# Adaptive Cluster-Based Normalization for Robust TOPSIS in Multicriteria Decision-Making
## 4 Case Study
\begin{table}
\begin{tabular}{c l l} \hline \hline
**City (Letter)** & **City** & **Description** \\ \hline City A & Hanoi, Vietnam & Low-cost city with functional infrastructure, ideal for regional events. \\ City B & Kathmandu, Nepal & Highly affordable but with limited infrastructure and moderate safety. \\ City C & Tokyo, Japan & Exceptional infrastructure, safety, and accessibility; high-cost city. \\ City D & Singapore, Singapore & Similar quality to Tokyo with slightly lower costs. \\ City E & Kuala Lumpur, Malaysia & Balanced city with high safety, accessibility, and moderate costs. \\ City F & Bangkok, Thailand & More affordable than Kuala Lumpur, with slightly lower safety scores. \\ City G & Colombo, Sri Lanka & Affordable with growing infrastructure and moderate accessibility. \\ City H & Manila, Philippines & Slightly higher cost with challenges in infrastructure and safety. \\ City I & Seoul, South Korea & High safety and good infrastructure, though slightly less accessible. \\ City J & Hong Kong, China & Highly accessible and secure, with costs similar to Tokyo. \\ City K & Ho Chi Minh City, Vietnam & Good safety and accessibility, with moderately higher costs. \\ City L & Jakarta, Indonesia & High accessibility and safety with balanced, moderate costs. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Potential cities for selection as hosts of an international event. involve gradual transitions rather than strict categorizations, allowing for a more nuanced and adaptable evaluation of urban characteristics as follows:  
1. Cost (C1): This criterion represents the financial affordability of the city. Since this cluster focuses on cost-effective locations, the cost should be as high as possible (fuzzy number (0.9, 1, 1)). A higher rating means the city is more budget-friendly in terms of living expenses, business operations, and overall affordability. 2. Infrastructure (C2): This refers to the quality and availability of public services, transportation, and essential facilities. Cities in this cluster should have a moderate level of infrastructure (fuzzy number (0.5, 0.6, 0.7)). This means they provide basic amenities but might require improvements in areas like roads, public transportation, healthcare, and digital connectivity. 3. Safety (C3): This criterion evaluates how secure the city is for residents, businesses, and visitors. These cities should have moderate safety levels (fuzzy number (0.4, 0.5, 0.6)). While they are generally safe, they may have certain areas that require extra precautions, such as higher crime rates or specific security concerns. 4. Accessibility (C4): This criterion assesses how well-connected the city is both regionally and internationally. The cities in this cluster should have moderate accessibility (fuzzy number (0.4, 0.5, 0.6)). They typically have good regional connectivity through local transportation networks but might lack direct access to global travel hubs, such as major international airports or high-speed rail links. 2. Cluster 2: High-Investment Cities with World-Class Infrastructure. Cities in this cluster are renowned for their exceptional infrastructure, including state-of-the-art venues, premium accommodations, and robust transportation networks. These cities are ideal for events that aim to project prestige or cater to high-profile attendees. High safety and accessibility scores further ensure a smooth and secure experience for participants. However, these advantages come with significant costs, which can impact profitability or restrict participation. Careful budgeting and strong justifications to stakeholders are essential to address these challenges. The following analyzes and discusses the values for each criterion in Cluster 2 using fuzzy numbers, which define the optimal range for cost, infrastructure, safety, and accessibility within this category as follows:  
1. Cost (C1): Should be as low as possible (fuzzy number (0.05, 0.1, 0.12)) because these are expensive cities, making budget management a challenge.