Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education

__________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Neutrosophic Sets and Systems, Vol. 93, 2025 Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Emadaldeen Hassan Alomar Department of Accounting and Finance, College of Business, Jazan University, Jazan, KSA, Saudi Arabia Email: [email protected] Abstract The dynamic nature of the accounting profession requires continuous evolution in teaching practices to ensure that graduates possess the analytical, ethical, and practical competencies demanded by modern business environments. This study aims to assess the impact of diverse pedagogical strategies on student performance in accounting education. By comparing traditional lecture-based instruction with innovative methods such as problem-based learning, case studies, flipped classrooms, blended learning, and simulation-based training, the research identifies how specific teaching approaches influence cognitive understanding, skill acquisition, and academic achievement. This study uses the decision-making methodology for this problem. The average method is used to compute the criteria weights. The COPRAS method is used to rank the alternatives. A Neutrosophic Set is used to solve the uncertainty in information. This research provides valuable implications for educators, curriculum developers, and policymakers in accounting education. It advocates for a balanced pedagogical model that combines interactive teaching, digital tools, and experiential learning to optimize student performance and align academic outcomes with the professional requirements of the accounting field. Keywords: Pedagogical Strategies; Student Performance; Accounting Education; Neutrosophic Numbers. ______________________________________________________________________________ 1. Introduction One of the most popular methods is fuzzy rule-based decision systems, which use fuzzy logic to control the underlying uncertainties and ambiguities in decision analysis while offering a solid basis for signature verification. Receiving false positives or false negatives is more likely when judgments are made with a high degree of ambiguity[1], [2]. When there is a significant amount of high-level ambiguity, fuzzy algorithms may have trouble discriminating real signatures from fakes. The explicit treatment of truth, indeterminacy, and falsity by neutrosophic logic extends the possibilities of conventional fuzzy logic. University of New Mexico Neutrosophic Sets and Systems, Vol. 93, 2025 751 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Neutrosophic logic (NL) models situations when the data contains a high degree of untruth, an unclear truth value, or a great degree of indeterminacy. When information is unclear or contradictory, NL's explicit consideration of indeterminacy as a distinct dimension is very helpful[3], [4]. This facilitates the differentiation of various causes and forms of uncertainty. When it comes to managing uncertain signatures, where the degree of honesty, indeterminacy, and falsification may vary, NL is particularly useful. There are several benefits to using Type-2 Neutrosophic Logic (T2NL) with the Footprint of Uncertainty (FOU) when uncertainty is common and needs to be precisely described. By including not only the level of membership but also the related uncertainty, FOU inclusion enables a more thorough demonstration of uncertainty[5], [6]. T2NL provides a more robust basis for managing imprecision and uncertainty than Type-1 Neutrosophic Logic (T1NL) since it replicates uncertainty at the membership function level as well as the membership values. Because it can now store uncertainty about uncertainty, T2NL can represent complicated uncertain data with more sophistication. Situations with unclear borders across many categories are better represented by membership functions with higher degrees of uncertainty. For the decision problem task, a type-2 Neutrosophic Engine improves the system's capacity to handle signature variability and uncertainty[7], [8]. This approach may deal with ambiguous situations where decision-making may be partially matched, which is typical in real-world situations, by permitting indeterminacy to be a function. Additionally, the approach is appropriate for largescale applications like banking and legal systems since it can be scaled to handle complicated verification scenarios and massive datasets. The primary contribution of the proposed work is the integration of the Impact of Pedagogical Strategies on Student Performance in Accounting Education with a type-2 neutrosophic similarity measure, which facilitates decision-making by capturing both the degree of match between education and the degree of uncertainty surrounding the match. This enables better decisionmaking, particularly when the properties of education accounting are unclear. Our model uses a COPRAS method to rank the alternatives. The average method is used to compute the criteria weights. 2. Accounting Education Accounting education plays a critical role in preparing future professionals to navigate complex financial environments, interpret data accurately, and make informed business decisions. As the global economy becomes increasingly dynamic and technology-driven, traditional lecture-based teaching methods alone are no longer sufficient to develop the analytical, ethical, and practical competencies required of accounting graduates[9], [10]. Consequently, educators and institutions are seeking to implement innovative pedagogical strategies that enhance student engagement, deepen conceptual understanding, and improve overall performance outcomes in accounting courses. Neutrosophic Sets and Systems, Vol. 93, 2025 752 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Over the past decade, the field of accounting education has undergone a paradigm shift from instructor-centered teaching toward learner-centered learning. This transformation emphasizes active participation, critical thinking, and experiential learning rather than passive knowledge acquisition[11], [12]. Methods such as case-based learning, problem-based learning (PBL), simulations, flipped classrooms, and blended learning models have been increasingly adopted to foster both academic achievement and professional readiness. However, the effectiveness of these pedagogical approaches varies across contexts, depending on factors such as course design, instructor expertise, technological integration, and students’ learning preferences. Assessing the impact of these diverse teaching strategies on student performance is therefore essential for evidence-based educational improvement[13], [14]. Student performance in accounting is multidimensional—it encompasses not only grades and test results but also the development of higher-order skills such as analytical reasoning, ethical judgment, and practical application of financial principles. Understanding how specific pedagogical strategies influence these outcomes provides valuable insights for curriculum designers, educators, and policymakers aiming to align teaching practices with contemporary professional demands. Moreover, the growing incorporation of digital tools, artificial intelligence, and soft skill development into accounting curricula has added new layers of complexity to pedagogical evaluation[15], [16]. It is no longer enough to measure learning outcomes solely through examinations; comprehensive evaluation must consider engagement, adaptability, collaboration, and problem-solving capabilities. Thus, a systematic assessment framework that combines quantitative and qualitative indicators is needed to capture the holistic impact of teaching methodologies on students’ academic and professional competencies. In this context, the present study seeks to explore and evaluate the impact of various pedagogical strategies on student performance in accounting education. By comparing traditional and innovative teaching approaches, the research aims to identify the strategies that most effectively promote deep learning, engagement, and professional skill development. Ultimately, such an evaluation contributes to enhancing the quality of accounting education, ensuring that graduates are not only technically proficient but also adaptive, critical, and ethically grounded professionals ready to meet the evolving challenges of the accounting profession 3. Neutrosophic Decision-Making Methodology This section shows the steps of the proposed approach under a type-2 neutrosophic set (T2NS). We compute the criteria weights and rank the alternatives using the COPRAS method. Figure 1 shows the steps of the proposed approach. This section is divided into three parts. In the first part, we show definitions of T2NS[17], [18]. In the second part, we compute the criteria weights. In the third part, we show the ranks of alternatives. First part, definitions of T2NS The operations of T2NS are shown as: Neutrosophic Sets and Systems, Vol. 93, 2025 753 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education 𝑄1⨁𝑄2= ( (𝑇𝑇𝑄1(𝑌)+𝑇𝑇𝑄2(𝑌)−𝑇𝑇𝑄1(𝑌)𝑇𝑇𝑄2(𝑌), 𝑇𝐼𝑄1(𝑌)+𝑇𝐼𝑄2(𝑌)−𝑇𝐼𝑄1(𝑌)𝑇𝐼𝑄2(𝑌), 𝑇𝐹𝑄1(𝑌)+𝑇𝐹𝑄2(𝑌)−𝑇𝐹𝑄1(𝑌)𝑇𝐹𝑄2(𝑌)), (𝐼𝑇𝑄1(𝑌)𝐼𝑇𝑄2(𝑌),𝐼𝐼𝑄1(𝑌)𝐼𝐼𝑄2(𝑌),𝐼𝐹𝑄1(𝑌)𝐼𝐹𝑄2(𝑌)), (𝐹𝑇𝑄1(𝑌)𝐹𝑇𝑄2(𝑌),𝐹𝐼𝑄1(𝑌)𝐹𝐼𝑄2(𝑌),𝐹𝐹𝑄1(𝑌)𝐹𝐹𝑄2(𝑌)) ) (1) 𝑄1⨂𝑄2= ( (𝑇𝑇𝑄1(𝑌)𝑇𝑇𝑄2(𝑌),𝑇𝐼𝑄1(𝑌)𝑇𝐼𝑄2(𝑌),𝑇𝐹𝑄1(𝑌)𝑇𝐹𝑄2(𝑌)), (𝐼𝑇𝑄1(𝑌)+𝐼𝑇𝑄2(𝑌)−𝐼𝑇𝑄1(𝑌)𝐼𝑇𝑄2(𝑌), 𝐼𝐼𝑄1(𝑌)+𝐼𝐼𝑄2(𝑌)−𝐼𝐼𝑄1(𝑌)𝐼𝐼𝑄2(𝑌), 𝐼𝐹𝑄1(𝑌)+𝐼𝐹𝑄2(𝑌)−𝐼𝐹𝑄1(𝑌)𝐼𝐹𝑄2(𝑌)), (𝐹𝑇𝑄1(𝑌)+𝐹𝑇𝑄2(𝑌)−𝐹𝑇𝑄1(𝑌)𝐹𝑇𝑄2(𝑌), 𝐹𝐼𝑄1(𝑌)+𝐹𝐼𝑄2(𝑌)−𝐹𝐼𝑄1(𝑌)𝐹𝐼𝑄2(𝑌), 𝐹𝐹𝑄1(𝑌)+𝐹𝐹𝑄2(𝑌)−𝐹𝐹𝑄1(𝑌)𝐹𝐹𝑄2(𝑌)) ) (2) 𝜇𝑄1= ( ( (1−(1−𝑇𝑇𝑄1(𝑌))𝜇), (1−(1−𝑇𝑇𝑄1(𝑌))𝜇), (1−(1−𝑇𝑇𝑄1(𝑌))𝜇) ) , ((𝐼𝑇𝑄1(𝑌))𝜇,(𝐼𝑇𝑄1(𝑌))𝜇,(𝐼𝑇𝑄1(𝑌))𝜇), ((𝐹𝑇𝑄1(𝑌))𝜇,(𝐹𝑇𝑄1(𝑌))𝜇,(𝐹𝑇𝑄1(𝑌))𝜇) ) (3) 𝑄1𝜇= ( ((𝑇𝑇𝑄(𝑌))𝜇,(𝑇𝑇𝑄1(𝑌))𝜇,(𝑇𝑇𝑄1(𝑌))𝜇), ( (1−(1−𝐼𝑇𝑄1(𝑌))𝜇), (1−(1−𝐼𝑇𝑄1(𝑌))𝜇), (1−(1−𝐼𝑇𝑄1(𝑌))𝜇) ) , ( (1−(1−𝐹𝑇𝑄1(𝑌))𝜇), (1−(1−𝐹𝑇𝑄1(𝑌))𝜇), (1−(1−𝐹𝑇𝑄1(𝑌))𝜇) ) ) (4) Second part, computing the criteria weights Create the decision matrix using the T2NS. These numbers are converted to crisp values. The decision matrices are combined into a single matrix. Neutrosophic Sets and Systems, Vol. 93, 2025 754 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Compute the criteria weights using the average method. Third part, ranking the alternatives using the COPRAS method Normalize the decision matrix 𝑍𝑖𝑗=𝐾𝑖𝑗 ∑𝐾𝑖𝑗 𝑚 𝑖=1 (5) Obtain the weighted decision matrix. 𝐻𝑖𝑗= 𝑍𝑖𝑗𝑊𝑗 (6) For beneficial and non-beneficial criteria, the max and min indices are computed. 𝐷+𝑖=∑𝐻𝑖𝑗 𝑔 𝑗=1 (7) 𝐷−𝑖=∑𝐻𝑖𝑗 𝑛−𝑔 𝑗=𝑔+1 (8) n-g: number of non-beneficial criteria. g: number of beneficial criteria. Obtain the relative value 𝑅𝑖= 𝐷+𝑖+∑𝐷−𝑖 𝑚 𝑖=1 𝐷−𝑖∑1 𝐷−𝑖 𝑚 𝑖=1 (9) Rank the alternatives. Figure 1. Steps of neutrosophic COPRAS. Neutrosophic Sets and Systems, Vol. 93, 2025 755 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Figure 2. Criteria of education. 4. Results & Discussion This section presents the results obtained from the proposed neutrosophic decision-making approach. The educational evaluation process begins with identifying the main assessment dimensions, which are summarized in Figure 2. These criteria represent the essential factors influencing the effectiveness of pedagogical strategies in accounting education—covering areas such as instructional clarity, student engagement, critical thinking, collaboration, and practical skill development. To determine the importance of each criterion, the average method was applied to calculate its respective weight. This procedure ensures that every criterion contributes proportionally to the final evaluation according to its perceived significance among the experts. The criteria weights, illustrated in Figure 3, reflect a balanced distribution between theoretical understanding and practical application, emphasizing both academic comprehension and problem-solving ability. Next, the COPRAS method was employed to establish the ranking of the alternative pedagogical strategies. A panel of ten experts and decision-makers participated in constructing the decision matrices, as presented in Tables A1–A10. Each expert provided evaluations using T2NS, a framework that captures the degrees of truth, indeterminacy, and falsity with inherent uncertainty, ideal for handling subjective human judgments. The neutrosophic numbers provided by the experts were then converted into crisp values, allowing the data to be processed numerically while preserving the richness of the original uncertainty information. All individual decision matrices were aggregated into a single comprehensive matrix, representing the collective expert judgment. This consolidated dataset Neutrosophic Sets and Systems, Vol. 93, 2025 756 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education served as the foundation for the COPRAS computation, from which the weighted evaluations and subsequent rankings of teaching strategies were derived. The outcome clearly demonstrates how the integrated neutrosophic–COPRAS approach provides a structured, transparent, and reliable framework for comparing educational methods within the field of accounting education. Figure 3. Criteria weights. The analysis begins by normalizing the decision matrix using Equation (5), as demonstrated in Table 1, to ensure that all criteria are expressed on a comparable scale. After normalization, the weighted decision matrix is obtained through Equation (6), as shown in Table 2, by applying the computed criteria weights to each normalized value. Next, the maximum and minimum indices for both beneficial and non-beneficial criteria are calculated according to Equations (7) and (8) to capture the relative contribution of each alternative. The relative value of every alternative is then derived using Equation (9), illustrated in Figure 4, which integrates all weighted evaluations into a single performance measure. Finally, the alternatives are ranked based on their relative values, as presented in Figure 5, revealing the most effective pedagogical strategies within the neutrosophic COPRAS framework. Table 1. Normalized decision matrix. CRIC1 CRIC2 CRIC3 CRIC4 CRIC5 CRIC6 CRIC7 CRIC8 CRIC9 CRIC10 CRID1 0.05444 0.05993 0.103755 0.1006 0.059608 0.094364 0.027174 0.036078 0.047756 0.077199 CRID2 0.069931 0.065665 0.037035 0.086615 0.105497 0.094364 0.035278 0.06143 0.078577 0.041255 CRID3 0.069833 0.069844 0.04648 0.071593 0.032311 0.053318 0.066362 0.064112 0.052415 0.072817 CRID4 0.076724 0.064287 0.071419 0.059864 0.052843 0.055052 0.06803 0.082102 0.06348 0.085299 CRID5 0.071397 0.074023 0.066673 0.069247 0.06836 0.075237 0.079662 0.08103 0.07562 0.066133 CRID6 0.086791 0.074023 0.084958 0.073217 0.06907 0.066605 0.076707 0.077276 0.073291 0.059626 CRID7 0.077897 0.07798 0.079514 0.0766 0.077302 0.058776 0.068936 0.072644 0.066258 0.071312 0.085 0.09 0.095 0.1 0.105 0.11 CRIC1 CRIC2 CRIC3 CRIC4 CRIC5 CRIC6 CRIC7 CRIC8 CRIC9 CRIC10 Neutrosophic Sets and Systems, Vol. 93, 2025 757 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education CRID8 0.075062 0.067488 0.072675 0.071728 0.076923 0.072317 0.071701 0.073912 0.056805 0.066664 CRID9 0.077946 0.074423 0.067696 0.072946 0.074558 0.069736 0.082523 0.071133 0.057835 0.063034 CRID10 0.08767 0.052283 0.074862 0.072901 0.081985 0.060427 0.07542 0.077958 0.055999 0.057678 CRID11 0.044568 0.064064 0.050295 0.06645 0.074227 0.064997 0.066981 0.078299 0.057074 0.061485 CRID12 0.037971 0.061886 0.046806 0.053774 0.050904 0.054291 0.068268 0.080786 0.052639 0.077509 CRID13 0.050726 0.072734 0.052854 0.054766 0.045369 0.047182 0.063358 0.061089 0.088075 0.076137 CRID14 0.056492 0.065354 0.065882 0.040105 0.070489 0.080019 0.069794 0.041002 0.085163 0.058386 CRID15 0.062552 0.056017 0.079096 0.029594 0.060554 0.053318 0.079805 0.041149 0.089015 0.065469 Table 2. Weighted decision matrix. CRIC1 CRIC2 CRIC3 CRIC4 CRIC5 CRIC6 CRIC7 CRIC8 CRIC9 CRIC10 CRID1 0.005115 0.00619 0.010239 0.010239 0.005785 0.010239 0.002617 0.003398 0.004895 0.008008 CRID2 0.006571 0.006782 0.003655 0.008816 0.010239 0.010239 0.003398 0.005785 0.008054 0.004279 CRID3 0.006561 0.007214 0.004587 0.007287 0.003136 0.005785 0.006392 0.006038 0.005372 0.007553 CRID4 0.007209 0.00664 0.007048 0.006093 0.005129 0.005974 0.006552 0.007732 0.006506 0.008848 CRID5 0.006708 0.007645 0.00658 0.007048 0.006635 0.008164 0.007673 0.007631 0.007751 0.00686 CRID6 0.008155 0.007645 0.008384 0.007452 0.006704 0.007227 0.007388 0.007278 0.007512 0.006185 CRID7 0.007319 0.008054 0.007847 0.007797 0.007503 0.006378 0.00664 0.006842 0.006791 0.007397 CRID8 0.007053 0.00697 0.007172 0.007301 0.007466 0.007847 0.006906 0.006961 0.005822 0.006915 CRID9 0.007324 0.007686 0.006681 0.007425 0.007236 0.007567 0.007948 0.006699 0.005928 0.006539 CRID10 0.008237 0.0054 0.007388 0.00742 0.007957 0.006557 0.007264 0.007342 0.00574 0.005983 CRID11 0.004188 0.006617 0.004964 0.006764 0.007204 0.007053 0.006451 0.007374 0.00585 0.006378 CRID12 0.003568 0.006392 0.004619 0.005473 0.004941 0.005891 0.006575 0.007608 0.005395 0.00804 CRID13 0.004766 0.007512 0.005216 0.005574 0.004403 0.00512 0.006102 0.005753 0.009027 0.007898 CRID14 0.005308 0.00675 0.006502 0.004082 0.006842 0.008683 0.006722 0.003862 0.008729 0.006056 CRID15 0.005877 0.005785 0.007806 0.003012 0.005877 0.005785 0.007686 0.003875 0.009124 0.006791 Figure 4. Relative values. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Neutrosophic Sets and Systems, Vol. 93, 2025 758 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education Figure 5. Ranks of alternatives. The ranked outcomes are consistent with the study’s educational context: student-centred and technology-enhanced pedagogies tend to achieve higher utilities across the criteria space, while purely lecture-based formats remain useful for foundational delivery but are comparatively weaker on engagement and applied performance. This aligns with the paper’s problem framing and with the documented shift toward active and blended learning in accounting education. 5.1. Limitations 1) The model relies on judgments from ten experts; although appropriate for neutrosophic MCDM, broader or more diverse expert panels could increase generalizability. 2) Education 3) Results depend on the specific T2NS type-reduction/crisping scheme used before aggregation; alternative but reasonable schemes may yield small shifts in utilities. 4) Education 5) The study evaluates ten criteria at a summary level (CRIC1–CRIC10); finer sub-criteria could reveal additional nuance across cognitive, affective, and practical dimensions. 6) Education 5. Conclusions The assessment of pedagogical strategies in accounting education underscores the critical role that teaching methods play in shaping student performance and professional readiness. The study demonstrates that while traditional approaches remain useful for foundational knowledge delivery, innovative and interactive pedagogies such as problem-based learning, case studies, and 0 2 4 6 8 10 12 14 16 Neutrosophic Sets and Systems, Vol. 93, 2025 765 ________________________________________________________________________________________________________ ____________________________________________________________________________________________ Emadaldeen Hassan Alomar, Neutrosophic-Based Assessment of the Impact of Pedagogical Strategies on Student Performance in Accounting Education CRIC1 CRIC2 CRIC3 CRIC4 CRIC5 CRIC6 CRIC7 CRIC8 CRIC9 CRIC10 CRID1 ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.70,0.75,0.80), (0.15,0.20,0.25), (0.10,0.15,0.20)) CRID2 ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.70,0.75,0.80), (0.15,0.20,0.25), (0.10,0.15,0.20)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) CRID3 ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) CRID4 ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) CRID5 ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) CRID6 ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) CRID7 ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) CRID8 ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) CRID9 ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) CRID10 ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) CRID11 ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) CRID12 ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) CRID13 ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) CRID14 ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.95,0.90,0.95), (0.10,0.10,0.05), (0.05,0.05,0.05)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) CRID15 ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.20,0.20,0.10), (0.65,0.80,0.85), (0.45,0.80,0.70)) ((0.40,0.45,0.50), (0.40,0.45,0.50), (0.35,0.40,0.45)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) ((0.70,0.75,0.80), (0.15,0.20,0.25), (0.10,0.15,0.20)) ((0.35,0.35,0.10), (0.50,0.75,0.80), (0.50,0.75,0.65)) ((0.60,0.45,0.50), (0.20,0.15,0.25), (0.10,0.25,0.15)) ((0.50,0.30,0.50), (0.50,0.35,0.45), (0.45,0.30,0.60)) Received: April 27, 2025. Accepted: Sep16, 2025