The advent of digital technologies has transformed accounting practices, leading to an unprecedented increase in the generation, processing, and reporting of financial data [1]. Modern digital accounting systems, including enterprise resource planning platforms, AI-driven transaction processors, and cloud-based reporting tools, have enabled organizations to automate and accelerate financial operations [2]. While these innovations improve efficiency and accuracy, they introduce new forms of algorithmic uncertainty and opacity that traditional accounting decision models struggle to accommodate [3]. Economic transparency, which historically has focused on clarity and completeness of disclosures, must now be reconsidered in the context of automated, algorithm-driven financial systems [4]. Understanding how stakeholders perceive and evaluate transparency in digital accounting environments is therefore a critical research challenge.

Traditional accounting research has emphasized structured reporting, compliance with regulatory standards, and auditing procedures to reduce information asymmetry between managers and stakeholders [5]. However, these approaches often assume that financial data is fully interpretable and humanly auditable, assumptions that are increasingly violated in highly automated systems [6]. For instance, machine learning models used for expense categorization or financial forecasting may produce outputs that are statistically accurate but semantically opaque to human auditors [7]. Similarly, blockchain-based ledgers ensure immutability and traceability but do not automatically guarantee interpretability for regulatory or managerial purposes [8]. These developments highlight the insufficiency of classical transparency metrics, as they fail to capture algorithmic indeterminacy and systemic complexity inherent in digital accounting processes [9].

In recent years, decision-making research has attempted to integrate advanced analytical tools, such as fuzzy logic, multi-criteria decision-making, and machine learning, to manage uncertainty in accounting environments [10]. Fuzzy logic has been used to model imprecision in audit risk and qualitative judgments [11], whereas neural networks and support vector machines have been applied to predict financial distress or detect fraudulent activity [12]. Despite these advances, existing approaches typically focus on predictive performance rather than on the structural modeling of uncertainty [13]. They often ignore the latent indeterminacy produced by automated and algorithmic accounting systems, leaving a methodological gap in the assessment of economic transparency [14].

Neutrosophic logic, which extends fuzzy logic by introducing explicit degrees of truth, indeterminacy, and falsity, provides a promising theoretical framework for representing uncertainty in complex domains [15]. Unlike classical or fuzzy logic, neutrosophic models accommodate contradictory, incomplete, or partially known information, making them particularly suitable for digital accounting systems where algorithmic outputs can be partially interpretable [16]. However, applications of neutrosophic logic in accounting remain limited, primarily focusing on theoretical modeling rather than on empirical inference using real or simulated data [17]. Furthermore, existing models rarely integrate machine learning to dynamically infer the neutrosophic components from data, which is essential in digital environments characterized by evolving processes and continuous automation [18].

Addressing these gaps, this study proposes N²-DADMET: A Neutrosophic–Neuro Digital Accounting Decision Method for Economic Transparency, a novel framework that models transparency as a learnable neutrosophic state rather than a fixed metric. In this framework, transparency is represented as a triplet of truth T_t, indeterminacy I_t, and falsity F_t, which are dynamically inferred from system-level accounting data using machine learning algorithms. This approach enables the framework to capture algorithmic ambiguity, automated processing effects, and potential distortions in digital accounting outputs. Unlike traditional models, N²-DADMET integrates structural uncertainty modeling with data-driven learning, offering a flexible and adaptive method for evaluating economic transparency.

The purpose of this research is threefold. First, it aims to extend the theoretical foundations of accounting transparency by formalizing algorithmic indeterminacy as a central component of decision-making in digital environments. Second, it introduces a methodological innovation by combining neutrosophic logic with neuro-learning to infer uncertainty states directly from empirical data. Third, it provides a practical decision-support framework for auditors, regulators, and financial analysts, enabling them to assess transparency with greater nuance and accuracy than existing deterministic or heuristic approaches allow. By learning transparency rather than assuming it, N²-DADMET aligns decision-making with the realities of modern digital accounting systems.

The necessity of this research is underscored by the increasing complexity of accounting environments due to automation, AI, and blockchain technologies. Conventional transparency measures fail to differentiate between measurement error, estimation risk, and algorithmic indeterminacy, which are critical for understanding stakeholder trust and system reliability [19]. N²-DADMET addresses this limitation by explicitly modeling these factors within a formalized, learnable framework. As digital accounting becomes ubiquitous, the ability to model, monitor, and interpret transparency dynamically is essential for effective auditing, regulatory compliance, and economic governance.

In summary, this study introduces a robust, adaptive, and theoretically grounded framework for understanding and evaluating economic transparency in digital accounting systems. By integrating neutrosophic logic with neuro-learning, N²-DADMET provides both conceptual clarity and computational capability, bridging the gap between algorithmic complexity and human interpretive capacity. The remainder of the article elaborates the theoretical underpinnings, formal methodology, and illustrative applications of the framework, highlighting its significance for academic research and professional practice in accounting.

Recent advances in digital accounting have transformed the methods of financial data generation, reporting, and auditing, highlighting the need for robust approaches to economic transparency [20]. Studies indicate that while automation and AI-driven processes improve operational efficiency, they simultaneously increase algorithmic opacity, making it difficult for stakeholders to interpret financial information accurately [21]. Blockchain-based solutions have been proposed to enhance traceability and immutability of financial transactions, yet these systems do not inherently resolve issues of interpretability or uncertainty from algorithmic processes [22]. This has led to a growing recognition that transparency in digital accounting environments is multidimensional, encompassing not only disclosure completeness but also cognitive reliability and trustworthiness of automated outputs [23].

Decision-making under uncertainty has been a significant focus in accounting research, particularly in contexts involving imprecise or incomplete information [24]. Traditional Multi-Criteria Decision-Making (MCDM) and fuzzy logic approaches have been applied to audit risk assessment, financial performance evaluation, and fraud detection [25]. Fuzzy logic allows modeling of vague or ambiguous expert judgments but often relies on predefined membership functions, which may not reflect dynamic system behaviors in automated accounting environments [26]. Similarly, conventional neural network models have been utilized to predict financial distress or detect anomalies in transactions; however, these approaches prioritize predictive accuracy over explicit modeling of uncertainty and algorithmic indeterminacy [27]. As a result, while machine learning enhances analytical capability, it does not fully address the structural complexity and hidden uncertainty inherent in digital accounting systems [28].

Neutrosophic logic, introduced by Smarandache, provides a formal framework for representing truth, indeterminacy, and falsity explicitly in decision-making contexts [29]. Applications of neutrosophic theory in engineering, risk assessment, and decision sciences demonstrate its capability to model contradictions and incomplete information [30]. In accounting, initial studies have explored neutrosophic sets for bankruptcy prediction, audit evaluation, and risk ranking, but these efforts remain largely theoretical and lack empirical implementation using digital accounting data [31]. Importantly, existing neutrosophic approaches typically rely on expert-assigned membership values, limiting adaptability and precluding integration with learning algorithms that can infer uncertainty from system behavior [32]. This presents a notable gap in the literature, particularly for environments where algorithmic processing, automated reporting, and dynamic transaction flows introduce continuous and non-deterministic uncertainty.

Hybrid approaches combining neutrosophic logic with machine learning have been proposed in other domains, such as engineering systems, supply chain risk management, and medical diagnostics, demonstrating improved capability to handle uncertainty and indeterminacy while leveraging data-driven inference [33]. These methods show that integrating learning mechanisms with neutrosophic modeling allows adaptive estimation of truth, indeterminacy, and falsity without reliance on static expert inputs [34]. However, applications of such hybrid methods in accounting remain scarce, and no prior study has operationalized neutrosophic-neuro frameworks for evaluating economic transparency in digital accounting systems. The absence of a unified, data-driven framework for learning transparency under algorithmic uncertainty represents a critical research gap with significant theoretical and practical implications.

Several studies have emphasized the importance of interpretability and transparency in AI-driven accounting processes. For example, research on Explainable AI (XAI) in finance indicates that transparency enhances stakeholder trust and decision-making effectiveness [35]. Similarly, work on audit automation stresses the need to evaluate not only the correctness of outputs but also the cognitive accessibility of algorithmic reasoning [36]. Despite these insights, there remains a lack of formalized methods that quantitatively model transparency as a multi-dimensional state encompassing truth, indeterminacy, and falsity within digital accounting environments [37]. Most current approaches provide either descriptive assessments or rely on deterministic measures, which fail to capture algorithmically induced uncertainty [38].

In summary, the literature identifies four critical gaps that motivate the current study: 1) existing transparency metrics do not account for algorithmic indeterminacy in digital accounting systems, 2) neutrosophic methods in accounting have not been integrated with empirical learning from system data, 3) machine learning approaches focus on predictive performance rather than uncertainty modeling, and 4) no prior framework explicitly combines neutrosophic logic with neuro-learning to evaluate economic transparency adaptively. Addressing these gaps, the proposed N²-DADMET framework represents the first attempt to unify neutrosophic modeling with data-driven learning mechanisms to assess transparency dynamically and comprehensively in digital accounting systems. This contribution is significant both theoretically, by extending the conceptualization of transparency, and practically, by providing a decision-support tool for auditors, regulators, and financial analysts.

To develop a robust framework for evaluating economic transparency in digital accounting systems, it is essential to define the foundational concepts and mathematical notations underpinning the proposed N²- DADMET framework. This section introduces the necessary preliminaries, including neutrosophic logic, representation of transparency states, and basic neuro-learning principles for inference. The formalization ensures a rigorous basis for the subsequent methodological development.

The proposed N²-DADMET framework is a novel integration of neutrosophic logic with machine learning-based inference, designed to evaluate economic transparency in digital accounting systems. Unlike conventional approaches that treat transparency as a static metric, N²-DADMET models transparency as a learnable neutrosophic state (Tt, It, Ft), capturing truth, indeterminacy, and falsity in algorithmically generated accounting outputs. The methodology consists of three interrelated components: problem representation, neutrosophic state modeling, and neuro-learning inference with decision-making.

To demonstrate the practical applicability and interpretability of the N²-DADMET framework, a simulated scenario of a digital accounting system is employed. The scenario reflects a mid-sized enterprise with automated transaction processing, algorithmic expense categorization, and cloud-based reporting. The simulation includes 5000 synthetic transactions over a one-year horizon, encompassing both routine and exceptional accounting events. Key system variables include transaction amounts, category codes, user roles, frequency of automated adjustments, and system flags for anomalies. This illustrative case highlights how N²- DADMET evaluates economic transparency dynamically, identifies transactions requiring audit attention, and adapts to evolving automated processes.

The application of the N²-DADMET framework demonstrates a meaningful advancement in the assessment of economic transparency in digital accounting systems. By integrating neutrosophic logic with machine learning, the framework captures both structural uncertainty and dynamic patterns in automated accounting processes. Unlike conventional methods that rely solely on deterministic measures or predictive models, N²- DADMET provides a multi-dimensional transparency metric encompassing truth, indeterminacy, and falsity. This capability is significant because modern accounting environments increasingly involve automated processes whose outputs may be statistically valid but semantically opaque or partially indeterminate. The results indicate that incorporating explicit indeterminacy allows the identification of transactions that would otherwise be misclassified as either fully transparent or non-transparent, enhancing decision-making reliability.

The framework’s ability to produce interpretable transparency scores addresses a critical challenge in digital accounting: the gap between algorithmic outputs and human audit interpretation. While neural networks have been widely employed for anomaly detection or fraud prediction in accounting, these models typically optimize predictive performance without quantifying uncertainty in outputs [40]. In contrast, N²-DADMET integrates a neutrosophic structure that enables the explicit decomposition of transparency into truth, indeterminacy, and falsity, facilitating audit prioritization and regulatory evaluation. This approach offers a conceptual advancement by linking algorithmic evaluation with the qualitative dimensions of transparency, a feature not present in prior hybrid fuzzy or neural approaches.

Comparing the outcomes of N²-DADMET with existing studies on AI-driven accounting and fuzzy logic models reveals both similarities and differences. Similar to previous applications of fuzzy inference in auditing [41], the framework supports graded evaluation of transaction reliability. However, unlike traditional fuzzy methods, which often treat uncertainty as a single scalar measure [42], N²-DADMET distinguishes between different sources of uncertainty and explicitly models falsity alongside indeterminacy. This distinction allows the framework to detect not only ambiguous but potentially misleading transactions, aligning closer with regulatory priorities and risk-based auditing. Additionally, while prior machine learning models have demonstrated accuracy in detecting anomalies, they often lack temporal adaptability [43]. In contrast, the recursive update mechanism in N²-DADMET allows continuous monitoring, capturing evolving patterns and shifts in algorithmic behavior over time.

The illustrative application further underscores the practical implications of this methodology. Routine transactions exhibit high truth and low indeterminacy, consistent with expectations for automated, standardized processes. More complex or anomalous transactions are appropriately flagged through increased indeterminacy and falsity components, demonstrating the framework’s sensitivity to process irregularities. This contrasts with classical scoring methods, which may fail to differentiate between high-risk and moderate-risk transactions when the overall numerical features appear similar. Consequently, N²-DADMET offers a decision-support tool that prioritizes audit attention based on multi-dimensional transparency, enhancing efficiency and focusing resources where they are most needed.

Furthermore, the sensitivity analysis illustrates the flexibility of the framework in accounting for organizational or regulatory priorities. Adjusting the weights of indeterminacy and falsity allows auditors to calibrate transparency scores according to context-specific risk tolerance, a feature rarely addressed in existing models. This adaptability positions N²-DADMET as both a theoretically rigorous and practically deployable tool for modern accounting environments. It also provides a foundation for integrating additional layers of transparency evaluation, such as ethical compliance or financial statement credibility, without substantial modifications to the underlying model.

In conclusion, the discussion emphasizes that N²-DADMET achieves conceptual and operational improvements over prior approaches. Its key contributions include the explicit modeling of multiple dimensions of transparency, integration with data-driven neuro-learning for adaptive inference, and practical interpretability for audit decision-making. By bridging algorithmic outputs and human evaluative processes, the framework addresses a persistent limitation in digital accounting research and practice. These advances highlight the potential of combining neutrosophic logic with machine learning for complex, automated decision environments and provide a foundation for future empirical validation and expansion into other domains of financial oversight.

This study introduces the N²-DADMET framework, a novel integration of neutrosophic logic and neuro-learning, designed to evaluate economic transparency in digital accounting systems. The framework conceptualizes transparency as a learnable neutrosophic state, explicitly capturing truth, indeterminacy, and falsity, thereby addressing the limitations of traditional deterministic or single-dimensional metrics. The application of the framework to a simulated accounting environment demonstrates its ability to differentiate routine, transparent transactions from complex or potentially misleading ones, providing interpretable transparency scores that are adaptable to both organizational and regulatory priorities. The results indicate that incorporating indeterminacy alongside truth and falsity enhances the identification of high-risk transactions, supports more informed audit decision-making, and improves the overall assessment of digital accounting processes.

From a theoretical perspective, N²-DADMET advances the conceptual understanding of transparency by highlighting its multi-dimensional nature in automated accounting environments. Unlike prior approaches, which often treat uncertainty as a single scalar value or focus exclusively on predictive performance, this framework enables structured modeling of algorithmic ambiguity and potential falsity. It demonstrates that transparency is not a fixed attribute but a dynamic construct that evolves with system behavior, automated decision rules, and process modifications. This conceptualization provides a foundation for future research exploring additional dimensions of transparency, including ethical compliance, audit reliability, and stakeholder trust, and establishes a bridge between advanced computational methods and practical accounting evaluation.

From a practical standpoint, the framework offers several actionable insights. First, auditors and regulators can use the transparency scores to prioritize transactions for review, focusing attention on areas where high indeterminacy or falsity may indicate risk. Second, the weighting parameters for indeterminacy and falsity provide flexibility, allowing organizations to tailor transparency assessments to context-specific risk tolerances or regulatory standards. Third, the dynamic updating mechanism ensures that transparency evaluation remains responsive to evolving accounting systems, supporting continuous monitoring and early detection of anomalies or irregularities. Finally, the framework’s interpretable outputs enhance stakeholder understanding, facilitating clearer communication of accounting risks, automated process reliability, and audit findings. Based on the findings, several practical suggestions emerge for enhancing economic transparency in digital accounting systems. Organizations should integrate data-driven transparency assessment tools, such as N²- DADMET, into their auditing and reporting workflows to complement conventional procedures. Audit teams should leverage the multi-dimensional transparency scores to allocate resources efficiently, focusing on transactions with higher indeterminacy or potential falsity. Regulatory bodies may consider adopting similar frameworks to monitor automated accounting environments, enabling proactive oversight and early identification of emerging risks. Additionally, the adaptability of the framework to different weighting schemes suggests that institutions can calibrate assessments according to industry-specific risk factors, transaction complexity, and organizational priorities.

In conclusion, the N²-DADMET framework provides a robust, interpretable, and adaptive methodology for evaluating economic transparency in modern digital accounting systems. By combining neutrosophic logic with neuro-learning, it addresses critical challenges associated with algorithmic opacity, evolving processes, and multi-dimensional uncertainty. The study demonstrates that transparency assessment can be both rigorous and actionable, supporting improved audit decision-making, regulatory compliance, and stakeholder trust. Future applications may extend the framework to integrate additional dimensions of financial evaluation, incorporate real-world enterprise data, and explore cross-industry generalization, establishing N²- DADMET as a foundational tool for advanced, data-driven transparency assessment in accounting and financial governance.

All aspects of the research and manuscript preparation were carried out by the author. The author has read and approved the final version of the manuscript.

This study did not receive any specific funding from public, commercial, or non-profit funding agencies.

All data are included in the text.

The author declares that he does not have any conflict of interest.