ideas to show the presented approaches are extensive powerful. [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]

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.

Multi-attribute decision-making approach is a widely used algorithm that needs some aggregation tools and several such aggregation operators have been developed in past decades to serve the purpose. Hamacher aggregation operator is one such operator which is based on Hamacher t-norm and t-conorm. It is observed that the Hamacher aggregation operators of intuitionistic fuzzy set, Pythagorean fuzzy set and that of picture fuzzy set has some limitations in their applicability. To serve the purpose, in this paper, some Hamacher aggregation operators based on T-spherical fuzzy numbers are introduced. The concepts of T-spherical fuzzy Hamacher-weighted averaging and T-spherical fuzzy Hamacher-weighted geometric aggregation operators are proposed which described four aspects of human opinion including yes, no, abstinence and refusal with no limitations. Such type of aggregation operators efficiently describes the cases that left unsolved by the existing aggregation operators. The validity of the proposed aggregation operators is examined, and some basic properties are discussed. The proposed new Hamacher aggregation operators are used to analyze the performance of search and rescue robots using a multi-attribute decision-making approach as their performance in an emergency is eminent. The proposed Hamacher aggregation operators have two variable parameters, namely q and γ which affects the decision-making process and their sensitivity towards decision-making results is analyzed. A comparative analysis of the results obtained using proposed Hamacher aggregation operators in view of the variable parameters q and γ is established to discuss any advantages or disadvantages. [ABSTRACT FROM AUTHOR]

The framework of T-spherical fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set and picture fuzzy set having a great potential of dealing with uncertain events with no limitation. A T-spherical fuzzy framework can deal with phenomena of more than yes or no type; for example, consider the scenario of voting where one's voting interest is not limited to "in favor" or "against" rather there could be some sort of abstinence or refusal degree also. The objective of this paper is to develop some correlation coefficients for T-spherical fuzzy sets due to the non-applicability of correlations of intuitionistic fuzzy sets and picture fuzzy sets in some certain circumstances. The fitness of new correlation coefficients has been discussed, and their generalization is studied with the help of some results. Clustering and multi-attribute decision-making algorithms have been proposed in the environment of T-spherical fuzzy sets. To demonstrate the viability of proposed algorithms and correlation coefficients, two real-life problems including a clustering problem and a multi-attribute decision-making problem have been solved. A comparative study of the newly presented and pre-existing literature is established showing the superiority of proposed work over the existing theory. Some advantages of new correlation coefficients and drawbacks of the pre-existing work are demonstrated with the help of numerical examples. [ABSTRACT FROM AUTHOR]

Human opinion cannot be restricted to yes or no as depicted by conventional fuzzy set (FS) and intuitionistic fuzzy set (IFS) but it can be yes, abstain, no and refusal as explained by picture fuzzy set (PFS). In this article, the concept of spherical fuzzy set (SFS) and T-spherical fuzzy set (T-SFS) is introduced as a generalization of FS, IFS and PFS. The novelty of SFS and T-SFS is shown by examples and graphical comparison with early established concepts. Some operations of SFSs and T-SFSs along with spherical fuzzy relations are defined, and related results are conferred. Medical diagnostics and decision-making problem are discussed in the environment of SFSs and T-SFSs as practical applications. [ABSTRACT FROM AUTHOR]

As we all know, the research and development (R&D) is crucial for enterprises. How to choose the R&D project is an important research topic, and at the same time, it is also a typical multi-attribute decision-making (MADM) problem. In this paper, we propose a novel MADM method for selecting the Yunnan Baiyao's R&D project of toothpastes. Firstly, we use T-spherical fuzzy sets (T-SFSs) to express the evaluation information of the toothpastes from decision makers to overcome the shortcomings existing that the traditional information form may cause information distortion. Secondly, we extend the generalized Maclaurin symmetric mean (GMSM) operator to T-spherical fuzzy environment and propose the T-spherical fuzzy GMSM operator (T-SFGMSM) and the T-spherical fuzzy weighted GMSM operator (T-SFWGMSM), where these operators are suitable for the situation which the input information is interrelated. Further, we put forward a novel MADM approach for selecting toothpaste product based upon the T-SFWGMSM operator, which can not only handle a more extensive scope of fuzzy information, but also process the interrelationships between multiple attributes. Lastly, we solve a R&D project selection problem for Yunnan Baiyao Co., Ltd. by the proposed method and make a detailed comparative analysis with other MADM methods to demonstrate the effectiveness and superiority of the novel approach. [ABSTRACT FROM AUTHOR]

Governments, institutions, and organizations focused on renewable and green energy problems have provided significant support and incentives for project development in recent years. Green transformation is fostered through environmentally friendly and clean energy practices, which are the key to a sustainable future for the entire world, and governments and enterprises shape their business and transactions within this framework. However, there are various challenges and obstacles in green energy applications, both in businesses and in government policies. The study, which focuses on green energy problems, seeks to connect energy with sustainable business strategies. Furthermore, because businesses are often concerned with social and environmental implications, it is believed that implementing a sustainable energy strategy will give long-term benefits to businesses. In this regard, this study aims to identify green energy problems in logistics companies and to select the best sustainable strategy. The hybrid T-spherical fuzzy (T-SF) methodology is introduced to solve the problem, including T–SF–subjective weighting, T–SF–criteria importance through intercriteria correlation (CRITIC), subjective and objective weight integrated approach (SOWIA), and T–SF–additive ratio assessment system (ARAS). According to the results, the most important green energy factor in logistics companies is determined as "energy security". The best sustainable strategy is identified as the "socially beneficial services supply strategy". The relevant results are critical for guiding companies, users, and stakeholders. • Green energy problems and factors for logistic companies are determined. • Comprehensive framework for selecting an ideal green sustainable strategy is proposed. • The advanced hybrid T-SF CRITIC-ARAS-based methodology is introduced. • The proposed MCDA tool can evaluate and rank indicators for green energy problems. • Recommendations for the implementation of green sustainable strategies are offered. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

T-spherical fuzzy set (T-SFS) is emerged as one of the effective tools for dealing uncertainty in decision-making process. Whereas, power aggregation operators help us in normalizing the impact of extreme values and capture the interconnectedness of the arguments. Meantime, one of the most prominent factors in multi-attribute decision-making (MADM) problems is the lack of awareness of biasness. Neutral operations highlight fair and unbiased character of decision makers. Thus, aiming these advantages and heterogeneity of arguments, a hybrid form of operators, weighted power partitioned neutral average operator and weighted power partitioned neutral geometric operator are developed under T-SFS environment for the first time. Beside these, power weighted neutral average, power ordered weighted neutral average, power hybrid neutral average operators, and their dual forms are initiated too. A new modified score function for T-SFS is formulated. Based on the developed operators and score function, an MADM algorithm is constituted and utilized in solving a hypothetical case study problem on hydrogen (H 2) refuelling station site selection. Finally, comparative study of the developed operators with other operators is carried out to explore the applicability and supremacy of the designed MADM algorithm. • Novel power partitioned neutral aggregation operators are pioneered. • Different power neutral operators for T-spherical fuzzy sets are initiated as well. • A new modified score function for T-spherical fuzzy sets is formulated. • An MADM algorithm to find the best one based on designed operators is constituted. • A hypothetical case study on hydrogen refuelling site selection is illustrated. [ABSTRACT FROM AUTHOR]