Applied Science and Innovative Research ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) Vol. 9, No. 3, 2025 www.scholink.org/ojs/index.php/asir 81 Original Paper Modeling the Future Olympic Games by Entropy Evaluation Zheng Cao, Yuhao Lu, Yusong Zhou & Yuzhang Hu Chengdu No.7 High School International Department High-tech Campus, Chengdu, China Received: September 22, 2025 Accepted: October 16, 2025 Online Published: October 23, 2025 doi:10.22158/asir.v9n3p81 URL: http://doi.org/10.22158/asir.v9n3p81 Abstract The goal of the IOC is to increase the number of sports, disciplines and events (SDEs), that resonate with modern values and appeal to a global audience (SDEs) to keep the Games relevant and influential. To evaluate which SDEs should be added to or removed from the 2032 Summer Olympics. We will create several mathematical models to evaluate SDEs against these criteria to provide sound recommendations. The model will be used for quantitative decisions to determine which SDEs are best suited to the evolving vision of the Olympic Games. In problem 1, there are five factors which are comprehensive global participation, gender ratio, environmental factors (carbon emissions, water use, ecological impact, energy use, waste use), cultural impact and attractiveness. Each factor is considered as a variable in these models. And the properties of these variables are supposed to be determined. Some are quantitative and some are qualitative. And some are constant, some are variable. In the five factors: comprehensive global participation is constant and quantitative. Gender ratio and environmental factors are variable and quantitative. Cultural impact and attractiveness are constant and qualitative. In problem 2, according to the factors, we build up a model or several models to evaluate the effects of these factors to the SDEs. And through the models, we get scores that can be used to help IOC to find whether the SDEs can meet the needs of the IOC or not and whether they can be added in the future Olympics Games or not. In problem 3, the models will be tested on at least three SDEs added or removed from the most recent Olympic Games (i.e., the 2020, 2024, and 2028 Games), as well as at least three SDEs that have appeared in consecutive Olympic programs since the 1988 Olympics or earlier. The data in HiMCM_Olympic_Data.xlsx provides information on the sports and disciplines that have appeared in each Olympic Games since the formation of the modern Olympic Games, as well as the number of events. The general applicability of the model is highlighted by selecting different sets of SDEs for evaluation. These models confirm the current Olympic status of these SDEs. The Fuzzy Comprehensive Evaluation Model can be used to calculate the entropy of each influencing factor of a sport, then calculate their www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 82 Published by SCHOLINK INC. respective weights, and finally calculate the total score of the sport and compare it with the standard score to see weather the sport can be added. In problem 4, identify three SDEs that could be added to as part of the 2032 Brisbane Games and list them first, second and third. In addition, there are other SDEs that should be determined whether they can be added to Olympics Games in 2036 and beyond. As result, there are two SDEs added to Olympics in 2036. In problem 5, by using the method model TOPSIS, the models are able to calculate the respective weights of each factor, and the models will be performed a sensitivity analysis to address the robustness of the model and determine that the weight of what aspects of the model is high, and discus that doesn’t the high weight of the aspect affect the model a lot. Then, through the discussion, it can response the strengths or weaknesses of our model. Especially, when the aspect is seen as a decision-making tool to the SDEs. In problem 6, writing a letter to conclude the results of all the models about SDEs and summarize the findings in a non-technical way. In addition, it should include our recommendations for which SDEs to add or remove and give an explanation why these models can support these conclusions. As a result, the models can well support these results. One of the contributions of this paper is the creation of a mathematical models to evaluate SDEs to determine whether they fit the requirements of IOC and be added to the future Olympics Games. Keywords SDEs, IOC's Standard, Fuzzy Comprehensive Evaluation Model, TOPSIS 1. Introduction The International Olympic Committee (IOC) is planning to hold the 2032 Summer Olympics in Brisbane, Australia. As the Olympic Games grow, the IOC aims to maintain the relevance and impact of the Games by adding sports, events or competitions (SDEs) that resonate with modern values and appeal to a global audience. Throughout the history of the Olympics, SDEs has been introduced, removed, and even reintroduced to reflect the times. In 2020, for example, karate, sport climbing, surfing and skateboarding make their Olympic debuts. However, karate is no longer an event at the 2024 Paris Olympics, and break dancing (also known as break dance) has been introduced. Looking ahead to the 2028 Games in Los Angeles, flag football, lacrosse and coastal rowing will be added, while baseball and softball will return to the 2028 Games after a 20-year absence. To guide these decisions, the IOC's Olympic Project Commission has developed a set of criteria to help ensure that each sport is in line with Olympic values. 1.1 Question Restatement ⚫ Question 1 Find several appropriate factors that probably affect evaluating the SDEs, and describe whether they are quantitative or qualitative, constant or variable, deterministic or probabilistic. ⚫ Question 2 Build a model to determine how the factors affect evaluating the SDEs, and find which of them can fit www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 83 Published by SCHOLINK INC. the requirements of IOC. ⚫ Question 3 Bring some of the SDEs into our model to rest our model, and then bring other SDEs into our model to evaluate whether they can be added to the future Olympics Games. In addition, explain how our model affirms these SDEs’ current Olympic status ⚫ Question 4 Predict which of the SDEs can be added or introduced in the Olympics Games in 2032 and 2036. ⚫ Question 5 Build up a new model to perform sensitivity analysis to address the robustness of your model, and determine which of the factor has the most effect, explain why. ⚫ Question 6 Write a letter addressed to the IOC summarizing your findings in a non-technical way, including the results of our model, our suggestions and why our model can support the conclusions. 1.2 Our Work The problem requires us to study the evaluation factors and evaluate SDEs against these criteria to provide sound recommendations. These will be used for quantitative decisions to determine which SDEs are best suited to the evolving vision of the Olympic Games. ⚫ Question 1 By referring to several previous Olympics Games, we conclude five main factors that will impact the SDEs to meet the requirements of IOC. ⚫ Question 2 We make two models, but we eventually decide to use the second model which is gray prediction model. And we can bring data of SDEs into the model in order to help IOC to evaluate which SDEs can meet their requirements. ⚫ Question 3 We choose three SDEs (swimming, cycling, athletic) which are continuously exist in the Olympics Games from 1988 to 2024 to figure out the standard point line, which is used to determine which SEDs can be added or removed. Also, we choose another three SDEs (baseball, karate, BMX freestyle) which are currently reintroduced in the Olympics Games, and with the previous three SDEs, then we bring their data into the model to test the model. In the end, we evaluate its general adaptation through the results. ⚫ Question 4 Through the gray prediction model calculation, we get three SDEs (surfing, skateboard, e-sport) that can be reintroduced or added in the Olympics Games in 2032, and we rank them, which can be considered first (e-sport), second (skateboard) and third (surfing). In addition, we build a new gray prediction model to predict other SDEs that can be reintroduced or added in the Olympics Games in 2036. And the result is that we find that climbing and break dance can be added in the Olympics Games in 2036. This is because their predicted values are always increasing. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 84 Published by SCHOLINK INC. ⚫ Question 5 In this question we use the method of distance of good-gad solution (TOPSIS)[3][4]. This method can figure out the different weights of each factor in our model. The factor that has the biggest weight means that the factor takes more points than others. Given this factor, we can conclude the benefits and disadvantages of the model. ⚫ Question 6 Given the conclusions in the previous five questions, we evaluate the general result, and give some suggestions. In the end, based on the features and the principles of our models, we should explain why they are able to support the result. 2. Assumptions and Justifications To simplify the problem, we make the following basic assumptions, each of which is properly justified. ⚫ Assumption 1: the SDEs are only affected by the five factors that we give, other factors don’t make any difference. ⚫ Justification: we only consider the five factors in our models. ⚫ Assumption 2: in the gray prediction model, the total scores of the SDEs coefficient is 100. ⚫ Justification: the sum of the weight of each factor is 1. ⚫ Assumption 3: the Olympics Games will always operate successfully. They will never be canceled or postponed by emergency, such as extreme weather or epidemic situation etc. ⚫ Justification: Tokyo Olympics Games in 2022 was remitted to 2023. 3. The Development of Models 3.1 Notations Table 1. Notations Symbols Description Unit TS Total score None GPS Global participation score None GS Gender score None ES Environmental score None CS Cultural score None AS Attractiveness score 100 million US dollars NOC Number of countries None NOP Number of players None NOE Number of events None NOIFM Number of international federation members None Wx Data of x part None www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 85 Published by SCHOLINK INC. PG Proportion gap None M The amount of male exercise None F The amount of female exercise None PMR The number of positive information reports published by the media None PAC The number of positive audience comments None V The value of that economic growth of the Olympic Games minus the input cost of Olympic Games None np Number of players None SPL Standard point line None 3.2 Model Overview To evaluate which SDEs should be added (or possibly removed) to the 2032 Summer Olympics. We will create a mathematical model to evaluate SDEs against these criteria to provide sound recommendations. The model will be used for quantitative decisions to determine which SDEs are best suited to the evolving vision of the Olympic Games and to consider which SDEs should be chosen by their total scores. In summary, the whole modeling process is shown in Figure 1. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 86 Published by SCHOLINK INC. Figure 1. Model Overview Step 1: We evaluated the influencing factors of the evaluation score from five aspects, namely the number of athletes participating in the competition, the ratio of male and female athletes, the impact on the environment (water use, carbon emissions, ecological impact, energy utilization), cultural impact, and attractiveness. Step 2: For each aspect, we considered one or two aspects for evaluation. Regarding the number of athletes participating in the competition, we searched for how many countries participated in the six events and how many athletes participated in total; For the ratio of male and female athletes, we searched for the proportion of male and female athletes participating in each event, and then calculated their ratio. For the environmental impact factors, we evaluated them from four aspects, namely water use, carbon emissions, ecological impact, and energy utilization. For these four aspects, we scored them based on their degree of environmental damage. If the impact is relatively low, the evaluation score can be given 4 points. If the impact is significant, the evaluation score can only be 1 point. For the last two aspects of cultural influence and attractiveness, their influence is diverse. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 87 Published by SCHOLINK INC. Step 3: For each project with different data, we will calculate an evaluation score based on the above standards, and then use this evaluation score to see how inclusive the project is internationally. Step 4: Finally, we will add up all sides of the evaluation sport’s score to obtain a total score, and then compare it with a standard point score to determine whether the sport could be chosen. 4. Problem 1: Factors for Addressing the IOC Criteria 4.1 Overview We consider the scoring factors to be comprehensive global participation, gender ratio, environmental factors (carbon emissions, water use, ecological impact, energy use, waste use), cultural impact, attractiveness. Global participation directly reflects the global popularity of a movement. When a sport is widely played in multiple regions and countries around the world (especially 75 countries on four continents), it can increase the global appeal of the Olympic Games. Increasing global participation means that more viewers can watch the game on TV or online without incurring too much additional cost and logistical burden. Wider global participation also indicates that the popularity of the campaign has been achieved without adding unnecessary logistical requirements. The sustainability and environmental impact of sports can affect the overall accessibility of the Games. If a sport has a low environmental impact (e.g. low carbon emissions, low resource consumption, etc.), it can reduce the cost and logistical requirements of event operations. Therefore, environmental factors are directly related to not adding too much logistics costs. The implementation of gender equality has increased the popularity of sports. In gender-equal sports, both male and female athletes have the same opportunity to participate, which broadens the audience of the sport and increases overall audience interest and participation, thus contributing to the appeal of the Olympic Games. Trends in modern society have fueled the popularity of new sports (such as e-sports, break dance, etc.) that appeal to a younger audience. The participation of young people not only makes the audience of the event more diverse, but also makes the event more innovative and attractive. Cultural influence is crucial in this process, as it can reflect a society's interest and enthusiasm for an emerging movement. The global comprehensive participation is a constant quantity, and the ratio of men to women is a quantitative variable and is variable. Environmental factors are variable and will vary from year to year with the Olympics. Cultural influences are also quantitative variables. Attractiveness is a qualitative variable, which is large or small influence, but we use the formula to quantify the influence, with a full score of 20, greater than 10 is large, and less than 10 is small. 4.2 Factor Analysis To ensure that each sport is in line with the Olympic values, the mind map below shows a summary of the IOC standards for the entire sport and what factors to consider when dealing with the IOC standards. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 88 Published by SCHOLINK INC. Figure 2. Factors for Addressing the IOC Criteria 1. Popularity and Accessibility One of its factors is global engagement - a measure of the movement's global reach, specifically the participation of different regions and countries. The quantification is the number of participating countries/regions and the number of active athletes. The units are the number of countries and the number of athletes. Reliability is relatively certain, as it is usually measured by data from international sports organizations. Another factor is television audience and media coverage - the number of television viewers for the sport and whether there is enough international media attention. Quantitative: Global TV audience, social media following, number of sponsors. The unit is the number of viewers, social media interactions. This is a probabilistic factor, and reliability can be affected by a variety of external factors (such as game time, media market, etc.). 2. Gender Equality The factor is whether there is a gender bias in the participation ratio of male and female athletes in the event. The quantification is the ratio of male to female competing athletes. The unit is percentage (%). With certainty, the data is relatively easy to obtain and is fixed, another factor is the equality of opportunity set by the event - whether it provides equal opportunities for male and female athletes to compete. Qualitative: Whether the event has equal events and MEDALS for men and women. Reliable and deterministic because it depends on the structural design of the event. 3. Sustainability The factor is the environmental impact - the impact on the environment during the organization of the www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 89 Published by SCHOLINK INC. event, such as carbon footprint, resource consumption, etc. Quantification is carbon emissions, energy consumption, waste generation. Units are tons of carbon dioxide, kilowatt-hours (kWh), and tons of waste. It is probabilistic and needs to be estimated according to the scale and infrastructure of the event, with certain uncertainty. Resource consumption and recycling - the efficiency of the use of resources and the recycling and reuse of waste during the event. Quantified is water and energy consumption, waste recovery rate. Units are liters (L), kilowatt-hours (kWh), recovery rate (%). With probability, the specific consumption depends on the actual operation of the event. 4. Inclusiveness Global participation and cultural diversity - whether the sport is able to reach across cultural and regional differences to attract athletes and spectators from different backgrounds. Quantitative is the number of participating countries, Cultural diversity index unit is the number of countries, cultural diversity index (e.g. Helfen formula). It is reliable and relatively certain, as it can usually be assessed through international data and survey reports. The social background of athletes and spectators - whether the economic and social background of athletes and spectators reflects social inclusion. Be identified as the athlete's financial source, whether there are athletes from low-income countries. It is probabilistic and may depend on the local social-economic situation. 5. Relevance and Innovation The factor is the appeal of young audiences - whether the sport can attract the interest of young people, especially Generation Z. Quantified is the proportion of young viewers and social media interaction data. The unit is audience age distribution and number of social media interactions. It is probabilistic and depends on cultural trends and social changes, and there may be some uncertainty. 5. Problem 2: Entropy Evaluation Model for Scoring SDEs In order to evaluate the best conformity to the Olympic criteria, we use five aspects: 𝑇𝑆 = 𝐺𝑃𝑆 + 𝐺𝑆 + 𝐸𝑆 + 𝐶𝑆 + 𝐴𝑆. (1) 1. The Global Participation Evaluation Score (GPS) 𝐺𝑃𝑆 = 𝑤1 × 𝑁𝑂𝐶 + 𝑤2 × 𝑁𝑂𝑃 + 𝑤3 × 𝑁𝑂𝐸 + 𝑤4 × 𝑁𝑂𝐼𝐹𝑀. (2) Because this TS is going to be a big number, to make it easier to calculate the total value of the final equation, let's divide the result of TS by 100. 2. Evaluation of men and women (GS) When analyzing this problem, we use the method of proportion gap: 𝐺𝑆 = 𝑀 𝑀+𝐹 − 𝐹 𝑀+𝐹 , (3) where M represents the amount of male exercise, F represents the amount of female exercise. Through this formula into the data for calculation, we can calculate its percentage. To make it easier to calculate the value of the final formula, we multiply the value of this ratio difference by 100. 3. Environmental Score (ES) The environmental score includes carbon emissions, energy consumption, water use, waste management www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 90 Published by SCHOLINK INC. and the final ecological impact. Each of these five aspects gets 10 points. The evaluation of carbon emissions is greater than 1 million tons CO2 gets 2 points, and 5* 100,000 to 300,000 gets 3-6 points. 300,000 to 100,000 accounts for 6-8 points, less than 100,000 will account for 8-10 points, for each different stage of his evaluation score will be different, and then the energy consumption, if his consumption is high, it will account for 2 points, if the consumption is moderate, it will account for 3-6 points, if he is more efficient use. If his consumption is very low, he can get a full score of 8-10 points, about water use, if there is too much waste, he can only score 2 points, if it is moderate, he can get 3-6 points, if it is effective management, it is 6-8 points, high use is 8-10 points, if there is waste management, Based on their recovery rate, we calculated that <30% corresponds to 2 points, 30-50 corresponds to 3-6 points, 50-80 corresponds to 6-8 points, and 80 corresponds to 8-10 points. The last aspect is that the ecological impact corresponds to 1-10 points from severe damage to minor damage, the more minor the impact, the higher the score, and vice versa, so an environmental impact score is a sum of these scores. Since there are five parts, and we assume they all have the same weight for environmental impact, we just divide the total by five. 4. Culture Score (CS) In this one, we will use the methodology for calculating the Cultural Diversity Index. Common cultural diversity indices are usually based on the following steps: Identify different cultural groups: First, define the cultural groups of the participants (or participating countries), often by country, language, or ethnic group. If more nuanced cultural classifications are taken into account in some analyses, multidimensional indicators such as language, religion, or tradition may be used. Calculating the distribution of cultural groups: The relative proportion of each cultural group is calculated. For example, consider how many different national, cultural, or linguistic backgrounds the participants come from, and what percentage of each group. The calculations are made using a mathematical model similar to Shannon Entropy: Shannon entropy is commonly used to measure the diversity and uncertainty of information, and in the Cultural Diversity Index, a higher entropy indicates greater cultural diversity. To facilitate the calculation of the final total value, we multiply its resulting value by 10. Shannon entropy can be expressed as: 𝐶𝑆 = −∑ 𝑝𝑖log(𝑝𝑖) 𝑛 𝑖=1 (4) where n is the number of cultural groups (e.g. the number of participating countries or languages), 𝑝𝑖 is the proportion of the 𝑖 cultural group (such as the proportion of entries from a certain language, ethnic group or country). Interpretation Entropy: The higher the entropy, the greater the diversity of cultures, and an entropy of 0 means that there is only one cultural group. The resulting entropy can be converted to a diversity index as needed for easy comparison. Here's an example: Suppose there are four countries participating in A sporting event (A, B, C, and D). If we know the www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 91 Published by SCHOLINK INC. number of participants from these countries is as follows: a) Country A: 50% of the athletes b) Country B: 30% of athletes c) Country C: 15% of athletes d) Country D: 5% of athletes We can calculate the cultural diversity index using the Shannon entropy formula: 𝐶𝑆 = −(0.5 log 0.5 + 0.3 log 0.3 + 0.15 log 0.15 + 0.05 log 0.05). (5) The entropy derived from this calculation gives a quantitative indicator of cultural diversity. If more countries and cultures participate, the entropy will be higher, indicating that the competition performs better in terms of cultural diversity. 5. Attractiveness Rating Score (AS) 𝐴𝑆 = 𝑤1 × 𝑃𝑀𝑅 + 𝑤2 × 𝑃𝐴𝐶 + 𝑤3 × 𝑉. (6) The weight of these three parts is 33.3%, 33.3%, 33.3%. To facilitate the calculation of the final total value, we divide its resulting value by 100. Nevertheless, the foregoing model we made is too ideal and impractical to account for which of the SDEs can be chose or removed. Thus, we use the gray prediction model with entropy evaluation method to find the weighting of each of the factors’ effects. 𝑇𝑆 = 𝑤1 × 𝐺𝑃𝑆 + 𝑤2 × 𝐺𝑆 + 𝑤3 × 𝐸𝑆 + 𝑤4 × 𝐶𝑆 + 𝑤5 × 𝐴𝑆. (7) We use the previous data we calculated to figure out the weighting. And because the sum of the weighting is 1. So, we assume that the total scores of the SDEs coefficient is 100. Then, we use one of the SDEs (swimming) of three Olympics Games (2024, 2020, 2016) to find the standard point line by multiplication of matrices. 𝑠𝑐𝑜𝑟𝑒 = [𝑤1 𝑤2 𝑤3 𝑤4 𝑤5] [ 𝐺𝑃𝑆2024 𝐺𝑃𝑆2020 𝐺𝑃𝑆2016 𝐺𝑆2024 𝐺𝑆2020 𝐺𝑆2016 𝐸𝑆2024 𝐸𝑆2020 𝐸𝑆2016 𝐶𝑆2024 𝐶𝑆2020 𝐶𝑆2016 𝐴𝑆2024 𝐴𝑆2020 𝐴𝑆2016 ] . (8) After calculating, we get three values 18.851, 18.853 and 17.965, we chose the minimum one and it’s divided by the sum of the three. Because: since even the smallest numbers are up to par, which means it already has representation. As the result, the rate is about 32.27%. Because the total score is 100, the standard point line is 32.27. 6. Problem 3: Test of Gray Prediction-based Model for Scoring SDEs To solve this problem, we first take three SDEs that have consistently appeared from 1988 to 2024, and then find that swimming, cycling, and athletics have always existed according to the data. For the most recent Olympic Games 2020 and 2024, the TS (Total Score) of these three sports in these two Olympic Games are shown in the table below: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 92 Published by SCHOLINK INC. Figure 3. TS of Swimming, Cycling, and Athletics in These Two Olympic Games Since the two sports with the lowest TS meet the requirements in 2020 and 2024, take the lowest TS sports in 2020, add the lowest TS sports in 2024, and divide their sum by two to find their average to get the standard point line score. Indicates that less than it is unqualified, and greater than it is qualified. The formula is as follows: 𝑆𝑃𝐿 = min(𝑠𝑐𝑜𝑟𝑒2020)+min(𝑠𝑐𝑜𝑟𝑒2024) 2 . (9) Since swimming in 2020 has the lowest score and cycling in 2024 has the lowest score, we plug the data into the above formula and get 84.16. In the following projects to be added in 2024 and 2028, we can calculate their TS as shown in the following table: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 93 Published by SCHOLINK INC. Figure 4. TS of Three New Sports We can see that only the baseball fits the bill, not the other two. To highlight the general applicability of the model, we must discuss the following three points: 1. Clarify the purpose and application scenarios of the model First, you need to clarify the purpose and application scenarios of the model. Different variables have different weights on the model. For example, in this model, the impact of combined participation and influence is relatively large in the evaluation of SDEs. Moreover, variable reference objects also have an impact on model evaluation. Just like different countries have different cultural influences or whether the unit of money is dollars or yuan. So, let's assume that the number of participants and economic growth are in reference to the country hosting the Games, and that economic growth is in dollar terms. Then, we must clearly understand what problems we hope to solve with the model - assessing which SDEs are acceptable for inclusion in the Olympics and which are not. And the context in which the model will be used. 2. Data quality assessment Integrity: Check that the data is complete with no missing values (the data is not clear in the number of media reports). Accuracy: Ensure that the data is accurate, with no errors or outliers (none). Consistency: Whether data is consistent across time or sources (consistency). Representation: Whether the data represents the actual scenario to which the model will be applied (yes). Therefore, in general, the overall difference has little impact and meets the applicability. 3. Suitability test The model is tested in real-world scenarios to verify its performance in real-world applications. By comparing the SDEs scores for cycling, swimming and athletics at the 2020 and 2024 Olympic Games, www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 94 Published by SCHOLINK INC. we calculated our SDEs standard scores. Then the standard score is compared with the coefficients obtained from the other three SDEs, and the actual test is carried out. In order to discuss how our model confirms the current Olympic status of these SDEs, we must revisit questions 1 and 2. In question 1, we confirmed that the total score is equal to the Global participation score plus the gender score plus the environmental score plus the cultural score and finally the attractiveness score. The calculation methods of the above five parts have been shown in question 2. Because the total data have basis and certain certainty and exclude certain probability, our model can confirm the current Olympic status of these SDEs in this way. For the gray prediction-based model, we evaluate it by the same SDEs of the first model. And the result is as same as the result of the first model that the scores of swimming, cycling and athletics are above the standard point line. Also, for baseball, BMX freestyle and karate, only baseball can meet the requirement. Its score is 34.67, which is higher than the standard point line 32.27. Because we use the gray prediction model with entropy evaluation method and calculating of the weighting of each factor, the results we calculate by the model are more accurate. Therefore, in fact that the gray prediction-based model is more adaptive than the simple model. 7. Problem 4: The Reintroduction of SDEs for 2032 and 2036 In discussions about the addition or reintroduction of the 2032 Brisbane Games. We will ensure that the following SDEs will likely be introduced as shown in the table below: Figure 5. The TS (Total Score) of SDEs Coefficient in 2024 www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 95 Published by SCHOLINK INC. The higher scores mean higher ranking. Thus, as the diagram shows, e-sport has the highest scores, so it is the NO.1. And skateboard is NO.2, surfing is NO.3. These three SDEs can be added in the 2032 Olympics. Except the three top SDEs, we also evaluate another two SDEs, which are climbing and break. Next, we need to use a gray prediction model to predict which special sports are likely to be included in the Olympics in 2036 and beyond. This means that we need to predict the change in its SDEs value. The graphs of the predicted values of climbing and break dance are shown below: Figure 6. Predicted Value of Climb 8. Problem 5: Sensitivity Analysis and Resolution of Model Stability In this question we use the method of technique for order preference by similarity to an ideal solution (TOPSIS) to solve it. TOPSIS is used to evaluate and rank each sample. There are five steps to analyze the question: 1. Prepare the data, and do the same trend processing and dimension problems. 2. To confirm the weight of each indicator, entropy weight method can be used, and custom weights can be defined (need to process by yourself, can use quantization -AHP). 3. Find the optimal and the worst matrix vectors (the system automatically handles them). 4. The distance between the evaluation object and the positive ideal solution D+ or the negative ideal solution D- is calculated respectively. 5. Combined with the distance value, the C value of the comprehensive degree score is calculated, and the ranking is carried out to draw a conclusion. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 96 Published by SCHOLINK INC. The table below shows the results: Table 2. Weight Calculation Result of Entropy Weight Method factor Information entropy Information effectiveness Weight (%) Global comprehensive participation 0.613 0.387 19.472 environmental influence 0.579 0.421 21.141 male-female ratio 0.613 0.387 19.472 cultural influence 0.613 0.387 19.472 attraction 0.593 0.407 20.444 The chart description: The above table shows the weight calculation results of entropy weight method, and analyzes the weight of each index according to the results. Intelligent analysis: The weight calculation results of entropy weight method show that: the weight of global comprehensive participation is 19.472%, the weight of environmental impact is 21.141%, the weight of gender ratio is 19.472%, the weight of cultural impact is 19.472%, and the weight of attraction is 20.444%, among which the maximum index weight is environmental impact (21.141%). The minimum value is global comprehensive participation (19.472%). Obviously, environment influence has the biggest weight, which means it take up more points than other factors. And this feature of our model will cause both benefits and negative effects. On the one hand, the advantage of the model is that the SDEs that we choose are relative more environmentally friendly. On the other hand, the disadvantages are that people probably ignore the essence and the purpose of the sports and it may limit people to choose viable kinds of sports. Oppositely, people put more attention on the environmental conservation. Figure 7. The Weight of the Five Factors in the Pie Chart www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 97 Published by SCHOLINK INC. 9. Problem 6: Non-technical Summary for the Solution to Evaluate SDEs The model we made is mainly used to figure out which SDEs confirm to the requirements that the IOC gives and whether they can be reintroduced and added or removed from the future Olympics Games. At the beginning of our work, we made two models, the first is simple that we calculate different scores of factors and add them up. The second model uses the gray prediction model with entropy evaluation method to find the weighting of each of the factors. But eventually, we decide to use the second one. Because the first model is too ideal and impractical to accurately calculate the values of SDEs coefficient. Firstly, we need find the factors. We find five factors that are global comprehensive participation, male- and-female-rate, environmental factors, cultural factors and appeal of the SDEs. The reason why we choose them is because that they are easy to evaluate and they are the main factors that will impact we evaluate which SDEs can be reintroduced or removed. And for the five variables, each of them has different arithmetic, like weighting operation and calculating their average values. In the end, we figure out the values of the single parts and add them up. Secondly, we use the gray prediction model with entropy evaluation method to find the weighting of each of the factors. Thirdly, we use the previous data of swimming, cycling and athletics from the Olympics Games in 2016 and 2024 to figure out the weighting. And because the sum of the weight is 1. So, we assume that the total scores of the SDEs coefficient is 100. Then, we use one of the SDEs swimming of three Olympics Games in 2024, 2020 and 2016 to find the standard point line by multiplication of matrices. After calculating, we get three values 18.851, 18.853 and 17.965. We choose the minimum one and it’s divided by the sum of the three. Because: since even the smallest numbers are up to par, which means it just reaches the minimum standard. As the result, the rate is about 32.27%. Because the total score is 100, the standard point line is 32.27. Last step, we find the SDE coefficient of karate, baseball and BMX freestyle. As a result, only baseball can be reintroduced in the future Olympics. Because its score is higher than the standard point line is 32.27. In addition, we have some suggestion: except the six SDEs above, we also calculate the value of other five SDEs: climbing, surfing, skateboarding, e-sports and break dancing. And we suggest that they can be reintroduced in the future Olympics as well. Because their SDE coefficients of them are bigger than the standard point line 32.27, which means based on the five factors, they confirm to the IOC’s requirements. Finally, we explain why our model support the conclusion. Our model utilizes entropy weight method and gray prediction, they can deal with uncertainty and multi-objective decision-making problems, and provide scientific and objective basis for decision makers. And by the method, we are able to find the weight of the five main factors (global comprehensive participation, male-and-female-rate, environmental factors, cultural factors and appeal of the SDEs). So, the model can find a data series of regularity, and by using the determined weights and the standardized data, the model can evaluate the www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 98 Published by SCHOLINK INC. comprehensive index of the objects. This value can be used to support decisions or research conclusions. Therefore, our model can support the conclusions. 10. Strength and Weakness 10.1 Strength For gray prediction model: 1. Low data requirements: the gray prediction method is especially suitable for the data prediction of small samples and poor information, and it has no special requirements for data distribution, and can handle various types of data. This is very important in practical applications, because the data in many fields are often difficult to meet the large sample conditions required by traditional forecasting methods. 2. High prediction accuracy: the gray prediction method can reduce the interference of random factors and improve the regularity of data by summing up the original data (1-AGO). This method makes the prediction result have high precision, especially suitable for short-term forecast. 3. Simple calculation: the calculation process of gray prediction method is relatively simple and easy to understand and master. It does not require complex mathematical models and a lot of computational resources, and is easy to be applied in practical problems. For entropy evaluation method: 1. Sensitivity: the entropy method is sensitive to small changes in the data. When the data of an indicator changes significantly, its weight will be adjusted accordingly, so as to more accurately reflect the impact of data changes on the evaluation results. 2. Objectivity: the entropy method determines the weight of the index completely based on the discrete degree of the data itself, avoiding the subjectivity and arbitrariness of artificial weights. This makes the evaluation results more objectively and fairly, and can better reflect the characteristics of the data itself. 3. Wide applicability: the entropy method can be applied to various data types and different evaluation fields, such as economy, society, environment, etc. As long as the data are measurable and comparable, the entropy method can be used for comprehensive evaluation[1][2]. For TOPSIS: 1. The TOPSIS method[3]4] does not require complex calculations and models, but only requires standardized data processing and simple mathematical operations to obtain results. The calculation process is relatively simple, and the results can be displayed through visual charts and other ways, so that decision makers can understand the decision results more intuitively. 2. Low data requirements: TOPSIS method has no strict restrictions on data distribution, sample size, and the number of indicators, which is suitable for both small sample data and large systems with multiple evaluation units and indicators. At the same time, the method does not need any hypothesis or statistical analysis of the data, only the weight of each attribute and the data of each decision scheme can be analyzed. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 99 Published by SCHOLINK INC. 3. Wide applicability: TOPSIS method is applicable to various data types and various decision- making problems, including evaluation, ranking, selection, etc. It can be applied to various decision- making fields, such as market research, product evaluation and enterprise management, and has a wide range of application prospects. 4. Strong comprehensiveness: TOPSIS method synthesizes a number of evaluation indicators and considers the weights and relationships among indicators, which can evaluate the decision-making scheme more comprehensively. By detecting the distance between the evaluation object and the best solution and the worst solution, the influence of multiple factors can be comprehensively considered to get the final decision result. 10.2 Weakness For gray prediction model: 1. Rely on small amounts of data: the gray prediction method is mainly based on a small amount of historical data, which may lead to a relatively low accuracy of the forecast results. Especially in the face of complex and changeable situations, due to the limitation of the amount of data, it may not be able to fully reveal the internal laws and changing trends of the system, thus affecting the accuracy and reliability of the prediction. 2. Sensitive to outliers: if there are outliers or abrupt points in the data, the prediction results of the gray prediction method may be greatly affected. Outliers may be caused by data measurement errors, data recording errors or system mutations, which will interfere with the establishment and prediction process of the gray prediction model, resulting in the predicted results deviating from the actual values. 3. Lack of mechanism: gray prediction method is mainly based on the law of the data surface, and lacks the in-depth analysis and explanation of the internal mechanism of things. This can make the prediction results difficult to interpret and verify, and also limits the application of gray prediction methods in some fields that require a deep understanding of the system mechanism. 4. Prediction accuracy is limited: the prediction accuracy of gray prediction model may not be high when dealing with complex and highly nonlinear data. In addition, since the gray prediction method mainly relies on cumulative generated sequences and differential equations to describe the dynamic behavior of the system, it may lead to filtering out some important information or details in the prediction process, thus affecting the accuracy of the prediction results. For entropy evaluation method: 1. Does not reflect the correlation between indicators: the entropy method mainly focuses on the degree of dispersion of a single index, but can’t directly reflect the correlation between indicators. In practical application, there is often a certain correlation between indicators, which may affect the result of comprehensive evaluation. Therefore, when using the entropy method, it may be necessary to combine other methods (such as principal component analysis) to eliminate redundant information between indicators. 2. Sensitive to extreme values: the entropy method is more sensitive to extreme values. If there is an www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 100 Published by SCHOLINK INC. extreme value in the data of an indicator, it may cause the entropy of the indicator to be small, thus giving a greater weight. This can skew the results of the comprehensive evaluation from reality, as the extreme values may not represent the true distribution of the overall data. 3. Unable to consider the practical significance of indicators: the entropy method is a weighting method based entirely on the characteristics of the data, which can’t consider the actual significance of the index. In practical applications, some indicators may have more practical significance, but because the data distribution is more uniform, the entropy method may give a lower weight. This may cause the results of comprehensive evaluation to be inconsistent with the actual demand. For TOPSIS: 1. Strong dependence on attribute weights: when TOPSIS method is used, each attribute needs to be weighted, and different weighting schemes will affect the final decision result. However, the determination of attribute weights often depends on the decision maker's subjective judgment, so it is easy to appear uncertainty and inconsistency. This subjectivity may lead to the deviation of decision results and affect the accuracy and reliability of decision making. 2. Strong sensitivity to data: in TOPSIS method, the quality of data has a great impact on the decision result. If there are outliers or missing values in the data, it will have a significant impact on the decision outcome. Therefore, before the TOPSIS method is used, the data needs to be carefully processed and cleaned to ensure the accuracy and integrity of the data. In some cases, accurate results cannot be obtained: when the index values of two evaluation objects are symmetrical about the line between the best and the worst scheme, TOPSIS method cannot obtain accurate results. In addition, TOPSIS method can only sort the advantages and disadvantages of each evaluation object, but can’t carry out file management, which limits the flexibility of its application to a certain extent. 11. Conclusion As the Olympics evolving, the purpose of IOC is to keep the Games both relevant and influential by adding SDEs. In order to help ensure that sport aligns with Olympic values, we conclude five main factors that will affect our evaluation, and make several models to figure out the coefficient that are used to evaluate the SDEs. The first model is gray prediction model with entropy evaluation method. We use it to find the weight of the five factors. And then, we bring some data of previous SDEs into the model to find the standard point line. Lastly, we bring the data of the test SDEs into the model. If the results are bigger than the standard point line, these SDEs can be added. If they are less than the standard point line, they will be removed from the Olympics Games or not be added. In addition, we utilize the gray prediction model to predict which SDEs are able to be added in the further future Olympics Games, and TOPSIS to perform sensitivity analysis and address the problem of model stability. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 101 Published by SCHOLINK INC. References Chu, T. C. (2002). Selecting Plant Location via a Fuzzy TOPSIS Approach. International Journal of Advanced Manufacturing Technology, 20(11), 859-864. Dong M. (1993). The Improvement of the Method of TOPSIS in Synthetic Queme & Sensitivity Analysis. Systems Engineering-theory & Practice. Huang, C. M., Shen, W. H., & Xiao, X. C. (n.d.). Gray modeling and tendency studying of Track and Field achievements of Olympics based on grey prediction theory. Jer, Min, Jou, et al. (1999). The Gray prediction search algorithm for block motion estimation. IEEE Transactions on Circuits & Systems for Video Technology. Jin, J. L., Wei, Y. M., & Ding, J. (2004). Fuzzy comprehensive evaluation model based on improved analytic hierarchy process. Journal of Hydraulic Engineering, 2(2004), 144-147. Kelemenis, Alecos, & D. Askounis. (2010). A new TOPSIS-based multi-criteria approach to personnel selection. Expert Systems with Applications, 37(7), 4999-5008. Li-Li, Zhu, & W. Zhao-Chi. (2003). Fuzzy combined evaluation model for the fighting efficiency of radar netting. Systems Engineering and Electronics, (2003). Wei, Guiwu. (2008). The method of TOPSIS to multiple attribute decision making with interval numbers based on "rewarding good and punishing bad". Mathematics in Practice & Theory, 10(10). Appendices Appendix A: Tools and Software MATLAB R2018b ECharts Appendix B: The MATLAB Code B.1 The Code for Problem 2 factor_scores = [ 49, 251, 51, 200, 0; 0.5, 0, 0, 0, 0; 2, 2, 2, 2, 2; 8, 0, 0, 0, 0; 2000, 5000, 20, 0, 0 ]; weights = [0.25, 1, 0.2, 1, 0.33 ]; every_scores = SDE_scores * weights'; total_scores = sum(every_scores); disp('total score of SDEs£º'); www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 102 Published by SCHOLINK INC. disp(total_scores); data = [ 80, 70, 90, 85, 75; 92, 78, 80, 86, 90; 85, 95, 88, 78, 91; ]; normalized_data = data./ sum(data); num_samples = size(normalized_data, 1); num_indices = size(normalized_data, 2); entropy = zeros(1, num_indices); for j = 1:num_indices p = normalized_data(:, j); p(p == 0) = []; entropy(j) = -sum(p.* log(p)); end weight = (1 - entropy)./ sum(1 - entropy); disp('Entropy of each index:'); disp(entropy); disp('Weight of each indicator:'); disp(weight); B.2 The Code for Problem 3 and 4 function prediction = gray_predict(factor_value) n = length(factor_value); x0 = factor_value(:); x1 = cumsum(x0); B = [-0.5 * (x1(1:n-1) + x1(2:n)), ones(n-1, 1)]; Y = x0(2:n); coeff = B \ Y; a = coeff(1); b = coeff(2); prediction = x0(1); for k = 2:n prediction = prediction + (x0(1) - b/a) * exp(-a * (k - 1)); www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 103 Published by SCHOLINK INC. end end future_years = 5; factor_value = [23, 20, 8, 5, 43 24, 22, 5, 4, 47 22, 0, 7, 8, 46 30, 16, 8, 7, 47 30, 23, 6, 7, 47 ]; preds = zeros(future_years, 1); for i = 1:5 preds(i) = gray_predict(factor_value(:, i)); end disp('Predicted rating:'); disp(preds); Report on use of AI ChatGPT Query: Output: Query: Output: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 3, 2025 104 Published by SCHOLINK INC. Query: Output: < Core Concept: A gray system refers to a system in which some information is known while some is unknown. The gray prediction model is designed to handle time series data with limited samples, irregularity, and uncertainty. Its basic idea is to reveal the regularity of the data sequence and predict future trends by establishing a gray differential equation based on the original data. Working Principle: Data Preprocessing: The original data is first processed to generate a new sequence with stronger regularity, typically through cumulative generation or other methods. Cumulative generation involves summing the data points in the same sequence to generate a new data point, creating a cumulative generation sequence. Model Establishment: Based on the processed data, a gray model, such as GM(1,1), is established. GM(1,1) is a commonly used gray prediction model that employs a first-order linear differential equation. Parameter Estimation: The parameters of the model are estimated using methods such as the least squares method. These parameters are crucial for the accuracy of the predictions. Model Validation and Optimization: The model is validated by examining the residual sequence to assess its fitting effect. Adjustments are made to optimize the model as needed. Prediction: Using the established gray model, future data points are predicted and solved.>