Aliya Fahmi

Fuzzy Rough Digraphs are insufficient for scenarios involving both positive and negative influences. To address the limitations of Fuzzy Rough Digraphs in modeling conflicting information, this paper introduces the Bipolar Fuzzy Rough Digraph (BFRD) as a new framework for decision-making under uncertainty. We define its fundamental properties, including the strength of paths, connectedness, vertex degree, the Regular BFRD. From these, we establish the concepts of the minimum dominating set and domination number. An algorithm is then developed to apply this framework to practical problems. The model’s efficacy is demonstrated through a real-world application: identifying an optimal set of rural areas for establishing medicine supplymarkets by finding the minimum dominating set. This work provides a robust mathematical tool for solving complex problems involving bipolarity and as a process innovation.

This paper presents a significant extension of the classical TODIM (an acronym in Portuguese for Interactive and Multicriteria Decision-Making) method, originally grounded in prospect theory, by integrating it with Complex Cubic Fuzzy data to form a novel decision-making framework, CCF-TODIM. The primary contribution lies in extending the classical TODIM technique by incorporating CCF sets, which offer a more expressive representation of uncertainty by simultaneously capturing membership, non-membership, hesitation, and complex evaluations. The proposed CCF-TODIM method is systematically developed, and its operational steps are detailed through a comprehensive numerical example. To demonstrate practical relevance and robustness,the framework is applied to a real-world case study that assesses the global economic impacts of the Afghan-American War. A comparative analysis with existing MADM approaches reveals the superiority of the CCF-TODIM model in terms of accuracy and adaptability. Furthermore, the impact of different distance measures on the final ranking of alternatives is investigated to validate the sensitivity and stability of the method. The study establishes CCF-TODIM as a powerful tool for handling ambiguous and complex decision environments, with broad applicability in socio-economic and geopolitical analysis.

In graph theory, dominance has been a key idea for examining influence, control, and optimization in various systems. By examining domination in rough m-polar fuzzy digraphs—a hybrid model that combines directed graphs, m-polar fuzzy logic, and rough set theory—this work presents a fresh expansion of this idea. This structure makes it possible to simulate multi-polardecision contexts, uncertainty, and imprecision in a single framework. We justify the requirement for a more sophisticated concept of domination in rough m-polar fuzzy digraphs by first going over the fundamental concepts behind them. After a formal definition of domination in this context is put forward, its basic characteristics and structural ramifications are thoroughly examined. After that, the study concentrates on two crucial operations: the strong product of rough m-polar fuzzy digraphs and the tensor product. We characterize these procedures in the new framework and examine their effects on the resulting graphs’ dominating parameters. Under multi-valued and uncertain circumstances, these operations help to generalize the relationships and interactions amongst intricate network topologies. A thorough numerical example is given to illustrate thesuggested notions’ applicability in real-world situations. Lastly, the use of domination in rough m-polar fuzzy digraphs is examined, emphasizing its potential in practical contexts like information systems, social network analysis, and uncertain decision-making. The study’s conclusions open up new possibilities for using domination theory in dynamic and unpredictable contexts and further the theoretical development of fuzzy and rough graph models.

Optimizing renewable energy project selection presents a complex challenge that demands intelligent decision-making under conditions of uncertainty. In multi-criteria decision-making (MCDM), the need to balance numerous conflicting factors makes these techniques invaluable for effective project evaluation and selection. This paper introduces a novel Triangular Intuitionistic Fuzzy Frank (TIFF) framework, which integrates triangular intuitionistic fuzzy averaging and geometric aggregation operators to enhance decision-making in renewable energy project assessment. We develop several new aggregation operators, including: Triangular Intuitionistic Fuzzy Frank Weighted Averaging (TIFFWA), Ordered Weighted Averaging (TIFFOWA), Hybrid Averaging (TIFFHA), Weighted Geometric (TIFFWG), Ordered Weighted Geometric (TIFFOWG), and Hybrid Geometric (TIFFHG). These operators, built upon the Frank t-norm and t-conorm, enable more accurate and adaptive evaluations by effectively managingvarying levels of uncertainty. In addition, novel scoring and precision functions are introduced to further refine the decision-making process, yielding more reliable outcomes. A step-by-step methodology is presented for applying the TIFF approach to renewable energy project selection, providing clear guidance for practical implementation. To validate the method, a numerical case study is conducted, demonstrating the superior performance of the TIFF framework compared to existing techniques. The results under-score the method’s efficiency, adaptability, and practical value as a robust tool for optimizing renewable energy project decisions under uncertainty.

This study introduces operational laws for Aczél-Alsina aggregation within the framework of generalized bipolar neutrosophic sets (GBNS), tailored for group decision-making scenarios. Novel aggregation operators, including the Generalized Bipolar Neutrosophic Aczél-Alsina Weighted Average (GBNAAWA), Generalized Bipolar Neutrosophic Aczél-Alsina Ordered Weighted Average (GBNAAOWA), Generalized Bipolar Neutrosophic Aczél-Alsina Hybrid Weighted Average (GBNAAHWA), Generalized Bipolar Neutrosophic Aczél-Alsina Weighted Geometric (GBNAAWG), Generalized Bipolar Neutrosophic Aczél-Alsina Ordered Weighted Geometric (GBNAAOWG), and Generalized Bipolar Neutrosophic Aczél-Alsina Hybrid Weighted Geometric (GBNAAHWG), are proposed to address complex decision-making processes under uncertainty. The methodology is demonstrated through a case study and an illustrative example to validate its practical applicability. Comparative and sensitivity analyses highlight the robustness and adaptability of the proposed operators in various decision contexts. Key findings, discussions, and limitations are presented to provide insights into the method’s effectiveness and areas for future research. This work contributes to advancing decision-making models by integrating Aczél-Alsina aggregation with bipolar neutrosophic theory, offering a novel approach to handling ambiguity and conflicting information.

This paper presents a series of innovative Bipolar Neutrosophic Aggregation Operators to address the complexity and uncertainty in Multiple Criteria Decision-Making scenarios. The newly proposed operators BNAAWA, BNAAOWA, BNAAHWA, BNAAWG, BNAAOWG, and BNAAHWG are designed to enhance aggregation under bipolar neutrosophic conditions, capturing a more nuanced view of decision-makers' preferences. We develop the MCDM method with the BNN. The effectiveness of these operators is demonstrated through a detailed case study, where they are applied to a complex decision-making scenario involving conflicting and uncertain criteria. Comparative and sensitivity analyses are conducted to assess the stability, reliability, and adaptability of each operator, benchmarking them against existing approaches. The results reveal that the proposed operators significantly improve decision-making accuracy by accommodating bipolar information and managing degrees of uncertainty more effectively. In the Results and Discussion section, we explore how each operator performs across varied MCDM contexts, highlighting the flexibility and robustness of the bipolar neutrosophic framework. The paper concludes by discussing the limitations of the proposed operators, offering insights into potential applications, and suggesting directions for future research to further refine bipolar neutrosophic-based MCDM approaches. This work contributes a comprehensive, operator-based method for enhanced decision-making under complex and uncertain conditions.

The study goals are to address the compound, multi-criteria decision-making tests associated with choosing the ideal scope for electric vehicle charging stations. This difficulty ascends due to the interaction of numerous quantitative and qualitative issues and the uncertainty characteristic in such assessments. Aliya et al. [37] introduced the concept of the cubic fermatean fuzzy sets, including their operational laws and score function. We develop the three aggregation operators including CFEFWA, CFEFOWA, and CFEFHWA operators with the cubic fermatean fuzzy set. Furthermore, uncertainty usually arises in Cubic Fermatean fuzzy sets and challenges related to selecting charging stations for electric vehicles. Therefore, the current study aims to provide an integrated decision-making method for handling multi-criteria CFFS electric vehicle charging stations. For CFFS, we propose some innovative Einstein operations to aggregate the decision data. To illustrate the effectiveness of our proposed technique, we apply it to an applied case of choosing EV charging positions and associate the outcomes with existing practices. The efficiency of the proposed method is assessed by comparing its fallouts with those obtained from existing methodologies. The results indicate that the introduced technique proposes extra value and is well aligned with current observations. Introduce three aggregation operators based on cubic fermatean fuzzy set to improve the decision-making for EV charging station locations. Propose an MCDM method with cubic fermatean fuzzy set To define the effectiveness of the proposed method through a practical case study and numerical example

Decision-making in uncertain and imprecise environments often requires robust mathematical frameworks capable of effectively representing and aggregating conflicting information. Circular Intuitionistic Fuzzy Sets (C-IFSs) are powerful tools for modeling such complexities by combining intuitionistic and cubic fuzzy set properties. In this study, we extend the applicability of C-IFSs by integrating them with the Hamacher operational framework, offering a more flexible and adaptive approach to aggregation. To this end, we propose six novel aggregation operators: Circular Intuitionistic Fuzzy Hamacher Weighted Average (CIFHWA), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Average (CIFHOWA), Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Average (CIFHHWA), Circular Intuitionistic Fuzzy Hamacher Weighted Geometric (CIFHWG), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Geometric (CIFHOWG), and Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Geometric (CIFHHWG). These operators are designed to address multi-criteria decision-making challenges with improved precision. We further develop score and accuracy functions to rank C-IFSs and propose a neural-based scheme employing cubic correlation coefficients to enhance computational efficiency. A detailed numerical example validates the framework’s effectiveness, illustrating its practical utility. Additionally, comparative analyses with existing techniques and sensitivity and robustness examinations demonstrate its superiority in handling complex decision-making scenarios. The findings underscore the advantages of using Hamacher-based operations with C-IFSs, offering a novel contribution to fuzzy decision-making and opening avenues for future research in uncertain data analysis.