## 1 Introduction
### Definition of Homogeneity in the Real Estate Market  
It is noteworthy that the exploration of similarity among real estate constitutes a pivotal stage in most analyses, serving diverse objectives related to classification processes involving categorization into relatively uniform or homogeneous groups. The concept of \"similarity\" is encountered frequently in our lives, and its definition is intuitively sensed by every individual. However, the most crucial question is: What does it mean for objects to be \"similar\"? Most of us would respond slightly differently yet possess the same key features. One thing we know for sure from this answer is the imprecise/fuzzy nature of the measurement of the concept of \"similarity\". In establishing what similarity entails, a precise definition of its criteria, measurement methods, and research methodology undoubtedly plays a significant role [6]. For example, from the perspective of computer vision, similar images are sought using the detection and comparison of key elements. Another question that may be posed is: Is an object that is \"similar\" the same as a 'homogeneous' object? The term \"homogeneous\" refers to a uniform entity composed of elements that do not differ from one another [7]. In everyday discourse, the terms \"similar\" and \"homogeneous\" are frequently interchanged and often perceived as synonyms. Nevertheless, they bear distinct definitions, and their connotations may vary contingent on the context. \"Similar\" pertains to the characteristics of elements or units sharing common aspects but allowing for some degree of difference. While similar elements are more varied than homogeneous ones, they still possess shared features that enable comparison or contrast [6]. Conversely, \"homogeneous\" describes the characteristics of elements or units that are nearly identical or very similar concerning specific features or parameters [8]. It is imperative to emphasize that the concept of market homogeneity is intricately linked to property similarity, and essentially, they should not be subjected to separate analyses. In general, this interdependence can be expressed through a mathematical function, denoted as:  
\[F(H,S)=k\cdot H(\alpha)\cdot S(\beta) \tag{1}\]  
where  
\(F\) represents the measure of homogeneity linkage between markets and property similarity;  
\(H\) denotes the degree of market homogeneity;  
\(S\) represents the measure of property similarity;  
\(k\), \(\alpha\), \(\beta\) are parameters that can be adjusted according to specific research objectives. The values of parameters \(\alpha\) and \(\beta\) influence the strength of the impact of the degree of market homogeneity and property similarity on the measure of linkage. Parameter k serves as a scaling constant (strengthening or damping), enabling the adjustment of the function's values to specific data or conditions. Evaluating real estate properties based on their similarity poses significant challenges due to the unique characteristics of each property, even within a single segment. Defining similarity becomes crucial for discerning homogenous property submarkets. Ref. [7] emphasizes that \"homogeneous\" transactions are not strictly precise but rather an approximate set determined by the definition of similarity, including the comparable area unit, features considered, methodology, methods selection, and result verification. To enhance real estate market analyses regarding property similarity, it is imperative to adopt suitable methods, procedures, and technologies based on the specificity of available information, as advocated by [8]. Ref. [9] underscores that statistical methods in real estate valuation, while unquestionable, are often misapplied without adequate knowledge, leading to conclusions based on erroneous premises. Numerous researchers focus on the potential application of hedonic modeling in market analysis, emphasizing the importance of determining the similarity of analyzed objects, whether properties or entire markets [10; 11].