Search Results (33)

The exponential growth of lithium-ion battery consumption has amplified the urgency of identifying sustainable and economically viable recycling solutions. This study proposes an integrated decision-making framework based on the T-Spherical Fuzzy Einstein Interaction Aggregator DEMATEL-CoCoSo approach to comprehensively evaluate and rank battery recycling technologies under uncertainty. Ten key evaluation criteria—encompassing environmental, economic, and technological dimensions—were identified through expert consultation and literature synthesis. The T-Spherical Fuzzy DEMATEL method was first applied to analyze the causal interdependencies among criteria and determine their relative weights, revealing that environmental drivers such as energy consumption, greenhouse gas emissions, and waste generation exert the most systemic influence. Subsequently, six recycling alternatives were assessed and ranked using the CoCoSo method enhanced by Einstein-based aggregation, which captured the complex interactions present in the experts’ evaluations and assessments. Results indicate that Direct Recycling is the most favorable option, followed by the Hydrometallurgical and Bioleaching methods, while Pyrometallurgical Recycling ranked lowest due to its high energy demands and environmental burden. The proposed hybrid model effectively handles linguistic uncertainty, expert variability, and interdependent evaluation structures, offering a robust decision-support tool for sustainable technology selection in the circular battery economy. The framework is adaptable to other domains requiring structured expert-based evaluations under fuzzy environments. Full article

Despite advancements in divergence and distance measures across fuzzy set extensions, the development of such measures for Globular T-Spherical Fuzzy Sets (G-TSFSs) remains significantly unexplored. Existing approaches often fall short in capturing the rich semantics and high-dimensional uncertainty that G-TSFSs represent, limiting their utility in complex decision environments. This study is motivated by the need to fill this critical gap and advance decision science through more expressive and structurally aligned tools. This paper introduces a suite of novel divergence measures (Div-Ms) specifically formulated for G-TSFSs, a powerful tool for capturing uncertainty in multi-criteria group decision-making (MCGDM) under complex conditions. These Div-Ms serve as the foundation for developing new distance measures (Dis-Ms) and similarity measures (SMs), where both Dis-Ms and SMs are symmetry-based and their essential mathematical properties and supporting theorems are rigorously established. Leveraging these constructs, we propose a robust G-TSF-TOPSIS framework and apply it to a real-world problem, selecting optimal solar energy systems (SESs) for a university context. The model integrates expert evaluations, assuming equal importance due to their pivotal and complementary roles. A sensitivity analysis over the tunable parameter (ranging from 4.0 to 5.0 with an increment of 0.2) confirms the robustness and stability of the decision outcomes, with no changes observed in the final rankings. Comparative analysis with existing models shows superiority and soundness of the proposed methods. These results underscore the practical significance and theoretical soundness of the proposed approach. The study concludes by acknowledging its limitations and suggesting directions for future research, particularly in exploring adaptive expert weighting strategies for broader applicability. Full article

Multiple criteria decision-making (MCDM) is a significant area of decision-making theory that certainly warrants attention. It might be difficult to accurately convey the necessary decision facts when navigating decision-making problems since we frequently run into complicated issues and unpredictable situations. To address this, introducing the novel idea of the bipolar pqr-spherical fuzzy set (${\mathrm{B}}_{\mathrm{pqr}}$SFS), a hybrid structure of the bipolar fuzzy set (BFS) and the pqr-spherical fuzzy set (pqr-SFS), is the main goal of this work. The fundamental (set-theoretic and algebraic) operations on ${\mathrm{B}}_{\mathrm{pqr}}$SFSs are explained as well as their relations to several known models. A distance measure, such as Euclidean distance, among ${\mathrm{B}}_{\mathrm{pqr}}$SFNs, is provided. Afterward, we expand the fundamental aggregation operators to the pqr-spherical fuzzy (${\mathrm{B}}_{\mathrm{pqr}}$SF) environment by developing bipolar pqr-spherical fuzzy-weighted averaging and bipolar pqr-spherical fuzzy-weighted geometric operators for aggregating ${\mathrm{B}}_{\mathrm{pqr}}$SFNs. According to the aforementioned distance measure and operators, an MCDM approach is established consisting of two algorithms, namely, the TOPSIS method and the method using the proposed operators in the ${\mathrm{B}}_{\mathrm{pqr}}$SF context. Moreover, a numerical example is provided in order to ensure that the presented model is applicable. By using the two algorithms, a comparative analysis of the proposed method with other existing ones is given in order to verify the feasibility of the suggested decision-making procedure. Full article

This paper presents an innovative methodology for the dynamic emergency response scheme selection (ERSS) problem in post-major natural disasters. It employs a combination of subjective and objective composite weights and the integrated ELECTRE-score approach. The study aims to provide a practical approach for continuously determining optimal decision schemes at various time points during the decision period in the aftermath of significant natural disasters while accommodating evolving real-world scenarios. Firstly, the probabilistic T-spherical hesitant fuzzy set (Pt-SHFS) captures decision-makers’ ambivalence and hesitation regarding diverse evaluation attributes of different schemes. Subsequently, Pt-SHFS is integrated with the best–worst method (BWM) to determine subjective weights, followed by the structured CRITIC method to amalgamate subjective weights and derive the final combination weights of criteria. Additionally, this paper proposes applying a penalty-incentive mechanism to establish dynamic attribute weights during scenario evolution. Furthermore, the ELECTRE-score method, which may fully exploit the advantages of non-compensation situations, is adopted to obtain more reliable dynamic optimal decision outcomes. Consequently, based on these foundations, an integrated dynamic ERSS approach is formulated to determine optimal dynamic emergency response schemes. Finally, a case study on the Gansu Jishishan earthquake, sensitivity analysis, comparative analysis, and continuous analysis are conducted to verify the practicality, stability, and effectiveness of the proposed approach. The result shows that the proposed comprehensive approach can depict variances among experts’ information, dynamically adjust attribute weights in response to evolving scenarios, and assign a score range and a representative score to each scheme at each decision state. Sensitivity and comparative analyses show this model has strong stability and dynamics. Furthermore, the proposed approach can effectively deal with the complex dynamic situation in the earthquake rescue process, such as the secondary collapse of buildings after the earthquake, the damage of materials caused by heavy rain, and the occurrence of aftershocks. The model can continuously optimize decision-making and provide scientific and reliable support for emergency decision-making. Full article

Selecting optimal design solutions is inherently complex due to multiple criteria encompassing users’ uncertain needs, experiences, and costs. This process must manage uncertainty and ambiguity, making developing a scientific, rational, and efficient guidance method imperative. Bipolar T-spherical fuzzy sets (BTSFS), a hybrid of bipolar fuzzy sets and T-spherical fuzzy sets, effectively handle the bipolarity inherent in all elements. In this work, we propose a Weighted Aggregated Sum Product Assessment (WASPAS) method based on BTSFS and the Aczel–Alsina T-norm (AATN) and T-conorm (AATCN) to address the problem of selecting conceptual design solutions. We first establish operational rules for BTSFS using AATN and AATCN and introduce weighted aggregation operators (BTSFAAWA) and geometric aggregation operators (BTSFAAWG) while examining fundamental properties, such as idempotency, boundedness, and monotonicity. Subsequently, we propose a two-stage BTSFS-based WASPAS method; criterion weights are calculated using the BTSFAAWA operator, and final rankings are obtained through comprehensive calculations using both the weighted sum method (WSM) based on BTSFAAWA and the weighted product method (WPM) based on BTSFAAWG. Finally, we validate the effectiveness of our method through a case study of the selection of cultural and creative products. Sensitivity and comparative analyses are conducted to demonstrate the advantages of our approach. Full article

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. Full article

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. Full article

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. Full article

Against the background of a major change in the world unseen in a century, emergencies with high complexity and uncertainty have had serious impacts on economic security and sustainable social development, making emergency management an important issue that needs to be urgently resolved, and the quality assessment of emergency information is a key link in emergency management. To effectively deal with the uncertainty of emergency information quality assessment, a new fuzzy multi-attribute assessment method is proposed in this paper. First, we propose the linguistic complex T-spherical fuzzy set (LCT-SFS), which can deal with two-dimensional problems and cope with situations in which assessment experts cannot give quantitative assessments. Then, the advanced linguistic complex T-spherical fuzzy Dombi-weighted power-partitioned Heronian mean (ALCT-SFDWPPHM) operator, which incorporates the flexibility of Dombi operations, is proposed. The partitioned Heronian mean (PHM) operator can consider attribute partitioning and attribute correlation, the power average (PA) operator can eliminate the effect of evaluation singularities, and the advanced operator can circumvent the problem of consistent or indistinguishable aggregation results, which provides a strong comprehensive advantage in the evaluating information aggregation. Finally, a fuzzy multi-attribute assessment model is constructed by combining the proposed operator with the WASPAS method and applied to the problem of assessing the quality and sensitivity of emergency information; qualitative and quantitative comparison analyses are carried out. The results show the method proposed in this paper has strong feasibility and validity and can represent uncertainty assessment more flexibly while providing reasonable and reliable results. The method can provide new ideas and methods for the quality assessment of emergency information, and promoting sustainable, efficient, and high-quality development of emergency management. Full article

The theory of spherical linear Diophantine fuzzy sets (SLDFS) boasts several advantages over existing fuzzy set (FS) theories such as Picture fuzzy sets (PFS), spherical fuzzy sets (SFS), and T-spherical fuzzy sets (T-SFS). Notably, SLDFS offers a significantly larger portrayal space for acceptable triplets, enabling it to encompass a wider range of ambiguous and uncertain knowledge data sets. This paper delves into the regularity of spherical linear Diophantine fuzzy graphs (SLDFGs), establishing their fundamental concepts. We provide a geometrical interpretation of SLDFGs within a spherical context and define the operations of complement, union, and join, accompanied by illustrative examples. Additionally, we introduce the novel concept of a spherical linear Diophantine isomorphic fuzzy graph and showcase its application through a social network scenario. Furthermore, we explore how this amplified depiction space can be utilized for the study of various graph theoretical topics. Full article

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. Full article

In this article, the parameter of the decision maker’s familiarity with the attributes of the alternatives is introduced for the first time in dynamic multi-attribute group decision making to avoid the disadvantages arising from the inappropriate grouping of decision makers. We combine it with fuzzy soft rough set theory and dynamic multi-attribute-grouping decision making to obtain a new decision model, i.e., dynamic chaotic multiple-attribute group decision making. Second, we provide an algorithm for solving this model under a weighted T-spherical fuzzy soft rough set, which can not only achieve symmetry between decision evaluation and fuzzy information but also establish a good symmetrical balance between decision makers and attributes (evaluation indexes). Finally, a specific numerical computation case is proposed to illustrate the convenience and effectiveness of our constructed algorithm. Our contributions to the literature are: (1) We introduced familiarity for the first time in dynamic multi-attribute group decision making. This makes our given dynamic chaotic multi-attribute group decision-making (DCMAGDM) model more general and closer to the actual situation; (2) we combined dynamic chaotic multi-attribute group decision making with T-spherical fuzzy soft rough set theory to make the model more realistic and reflect the actual situation. In addition, our choice of T-spherical fuzzy soft rough set allows the decision maker to engage in a sensible evaluation rather than sticking to numerical size choices; and (3) we constructed a new and more convenient sorting/ranking algorithm based on weighted T-spherical fuzzy soft rough sets. Full article

The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncertainty compared to the picture fuzzy sets and spherical fuzzy sets. It plays a key role in modeling problems that require two-dimensional data. The present study purposes the aggregation technique of Ct-SFSs with the aid of Aczel–-Alsina (AA) operations. We first introduce certain novel AA operations of Ct-SFSs, such as the AA sum, AA product, AA scalar multiplication, and AA scalar power. Subsequently, we propound a series of complex t-spherical fuzzy averaging and geometric aggregation operators to efficiently aggregate complex t-spherical fuzzy data. In addition, we explore the different characteristics of these operators, discuss certain peculiar cases, and prove their fundamental results. Thereafter, we utilize these operators and propose entropy measures to frame a methodology for dealing with complex t-spherical fuzzy decision-making problems with unknown criteria weight data. Finally, we provide a case study about vehicle model selection to illustrate the presented method’s applicability followed by a parameter analysis and comparative study. Full article

The T-Spherical fuzzy set (TSFS) is the most generalized form among the introduced fuzzy frameworks. It obtains maximum information from real-life phenomena due to its maximum range. Consequently, TSFS is a very useful structure for dealing with information uncertainties, especially when human opinion is involved. The correlation coefficient (CC) is a valuable tool, possessing symmetry, to determine the similarity degree between objects under uncertainties. This research aims to develop a new CC for TSFS to overcome the drawbacks of existing methods. The proposed CCs are generalized, flexible, and can handle uncertain situations where information has more than one aspect. In addition, the proposed CCs provide decision-makers independence in establishing their opinion. Based on some remarks, the usefulness of the new CC is reviewed, and its generalizability is evaluated. Moreover, the developed new CC is applied to pattern recognition for investment decisions and medical diagnosis of real-life problems to observe their effectiveness and applicability. Finally, the validity of the presented CC is tested by comparing it with the results of the previously developed CC. Full article

Sustainable transportation has a significant impact on factors related to urban development and economic development. Therefore, much research is being undertaken to select the best strategies to manage sustainable transportation. Transportation requires a carefully designed method to manage the development of mobility modes in terms of the pollution they produce or the use of renewable energy sources. However, due to numerous preferences of decision-makers and data uncertainty problems, it is challenging to select the optimal strategy. In this paper, we focus on creating a framework for determining the best strategy for sustainable transportation management. For this purpose, T-spherical fuzzy graphs will be used, which, together with the combination of Laplacian Energy, can accurately represent decision-makers’ preferences in an uncertain environment. Due to the lack of limitations of T-spherical fuzzy graphs and its numerous membership functions, decision-makers can decide which factor seems most important for selecting the optimal sustainable transportation strategy. Additionally, due to the applicability, the SFS TOPSIS approach has been used in this approach. The obtained results demonstrate the high performance of the proposed approach and the applicability of the approach in management and sustainable transport problems. Full article