# Adaptive Cluster-Based Normalization for Robust TOPSIS in Multicriteria Decision-Making
## 4 Case Study  
This case study focuses on selecting the most suitable city to host an international event scheduled to take place in two years. The decision is complex, involving the evaluation of key factors such as costs, logistics, attendee experience, and overall event impact. To facilitate the process, a dataset of potential host cities was analyzed and grouped into clusters based on economic characteristics, infrastructure quality, safety, and accessibility. Table 1 presents an overview of the cities, each identified by a letter for clarity. These cities were thoroughly assessed, with descriptions highlighting their individual strengths and challenges. This structured approach provides valuable insights, supporting decision-makers in identifying the best location to ensure the event's success. In total, 12 cities were evaluated using four criteria: cost, infrastructure, safety, and accessibility. These alternatives were selected to reflect a realistic shortlisting scenario, where decision-makers typically narrow down options based on preliminary screening. While the dataset is moderate in size, it captures a diverse range of urban profiles and geographic contexts. The structure of the data--organized as fuzzy evaluations per criterion--allows for nuanced analysis and robust comparison across alternatives. The cities were evaluated based on the following four key criteria, each playing a crucial role in determining their suitability to host the international event:  
1. Cost (C1): The estimated total expense of hosting the event, measured in millions of dollars. This criterion reflects the financial feasibility of each city and its potential impact on the event's budget. Figure 1: Overview of the proposed decision-making workflow, combining fuzzy evaluation, cluster assignment, and logarithmic normalization within the TOPSIS framework. The dashed outline boxes represent the contributions of the proposed methodology. Infrrastructure (C2): A score from 1 to 10 that represents the quality of venues, transportation systems, accommodations, and other facilities required to host a large-scale international event. * Safety (C3): An index (1 to 10) measuring overall safety in the city, including crime rates, political stability, and emergency preparedness. A higher score indicates a safer environment for attendees. * Accessibility (C4): A score from 1 to 10 reflecting the city's connectivity and ease of access, including international/domestic flight availability, public transit, and road infrastructure. To streamline the decision-making process, the cities under consideration were grouped into three clusters based on shared characteristics, including cost, infrastructure, safety, and accessibility. Each cluster represents a distinct category of cities, enabling decision-makers to narrow their focus and evaluate alternatives more effectively as follows:  
1. Cluster 1: Cost-Effective Cities with Moderate Infrastructure. This cluster consists of budget-friendly cities, making them attractive options for events with tighter financial constraints. Their lower costs allow organizers to allocate resources to other areas, such as marketing or improving the attendee experience. These cities may also attract higher attendance from local or regional participants due to their affordability. However, they present certain challenges. Infrastructure may require temporary enhancements to meet the needs of an international audience, and their safety and accessibility scores are generally moderate--requiring careful planning to ensure a successful event. In the following, the values presented for each criterion are analyzed and discussed using fuzzy numbers, which represent the optimal values for each criterion within this cluster. These fuzzy values indicate the most desirable levels for cost, infrastructure, safety, and accessibility, providing a degree of flexibility rather than rigid, fixed values. By applying fuzzy logic, this approach acknowledges that real-world city classifications