## 1 Introduction
Additionally, ambiguous responses (e.g., \"Don't know\", \"No answer\", or \"Refused\") coded as 99, are often excluded. For instance, the analysis of the 'Quality of Life in European Cities' survey [19] is based on single items, excludes this type of responses, and merges satisfaction categories. This exclusion can result in the loss of valuable information about respondent uncertainty, potentially affecting the accuracy of findings and insights into areas where respondents may lack confidence or knowledge. Moreover, the complexity of QoL cannot be fully represented through single-ranking criteria, underscoring the need for more sophisticated multi-criteria analysis methods. Composite indicators, based on multi-criteria decision-making (MCDM) methods, are frequently applied to summarize information, with the aim of capturing underlying concepts [20; 21; 22]. These indicators often rely on reference-based aggregation formulas, such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [23; 24; 25; 26; 27; 28] or Hellwig methods [29; 30], to synthesize data across multiple criteria. The TOPSIS method was originally proposed by [PERSON] and [PERSON] in 1981 [24]. Over the years, TOPSIS has evolved, leading to the development of various modifications, extensions, and new variants, enhancing its applicability across different fields. The TOPSIS method has been extended in several directions, including the implementation of different types of data, data normalization techniques, weights, and distance measures. A summary of various TOPSIS methods, their extensions, and applications can be found in [23; 25; 26; 28]. [PERSON] et al. [31]provided a review of multi-criteria decision-aid methods from 1977 to 2022, showing that the TOPSIS method remains highly popular and ranks second only to the AHP approach in terms of the number of publications over the four decades studied. The growing popularity of TOPSIS can be attributed to its simplicity, ease of implementation, flexibility in handling complex decision-making problems with multiple criteria, and its unique ability to relate alternatives to an ideal solution (ideal point) [28; 32; 33]. While TOPSIS is effective in many contexts, it can overlook or oversimplify responses, especially when dealing with ordinal data and uncertain categories. The classic TOPSIS method is well-suited for precise data but not ideal for ordinal survey data or ambiguous information. Applying it to survey data would require transformations, such as merging certain categories and representing them as a percentage of each response's occurrence. However, these adjustments add extra steps and can result in a loss of valuable information conveyed by the survey responses  
Some multi-criteria methods, while incorporating various linguistic approaches to data representation--such as using the Generalized Distance Measure 2 (GDM2) [34] for distance calculation or employing fuzzy set representations for linguistic variables [35; 36; 37; 38]--still face challenges in effectively managing uncertainty or handling missing responses. TOPSIS with GDM2 [39; 40; 41; 42] is a modification of the classic method that replaces the standard Euclidean distance with a GDM2 distance measure. This modification allows for better handling of ordinal data, making it suitable for analyzing survey data; however, it does not address undefined or missing responses. Intuitionistic fuzzy sets provide a more flexible framework than classical fuzzy sets by incorporating membership, non-membership, and hesitation degrees. In Intuitionistic Fuzzy TOPSIS (IF TOPSIS), each criterion value is represented as an intuitionistic fuzzy number, which consists of these three components. IF TOPSIS extends the classic method by using intuitionistic fuzzy sets to model uncertainty. This approach is particularly effective in handling uncertainty in survey data, especially in situations where responses reflect positive opinions, negative opinions, or \"I don't know\"/\"refused\" answers.