## 1 Introduction
However, the use of intuitionistic fuzzy sets allows for the inclusion of uncertainty in responses [43; 44; 45], but this comes at the cost of aggregating positive and negative assessments from respondents. This aggregation process can limit the ability to fully differentiate between varying levels of positive or negative opinions, potentially leading to the loss of valuable information. These challenges underscore a methodological gap, particularly in multi-criteria methods that retain the full depth of information in survey responses. This paper presents a novel adaptation of the TOPSIS method, incorporating a Belief Structure (BTOPSIS) to evaluate survey data [46], demonstrating its novel and versatile use in this context. The BTOPSIS method integrates uncertain answers (e.g., \"I don't know\" or refusals) directly into the analysis, enhancing the ability to capture response distributions across categories and inherent uncertainties in survey data. Using the Belief Structure (BS) model to represent questionnaire responses measured on an ordinal scale, BTOPSIS begins by organizing multi-criteria questionnaire data into a belief decision matrix. Each response is represented using the BS model and then normalized. Positive and negative ideal belief solutions are identified based on TOPSIS principles, and a belief distance metric is introduced to quantify differences, facilitating comparison. Alternatives are ranked by their proximity to ideal solutions, resulting in an index that orders alternatives based on their closeness to ideal criteria. Finally, a sensitivity analysis is conducted to assess the stability of the BTOPSIS rankings under different utility function parameters, further demonstrating the robustness of our approach. BTOPSIS offers distinct advantages. First, it includes uncertain responses, avoiding the common exclusion of these categories and providing a fuller spectrum of respondent uncertainty. Second, representing survey data in the form of a Belief Structure is straightforward, logical, and easy to interpret. Third, BTOPSIS ranks responses based on their proximity to ideal and anti-ideal reference points, preserving all ordinal distinctions. By utilizing both the Positive Ideal Belief Solution (PIBS) and the Negative Ideal Belief Solution(NIBS), BTOPSIS enables robust comparisons over time and between objects. This approach also allows new objects to be incorporated without altering existing scores, preventing rank reversal and enhancing analysis stability. Finally, BTOPSIS is intuitive and computationally efficient, allowing for straightforward interpretation and visualization. This study applies BTOPSIS to analyze the quality of life using data from the 2023 'Quality of Life in European Cities' survey [19; 47]. Our approach provides deeper insights into urban life, refining city rankings and delivering accurate, comprehensive assessments of citizen satisfaction across key domains. Additionally, we compare BTOPSIS to traditional methods, illustrating its strengths and identifying limitations in other multi-criteria approaches. To the best of the authors' knowledge, this is the first instance of using the BTOPSIS framework to analyze survey data. In summary, this study contributes scientifically by proposing an adaptation of BTOPSIS for ordinal survey data analysis with uncertain responses. It also presents a new method for evaluating a city's performance through residents' perceptions of QoL, highlighting factors impacting well-being and urban satisfaction. By focusing on the lived experiences and opinions of citizens, this research provides deeper insights into how urban environments impact individual well-being. This approach can inform urban planners and policy-makers about the nuanced factors that contribute to residents' satisfaction, ultimately guiding improvements in urban living conditions and advancing smart city initiatives. The structure of this paper is as follows. After the introduction, Section 2 provides a brief literature review concerning smart cities and quality of life in cities.