**Vasyl Kut, Uzghorod National University**

**Natalia Kunanets, Lviv Polytechnic National University**

**Pavlo Fedorka, Uzghorod National University**

**Introduction**

In Ukraine, the majority of projects related to the use of Smart technologies are being gradually implemented, so it is logical to achieve the goal by using the best examples and experiences of cities and regions that have already received the status of smart ones and have experience in the implementation and practical application of various technological smart solutions.

**State of ****the research ****problem **

We shall consider the European experience of implementing smart technologies using the example of developments introduced in the Italian capital, Rome. The authors of the paper [1] believe that in order to achieve the status of a smart region, it is necessary to solve a number of problems related to the use of information technology and data processing, which will help reveal the potential of the region, creating the new opportunities for the population employment and the growth of its development rates. It is examined in detail the main factors contributing to the use of natural resources, the provision of greater sustainability of the region’s development and the effective implementation of innovations, the development of various ways of solving problems.

Another example from the so-called Nordic countries is the Smart Region of Helsinki. The authors of another article believe that the Helsinki-Usimaa region has been successfully implementing the concept of Smart Specialization for the development of the region in recent years [2]. Such an innovative policy implies that each country and region must recognize and choose its assignment, underline the strengths, and emphasize selected areas in its future efforts and investments.

The smart region is managed with the help of the information technology platform to improve the quality of services offered to citizens and make all management processes more efficient.

To create a comfortable communicative environment in a smart region, it is advisable to develop an information technology platform that will combine various software applications, information technologies, and open information resources.

Currently, there is no established definition of an information technology platform (IT platform). According to the researchers, IT platforms can include a variety of technologies, such as virtualization, user accounts, data security, data analytics, distributed access to data, and process management in various areas of activities of a smart region. They may be designed to support the operation of certain types of software products, such as web applications, mobile applications, or information systems.

Fishman notes that in the process of development of information technologies, the concept of information technology platform is increasingly considered a technological trend that provides the basis for the deployment of a significant number of applications and business processes [3]. A number of researchers have implemented this concept in some academic disciplines. Researchers from the University of Massachusetts [4] regard the platform as a means that allows you to combine the functionality of the developed application with the purpose of the applications presented in a set of applications located on the platform, which ensures their joint use. This approach helps save time and the amount of cloud storage.

** ****A conceptual model of the information technology platform**

An information technology platform (IT platform) is a convenient environment for creating, deploying, and managing various software applications, which combines hardware, an operating system, and different software components.

IT platforms can include a variety of technologies, such as virtualization, user accounts, data security, data analytics, distributed access to data, and process management in various areas of activity of a smart region. They may be designed to support certain types of software, such as web applications, mobile applications, or information systems.

With the use of an information technology platform, the operation of a smart region takes place, as it primarily contributes to the improvement of the quality of services offered to citizens. IT platforms allow you to create, test, implement and manage software applications in a convenient way, which contributes to increased productivity and lower costs for the development and operation of a software product. Also, they can help ensure standardization of technologies, which allows to reduce the complexity and increase the efficiency of the information system development.

The conceptual model of the information technology platform can be presented in the form of a five-element tuple:

*ITP={S,E,R,M,F}*

Each element of the information technology platform (IT platform) using a formula, or a mathematical expression could be formalized. There are examples for each element:

S (a set of classes of information technologies):

*S={IT _{1}, IT_{2}, IT_{3}, …}*

E (an environment where information processes take place):

*E={ENV _{1}, ENV_{2, }ENV_{3}*

*}*

R (a set of information resources (databases, data warehouses, data kiosks, data showcases, data lakes, data warehouse lakes, data factories, data spaces), which allows to support the information processes that flow in a complex system of a smart region):

*R={RES _{1}, RES_{2}, RES_{3},…}*

M (Management Mechanisms):

*M={MGMT _{1}, MGMT_{2}, MGMT_{3},…}*

F (functionality, a set of subjects (agents) located on an information technology platform. Information systems that ensure the functioning of the region act as agents. The combination of these components allows the creation of new information systems for the needs of a smart region.):

*F={FUNC _{1}, FUNC_{2}, FUNC_{3},…}*

Each element can be formalized with specific details, descriptions, or characteristics. Expressions can be more complex if each element needs to be detailed according to a specific context or an object of study.

If you specify the subject area of the information technology platform as a tool for the development of the tourism industry of the smart region, it is possible to formulate the definition with a more specific formula:

*IT_Platform_Tourism = (S_Tourism, E_Tourism, R_Tourism, M_Tourism, F_Tourism)*,

where *S_Tourism* is a set of information technologies specific to the tourism industry.

*E_Tourism* is an environment created for convenience and efficiency in the field of tourism.

*R_Tourism* is information resources related to tourist objects, services, and events.

*M_Tourism* is management mechanisms designed for effective management of tourism resources and information systems.

*F_Tourism* is functionality that provides information support for tourism services, improving the convenience and efficiency of the tourist experience, information systems, and mobile applications.

This formula makes it possible to describe the information technology platform more specifically for the tourism industry of the smart region and to highlight its constituent parts.

Considering the given definition, each component can be expressed separately as follows:

A set of information technologies for the tourism industry:

*S_Tourism={IT _{1}, IT_{2}, IT_{3},…}*

IT Platform (Tourism) = (Mobile Applications + Travel Agency Websites + Geolocation Technologies + Online Booking Systems + Social Media + Image Recognition Technologies + Analytics and Big Data + Artificial Intelligence + VR and AR Technologies + Blockchain)

This formula includes the main information technologies that are used to create and manage information systems and resources in the tourism industry of a smart region. The formula could be expanded including more specific technologies and tools that apply in a particular case.

An environment for convenience and efficiency in tourism:

*E_Tourism=Environment*

*R_Tourism={Resource1, Resource2, Resource3,…}*

The environment for convenience and efficiency in tourism can be formulated in the following way. It is an integrated system of information technologies, platforms, and applications aimed at improving convenience and efficiency in the field of tourism. It includes mobile applications, travel agency websites, geolocation technologies, online booking systems, social media, image recognition technologies, analytics and Big Data, artificial intelligence, virtual and augmented reality, blockchain technologies, as well as other innovative solutions. which contribute to improving the experience of tourists, optimizing booking processes and improving the quality of service in the tourism industry.

This environment creates an information platform that brings together tourists, tour operators, hotels, restaurants, and other industry players to jointly improve and optimize tourism experiences and services.

This definition can be formalized as follows:

*S={IT _{1}, IT_{2}, IT_{3},… IT_{n}},*

where S is a set of information technologies for the tourism industry, *IT _{1}, IT_{2}, IT_{3},… IT_{n}* are specific information technologies, including mobile applications, travel agency websites, geolocation technologies, online booking systems, social media, image recognition technologies, analytics and Big Data, artificial intelligence, virtual and augmented reality, blockchain technologies and other innovative solutions.

This formula represents a set of information technologies that are used to improve and optimize the tourist experience and service in the field of tourism.

*E_Tourism= Environment*

Information resources related to tourist facilities, services and events are:

*M_Tourism={Management1, Management1,…}*

The set of information resources related to tourist objects, services and events can be formulated as follows:

*IR={IR _{1}, IR_{2}, IR_{3},.. IR_{n}},*

where is a set of information resources related to tourist objects, services, and events, *IR _{1}, IR_{2}, IR_{3},.. IR_{n}* are specific information resources. These resources may include tourist websites, mobile applications, travel service databases, information brochures, social media platforms, online booking platforms, user reviews, videos, photos, and other sources of information, relating to tourist facilities, events, and services in the smart region.

This formula reflects the set of available information resources that can be used to provide information on tourist facilities, events, and services in a smart region.

*R_Tourism={Resourse _{1}, Resourse_{2}, Resourse_{3},…}*

Management mechanisms for effective management of tourist resources and information systems are:

*M_Tourism={Management1, Management1,…}*

Functionality that provides information support for tourist services, increasing the convenience and efficiency of the tourist experience is:

*F_Tourism=Functionality*

Management mechanisms for effective management of tourism resources and information systems can be formulated as follows:

*M={M _{1}, M_{2}, M_{3},… M_{n}},*

where *M* is a set of management mechanisms to ensure effective management of tourist resources and information systems, *M _{1}, M_{2}, M_{3},… M_{n}* are specific management mechanisms and tools. These mechanisms may include planning methods for the development of tourism resources, information systems and technologies, monitoring and analysis of resource use, reporting and control systems, development strategies, risk management methods, performance evaluation methods, as well as other tools and processes that contribute to ensuring effective management of tourist resources and information systems in a smart region.

*F_Tourism=Functionality*

Therefore, each component can be expressed separately as shown above, and then combined into a general formula for an information technology platform for the tourism industry of a smart region.

**Mathematical models of interrelationships of platform elements**

Relationships between elements can be represented by a mathematical apparatus, using graphs, matrices, and mathematical functions. There are a few ways to do this:

Graphs (Networks). It can be created a graph where vertices represent elements (for example, information technology, tourism resources, etc.), and edges represent relationships between them. The weights of the edges can indicate the strength of the relationship.

Matrices. Using matrices, a matrix of relationships could be created, where the rows and columns correspond to the elements, and the elements of the matrix indicate the presence or strength of the relationship between the elements.

Using the matrix, the relationships between the elements of the platform can be revealed. You can build a matrix where the rows and columns correspond to the elements of the platform, and the values in each cell of the matrix reflect the relationships or the degree of similarity between these elements.

There is an example of how the initial matrix of relationships between some elements of the platform might look like:

Element 1 | Element 2 | Element 3 | Element 4 | |

Element 4 | 1.0 | 0.8 | 0.2 | 0.6 |

Element 2 | 0.8 | 1.0 | 0.4 | 0.7 |

Element 3 | 0.2 | 0.4 | 1.0 | 0.3 |

Element 4 | 0.6 | 0.7 | 0.3 | 1.0 |

Element 1 – resources

Element 2 – technologies

Element 3 – systems

Element 4 – environment

In this matrix, values from 0.0 to 1.0 indicate the degree of similarity between the corresponding pairs of elements. If the value is close to 1.0, it means high similarity between items, and if the value is close to 0.0, it means low similarity. Such a matrix can be used, for example, to build a recommender system or to analyze the relationships between platform elements.

Functions. Mathematical functions can be defined that describe the relationships between elements. For example, similarity features can be used to determine the degree of similarity between information technologies or resources.

Mathematical models. You can create mathematical models that describe the behavior and relationships between elements. For example, an information distribution model or a tour selection model can indicate the relationships between information technology and users.

Mathematical models can be used to express the behavior of the platform in the context of recommender systems. One common mathematical model for this is the matrix factorization model.

The matrix factorization model is used to decompose the matrix of interactions between users and objects (for example, information technologies or resources) into the product of two matrices – one matrix reflects the properties of the information system, the other one shows the properties of information technologies. This approach allows modeling and predicting interactions between users and objects on the platform.

Mathematically, this model can be expressed as:

(1)

where is a a matrix of interactions between users and objects (for example, user ratings for objects).

*U* is a matrix of user properties (user factors).

*V* is a matrix of object properties (factors of objects).

*˄T* is the transposition operator of the matrix *V*.

The goal of this model is to find the factors of users and objects that best explain the observed interactions in matrix R. Knowledge of these factors can be used for recommendations, predictions of user actions, or optimization of information systems located on an information technology platform.

Usually, this model is optimized using machine learning methods, such as Least Squares, Gradient Descent, etc.

Thus, mathematical models, in particular the matrix factorization model, can be used to describe and predict platform behavior in the context of recommender systems.

Depending on the specific task and nature of relationships, you can decide on a convenient mathematical tool for formalizing these relationships.

Similarity functions are used to determine the degree of similarity between objects, such as information technologies or resources in recommender systems. These functions evaluate similarity based on various attributes or characteristics of objects. There are some typical similarity functions:

Cosine Similarity: This function measures the angle between vectors that represent objects. The smaller the angle between the vectors is, the higher the similarity will be. This method is often used for text analysis and other data that can be regarded as vectors. Cosine similarity is a popular method for determining the degree of similarity between vectors, and it is used in recommender systems. An example of using cosine similarity to compare information resources and information technologies is observed.

There are several information resources (R1, R2, R3) and several information technologies (T1, T2, T3). We would like to determine how similar information resources are to information technologies based on their characteristics.

To do this, each information resource and information technology in the form of vectors, where each component of the vector corresponds to a certain characteristic can be introduced. For example, you can use characteristics such as topic, volume, popularity, etc.

Then we can calculate the cosine similarity between each pair of information resources and information technologies. The cosine similarity formula looks like this:

(A, B) = (A • B) / (||A|| • ||B||)

where A and B are vectors that represent two objects (for example, an information resource and an information technology).

(A • B) is a scalar product (a procedure calculated as the sum of the products of the corresponding components of two vectors).

||A|| та ||B|| are the lengths of the vectors A and B, calculated using the Euclidean norm, and they represent the square root of the sum of the squares of all the components of the corresponding vector.

Cosine Similarity determines the degree of similarity between two vectors. The closer the result is to 1, the greater the similarity will be. If the vectors A and B are identical, the Cosine Similarity will be 1. If they are completely different, the Cosine Similarity will be 0.

After calculating the cosine similarity for all possible pairs of objects, we can determine which information resources are similar to certain information technologies based on the angle between their vectors. The smaller the angle (higher cosine similarity) is, the higher the similarity will be.

For example, if the cosine similarity between R1 and T1 is 0.9, it means that the information resource of R1 is similar to the information technology of T1. We may use these results to make recommendations to users who use certain information technologies similar to those used by other users.

This formula calculates the cosine of the angle between vectors A and B, and it can be used to determine the degree of similarity between two objects. The closer the cosine similarity value is to 1, the higher the similarity is between objects.

Jaccard Similarity: This function measures the similarity between sets of objects. It calculates the commonality of objects in sets relative to their union.

The Jacard similarity formula between two sets A and B looks like this:

*Jaccard Similarity (A,B)=|A*∩*B|/|A*∪*B|*

where A and B are sets of elements (for example, user interests or technology characteristics).

|A| is the number of elements in the set A.

|B| is the number of elements in the set B.

*|A*∩*B| *is the number of common elements between set A and set B.

*|A*∪*B| *is the number of unique elements included in both sets A and B.

Jaccard Similarity is used to measure the similarity between two sets. In the case of a recommender system, one can use this method to compare similarities between user interests or information technology characteristics.

An example of using Jacquard similarity is:

There are two users who choose information technologies for tourist services. User A selected technologies {GPS, Mobile App, Face Recognition} and User B selected {GPS, Mobile App, Data Analytics}. It will be calculated the Jacar similarity between their choices:

A ∩ B = {GPS, Mobile App} (common elements) A ∪ B = {GPS, Mobile App, Face Recognition, Data Analytics} (all unique elements)

Jacar similarity is calculated as:

Jaccard Similarity (A, B) = |A ∩ B| / |A ∪ B| = 2 / 4 = 0.5

Therefore, the Jacar similarity between users A and B is 0.5, indicating a moderate similarity in their technology choices for tourism services.

Euclidean Distance: This function calculates the distance between points in space, representing the characteristics of objects. The smaller the distance is, the greater the similarity will be.

The formula for the Euclidean distance between two points A and B in n-dimensional space looks like this:

(2)

where A and B are n-dimensional vectors that represent objects (for example, users or information technologies).

A_{i} and B_{i} are the coordinates of the corresponding points A and B in the i-th dimension.

n is the number of dimensions or characteristics.

Euclidean Distance is used to measure the distance between two points in space. In the case of a recommender system, you can use this method to evaluate the similarity between users or objects based on their characteristics or choices.

An example of using Euclidean distance is:

There are two users and the characteristics of their information technology choices:

User A: {0.2, 0.4, 0.1, 0.7, 0.5} User B: {0.4, 0.6, 0.2, 0.6, 0.8}

Now it is calculated the Euclidean distance between them using the formula:

Euclidean Distance

Therefore, the Euclidean distance between users A and B is approximately 0.44. This indicates the average distance between their characteristics of information technology choices.

Pearson Correlation Coefficient: This function measures the degree of linear relationship between two sets of data. It is often used for recommendations where characteristics may be numerical.

The Pearson Correlation Coefficient is used to measure the degree of correlation or linear relationship between two variables. In recommender systems, it can be used to estimate the similarity between users or objects based on their ratings or characteristics.

The formula for the Pearson correlation coefficient for two variables X and Y is the following one:

(3)

where x_{i }and y_{i }are the values of variables X and Y in observations i.

|X and Ῡ| are mean values of variables X and Y.

Pearson correlation coefficient values range from -1 (complete anticorrelation) to 1 (complete correlation), where 0 indicates no correlation.

An example of using the Pearson correlation coefficient is:

Two users are considered who rated the same tours:

User A:

sightseeing tour 1: 5

sightseeing tour 2: 4

sightseeing tour 3: 3

User B:

sightseeing tour 1: 4

sightseeing tour 2: 3

sightseeing tour 3: 5

Firstly, we will find the average ratings for each user:

Average ratings are:

Now it is calculated the Pearson correlation coefficient between users A and B using the formula:

Therefore, the Pearson correlation coefficient between users A and B is 0, indicating no correlation in their ratings.

These features help determine the degree of similarity between information technologies or resources. They can be used to calculate recommendations based on similarities between users or objects.

This approach makes it possible to form an information technology platform of a smart region and its subsystem that is the tourism industry by setting various parameters.

The Smart Region of Transcarpathia IT platform can include a variety of functions, including:

- infrastructure virtualization,
- storage of user accounts,
- secure data storage,
- support of data analysis procedures,
- provision of distributed access to data,
- management of processes in a smart region.

**Conclusions**

A conceptual model of the information technology platform was formed in the form of a tuple consisting of a set of information technology classes, a set of information resources (databases, data stores, data kiosks, data showcases, data lakes, data storage lakes, data factories, data spaces), which allows informationally support the processes that flow in the complex system of a smart region, the functionality that is a set of information systems that ensure the functioning of the region, management mechanisms.

References

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