2.1 Integration of DSS and BIM

The integration of DSS and BIM has amassed attention due to its potential to enhance recommendation systems, particularly in context of AEC industry. DSS provides analytical techniques to process complex data, while BIM offers detailed digital representation of construction projects. Combining these two paradigms enables refined decision making regarding design, cost estimation and project management.

For instance, ^{Fazeli et al. (2020)} proposed an integrated BIM-DSS framework for cost estimation, enabling real-time budgeting and financial recommendations. This semi-automated, BIM-based cost estimation offered a flexible and adaptive framework for assessing the financial impact of various design scenarios. The BIM-centric approach demonstrated superior performance compared to traditional methods, particularly in terms of efficiency and accuracy.

A critical aspect of a DSS's effectiveness in processing large datasets is its evaluation metric or scoring function ^{(Boukhayma et al., 2020)}. These metrics, which are quantifiable measures, play a pivotal role in assessing the efficiency, utility, and output quality of a system within a DSS framework ^{(Hossin & Sulaiman, 2015)}. By delivering objective, numerical insights, evaluation metrics provide a clear understanding of how well the system achieves its intended goals and requirements. Moreover, they form a crucial link between theoretical models and real-world applications ^{(M. Zhang, 2015; Hastie, 2012)}. These metrics facilitate a deeper quantitative analysis of the DSS's internal mechanisms, including its accuracy, computational efficiency, and user satisfaction (ENSIAS, Mohammed V, Morocco et al., 2020). Such comprehensive evaluations enable continuous improvement of DSS, ensuring it remains an indispensable tool for decision-making in increasingly complex environments.

Another application of this is in sustainability and energy efficiency in building design by ^{(Fenz et al., 2023)} and ^{(Shen et al., 2023)}, where BIM models are linked with DSS to optimize energy performance. The system simulates various design options, such as HVAC systems or material choices, and provides a decision matrix to help engineers choose the most energy efficient solution. Common tools for this include Green Building Studio and EnergyPlus, with decision evaluation indicators such as energy consumption (kWh/m²/year), CO2 emissions, and LEED certification levels guiding the decision process.

BIM models that incorporate time (4D) and cost (5D) allow project managers to evaluate the effects of schedule changes, cost fluctuations, and resource allocation is yet another case of BIM-DSS integration is in construction scheduling and cost estimation ^{(Kubba et al., 2012)}. DSS tools like Primavera and Synchro help project managers analyze project timelines, labor costs, and material expenses to develop alternative project scenarios. Decision indicators in this context often include total project cost, project completion time, labor hours, and budget variance. Furthermore, BIM-DSS integration proves useful in disaster management and emergency planning by simulating scenarios such as earthquakes or fires, which help design effective response strategies ^{(Alavi et al., 2022)}. Systems like ALOHA and Simudyne use BIM data to provide realtime feedback on evacuation routes and structural integrity, with indicators such as time to evacuate, structural safety index, and risk mitigation score.

In facility management and asset maintenance, BIM models linked with DSS are used to predict and plan the maintenance needs of building systems like HVAC or electrical networks. Tools like IBM Maximo and Archibus help managers make data driven decisions on equipment repairs, replacements, and upgrades by evaluating equipment lifespan, failure rates, and maintenance costs ^{(Dashti et al., 2021)}. Key indicators include equipment downtime, maintenance costs, and life cycle cost. Lastly, urban planning and infrastructure development are increasingly benefiting from BIM-DSS linkages. City planners use these systems to evaluate transportation systems, public facilities, and utilities, allowing for more informed long-term planning. Tools such as InfraWorks and ArcGIS help assess transportation flow, population growth, and environmental impacts, with decision indicators including traffic density, infrastructure cost, environmental impact score, and population growth rate.

The integration of BIM with DSS offers a powerful way to optimize decision making in AEC projects. By linking comprehensive digital models with sophisticated analytical tools, stakeholders can evaluate design alternatives, costs, risks, and sustainability metrics, leading to more informed and data informed decisions across various domains of construction industry.

2.2 Evaluation Metrics in DSS for BIM Assessment

In the context of BIM centered DSS, evaluation metrics are not only essential for processing and interpreting BIM data but also play a pivotal role in ensuring the system provides accurate and meaningful recommendations. The selection of appropriate metrics is critical, as it directly influences the ability of recommendation systems (RS) to effectively rank and compare BIM models based on user specifications, design constraints, and project requirements. A well chosen metric enables the system to capture the nuances of the data. Thereby, aiding in the precision of recommendations and aligning them more closely with user needs.

Although a variety of metrics have been investigated for such applications, Euclidean distance and Cosine similarity remain two of the most frequently employed due to their computational efficiency and effectiveness in handling low dimensional datasets. Euclidean distance calculates the direct, straight line distance between two points in multidimensional space, making it intuitive for spatial comparisons. In contrast, Cosine similarity measures the cosine of the angle between two vectors, which makes it particularly suitable for evaluating the orientation of data points, regardless of their magnitude. This makes Cosine similarity useful in applications where the relative positioning of data, rather than their absolute values, is important.

However, when these metrics are applied to high dimensional BIM datasets, they encounter notable limitations. Euclidean distance, for instance, suffers from what is commonly known as the "curse of dimensionality," where its ability to differentiate between data points diminishes as the number of dimensions increases. This phenomenon causes distances between points to converge, reducing the metric's effectiveness in distinguishing between BIM models with complex, high dimensional attributes. Similarly, Cosine similarity, while proficient at identifying directional relationships in low dimensional spaces, may fail to provide significant differentiation between vectors in high dimensional BIM data, where many points may appear to have similar orientations despite their distinct attributes. These challenges underscore the need for advanced or hybrid metrics to address the intricacies of high dimensional BIM models ^{(Yang & Alessandrini, 2019)}. To address this, advanced techniques such as dimensionality reduction methods Principal Component Analysis, t-SNE) or hybrid metrics combining multiple measures could be explored. These approaches can better capture the intricate relationships within the data

The concept of "garbage in, garbage out" (GIGO) is particularly pertinent when discussing evaluation metrics for data driven systems, including artificial intelligence and machine learning models ^{(Geiger et al., 2020; Canbek et al., 2022)}. Inadequate or improperly chosen evaluation metrics can degrade the quality and reliability of a system’s output, potentially leading to flawed decision making. Without appropriate metrics to regulate the system's performance, several critical issues may arise, such as misleading performance assessments or failure to detect input biases ^{(Kilkenny et al., 2018)}. To mitigate these risks, conducting a thorough sensitivity analysis of the evaluation metrics used in DSS is essential. This involves selecting metrics from a diverse set that captures different dimensions of model performance, depending on the specific problem and domain context. Generic metrics may fail to robustly capture the unique output requirements of complex systems like BIM and DSS, underscoring the need for developing domain specific metrics tailored to the particular nuances of these systems.

In a digital landscape where information is generated at an unprecedented volume and velocity, scoring functions play a crucial role in extracting meaningful insights, thereby facilitating informed, fact based decision making ^{(Asudeh et al., 2019; Stojkovic et al., 2017)}. These metrics are instrumental in enabling more accurate and effective decisions that lead to improved outcomes ^{(Ayman et al., 2022)}. Additionally, scoring functions promote the paradigm of continuous improvement by systematically evaluating the system's performance, allowing for ongoing enhancements and adaptability in dynamic environments.

The scope of this study focuses on a comprehensive examination of Minkowski like distance functions, specifically Euclidean and soft cosine distance metrics, which are fundamental evaluation measures widely used in fields such as machine learning, data analysis, and RS. These metrics play a critical role in real world applications like clustering and text document analysis, where they facilitate the measurement of similarity or dissimilarity between data points, contributing to more accurate and efficient model performance ^{(Korenius et al., 2007)}. Therefore, refining these metrics for domain specific applications will further enhance their effectiveness in complex data environments.

In the context of the modern AEC industry, such study holds undeniable significance. The integration of BIM and DSS is driving a paradigm shift within the construction sector ^{(Nursal et al., 2015a)}. The fusion of these two technologies offers substantial potential for optimizing workflows across the industry. However, to fully realize these benefits, the establishment of a suitable evaluation criterion is essential, ensuring that the system generates accurate recommendations based on user input. Furthermore, this need aligns with broader technological advancements in BIM, AI, and the construction industry, addressing critical concerns such as safety and sustainability ^{(Boukhayma et al., 2020)}. BIM based DSS has the potential to dramatically enhance project design and management, ultimately reducing costs and minimizing delays in the high stakes construction environment ^{(Geil, 2011)}. The integration supported by robust evaluation metrics, represents a transformative approach that can significantly elevate the efficiency and sustainability of the construction industry.

2.3 Practical Implications of Metric Selection

Similarity metrics are extensively utilized in recommendation systems, especially for items with multiple features. These metrics can be optimized and tailored to enhance the performance of DSS in various scenarios. By effectively applying Euclidean and Cosine similarity, the system can better manage complex, multidimensional data and deliver more precise and relevant recommendations.

From a practical standpoint, the selection of evaluation metrics within a DSS has significant implications for the outcomes and overall success of a project. Accurate ranking and selection of BIM models based on user preferences can lead to improved design decisions, directly influencing the quality and efficiency of AEC projects, which are inherently complex and resource-intensive. Consequently, investigating the impact of various evaluation metrics on the performance of BIM-centric DSS is crucial to optimizing decision-making processes in these demanding environments.

In a recommendation system used for suggesting BIM models, user satisfaction is heavily influenced by the accuracy of the system’s recommendations. Therefore, it is crucial to understand the specific conditions under which the aforementioned metrics perform well and identify instances where they may fall short. The literature review examines scenarios where these two metrics demonstrate clear advantages, while also highlighting their potential limitations and drawbacks. This enables professionals to make informed decisions about when and how to apply these measures effectively.

A thorough examination of Euclidean and Cosine similarity metrics across various applications, including BIM models, reveals a significant gap in the literature regarding the lack of comprehensive analysis on how these metrics can be used together within BIM based DSS. This omission is crucial, as it overlooks the potential interactions that may arise from combining the two metrics, especially in handling high dimensional data typical of BIM systems. A deeper understanding of the complementary strengths and potential enhancements offered by integrating these metrics could lead to more effective decision support and recommendation systems in BIM applications ^{(Omar, 2014)}. This makes the exploration of their combined use a highly valuable area for further research.

Focusing on their effectiveness in handling multifeatured user input, this study aims to clarify how Euclidean and Cosine similarity metrics can be optimized for maximum impact in BIM model DSS. Given that user satisfaction relies on recommendation accuracy, it is crucial to identify the conditions where these metrics perform well and where they fall short ^{(Inhan et al., 2024)}. A deeper understanding of these metrics will provide valuable insights into their strengths and limitations in complex data environments.

A DSS is a sophisticated information system engineered to assist in making data driven, decision making. DSS leverages advanced algorithms, data analytics, and modeling techniques to streamline decision making processes. By integrating and synthesizing data from multiple sources, DSS processes complex datasets to generate insights, offering clear and actionable information. These systems enhance decision making efficacy by providing an intuitive interface that translates raw data into comprehensive, accessible formats tailored to strategic planning and operational needs. By delivering critical, context specific knowledge they play a pivotal role in recommendations. This contributes to improved overall organizational reputation ^{(Yasnoff & Miller, 2014; W. Holsapple, 2008)}. Additionally, DSS employs evaluation metrics and scoring functions to systematically assess alternatives, allowing for more informed and quantitatively-backed decision outcomes.

2.4 Theoritical Review

Each evaluation metric offers distinct advantages and limitations depending on the specific context ^{(Linnet, 1988)}. Drawing from the extensive body of literature on cluster analysis, Euclidean similarity is frequently employed as a reliable method. The effectiveness of Euclidean distance, which underpins Euclidean similarity, is consistently highlighted for its robustness and accuracy in pattern recognition and data clustering applications ^{(Dhawan et al., 2015)}.

(1)

Due to arbitrary scaling caused by small errors in input vectors, Euclidean similarity can inaccurately reflect dissimilarity between vectors. This makes Euclidean distance impractical for use in high dimensional spaces or with large datasets without appropriate adjustments. When dealing with multidimensional vectors, it is crucial to normalize each vector component to mitigate the influence of one component over another, as Euclidean similarity is sensitive to differences in scale.

Cosine similarity is another widely used scoring metric, which ranks items by measuring the angle between their vectors ^{(J. Zhang et al., 2022)}. Unlike Euclidean distance, this metric is scale-invariant and insensitive to the magnitude of the vectors, making it particularly useful for comparing data regardless of size. Due to its focus on direction rather than magnitude, cosine similarity is considered an unbiased and effective method for analyzing multidimensional data.

(2)

The combined Cosine-Euclidean similarity distance measure is a hybrid metric that integrates both cosine similarity and Euclidean distance. This measure captures both angular relationships and magnitude differences between vectors. By balancing the direction sensitive nature of cosine similarity with the magnitude aware Euclidean distance, this metric provides a more comprehensive assessment of similarity. It is particularly useful in situations where both vector orientation and distance contribute to meaningful comparisons, enhancing accuracy in multidimensional or complex datasets. The combined Cosine-Euclidean similarity distance measure is given by

(3)

The equation combines both distance measures, effectively balancing their respective influences on the overall similarity score. This hybrid metric enables the consideration of both the position (from Euclidean distance) and direction (from cosine similarity) of data points within a unified distance framework. Consequently, the resulting similarity score is more refined and comprehensive than those derived from either individual metric alone ^{(Mohd & Abdullah, 2018)}. Alternatively, a parallel approach can be applied, where both similarity metrics are calculated independently, and N items are selected from each ranked list after the ranking process.

Despite advancements in BIM and DSS technologies, there remains a significant gap in comprehensive studies comparing different scoring methods used within DSS for BIM model assessment. Existing research tends to focus either on the implementation of BIM or the independent development of DSS, overlooking the critical influence that various scoring methodologies have on the evaluation processes ^{(Mattiussi et al., 2014, Liu et al., 2019)}. This gap underscores the need for a systematic study to evaluate and compare these scoring methods, assessing their effectiveness and suitability across diverse application scenarios. There is a notable gap in research regarding studies that utilize a combination of the previously discussed scoring metrics. The potential advantages of integrating Euclidean distance and cosine similarity for item ranking in DSS remain largely unexplored. Existing literature indicates that, when used independently, both metrics often provide inadequate recommendations within DSS frameworks. Despite the scaling sensitivity of Euclidean distance and the magnitude insensitivity of cosine similarity, the two are seldom combined. However, studies suggest that a hybrid scoring function could offer improved similarity scores and more accurate recommendations.

3.1 User Input Requirements

The input for DSS consists of 9 choices with multiple sub-options. The menu items include number of floors, minimum area, maximum area, balcony, toilets per floor, number of basements, parking type, façade type and roof type. The input range for each input is constrained. Firstly, the number of floors varies from two to ten, the area varies from 90㎡ to 300㎡. Secondly, the balcony option has only two choices, yes or no for the presence or lack of balcony and the toilets per floor ranges from 3 to 5 where as the number of basement ranges from none to 4. Thirdly, there are two available parking types, namely ground and basement and a total of 8 façade types with only two specific roof types, that is flat and sloped.

The data type for input to the DSS is as following, the building's available space can be anywhere from 90 square meters to 300 square meters and he option for a balcony is a straightforward "Yes" or "No," indicating whether one is present or not. Users can choose between 3 and 5 options for the number of restrooms per floor. There can be as few as one basement and as many as four. While there are two distinct roof types "flat" and "sloped", and a total of eight façade types to choose from when customizing the building design, parking options include "ground" and "basement." This combination of choices leads to a total of (21×2×3×5×8×2) 10,080 unique design choices.

The system is designed to recommend BIM models for office and residential building design based on the input parameters described above. The system links user defined preferences with the BIM model, enabling precise and context aware design recommendations. The system guide final recommendation by presenting the most suitable design options that align with user requirements.

Two scoring functions are used by the DSS to make design recommendations. First, it scores and ranks the options in the database using the weighted norm (weighted Euclidean distance), resulting in the top two design options. In order to arrange the database entries and present the chosen design option, the RS secondly uses cosine similarity. These two scoring methods were selected to make up for each other's shortcomings. When the user input vector is far from the target, the weighted Euclidean distance frequently performs well as compared to cosine similarity. Euclidean distance is given by:

(4)

Where xu is the user input vector, xi is the input vector of ith model file in the database, wi is the weight of a particular input feature and is the distance between input features. This can be seen in <Fig. 5> where the distance to all points is calculated for a given point.

(5)

Fig. 3. Euclidean similarity score in a feature cluster

For the weighted Euclidean distance, a score normalization procedure is established to ensure consistency between the scores produced by these two metrics. The scores from various metrics are made compatible with one another by using the following normalization procedure, which can be universally applied to other metrics if necessary.

The scoring criteria uses Eq. (3) to rank the database in order and yields the first three results to the DSS. An alternative method for the recommendation is to utilized both the scoring metrics independently. The pseudocode for such scoring is as

Similarly, the cosine similarity is given by the following equations.

Fig. 4. Scoring Logic

(6)

(7)

Both the similarity scores as used to generate two ranking for the database. The evaluation criteria return a total for three designs. The first two are returned from the Euclidean distance ranking whereas the last one is selected from the cosine similarity ranking. This is done so as to complement the flaws of the evaluation metrics, as the Euclidean scoring is good at differentiating between spaced clusters of data whereas cosine similarity gives better results for points inside the cluster. Overall, the result from Eq. (3) gives better results and is much simpler to implement.

Fig. 5. Cosine similarity score in a feature cluster

If a user's input vector is [6 floors, 200㎡, Balcony: Yes, 4 toilets per floor, 2 basements, Parking Type: Basement, Façade Type 5, Roof Type: Flat], the DSS might identify BIM Model A as an exact match with a distance of zero, BIM Model B as a close second with a minimal distance, and BIM Model C as a highly similar alternative based on cosine similarity.

Fig. 6(a). A DSS Utilizing the Scoring Metric

<Fig. 6(a)> depicts a user interface for an office space recommendation system. The interface allows users to specify various preferences related to office building design. The tool is intended to help users generate or select office designs based on their individual needs. In the central section of the interface, users can input specific requirements, such as the number of floors, the minimum and maximum area in square meters, whether the office should include a balcony, and the number of toilets per floor. Additionally, there is an option to specify the location of the core, referring to where essential building elements like stairs and elevators should be placed.

The final recommendations presented to the user include three BIM model alternatives: two from the Weighted Euclidean Distance ranking and one from the Cosine Similarity ranking. This ensures that the user receives a comprehensive set of options that cater to both precise and nuanced design requirements. For instance, Design Option 1 would perfectly align with the user's specifications, while Design Option 2 offers a slight variation in area without compromising other key parameters. Design Option 3 provides an alternative that maintains high contextual similarity, beneficial in scenarios where clustered design options offer additional benefits not captured by an exact match.

Fig. 6(b). An NLP based DSS Utilizing the Scoring Metric for Recommending BIM

<Fig. 6(b)> continues the theme of the office space recommendation system and features another DSS interface. This segment appears to be designed for clients to enter specific details or specifications regarding the office they wish to design. There's a prompt instructing users to "Enter specifications of office," indicating that this section is focused on textual input. Nevertheless the evaluation metrics are utilized in this system to achieve the same result as the DSS shown in <Fig. 6(c)>.

Fig. 6(c). Result of the DSS from hybrid scoring metric

4.1 Implications of Findings

The metrics for BIM centered DSS has demonstrated promising accuracy and effectiveness in aligning with user preferences and requirements. The system caters to the diverse needs and preferences of user. The effective use of both weighted Euclidean distance and cosine similarity algorithms ensures that the recommendations are not only varied but also closely tailored to the specific user input.

However, it is critical to recognize that the effectiveness of the DSS is heavily dependent on the scoring algorithm, database quality and diversity. To maintain accuracy with the chosen scoring algorithms, the database must be updated and expanded on a regular basis. Furthermore, the DSS may encounter limitations in situations where input features are less distinguishable, necessitating additional research to address these challenges. The findings demonstrate that this dual-scoring method is highly effective in generating design recommendations that closely align with user preferences, particularly in the context of BIM.