The department develops various mathematical models that can simulate real-world processes.
In particular, research focuses on mathematical models of uncertainty based on mathematical tools, including fuzzy sets and relational equations, as well as their extensions.
From classical max–∗ systems to their various generalizations, including those involving balanced sets. This includes the development of algebraic and computational methods for determining families of solutions, reduced matrices, and applications in optimization and attribute reduction.
The properties of balanced operators have been introduced and investigated, enabling a deeper analysis of information while taking data structure into account. The developed methods allow for the modeling of decision-making processes, the analysis of multi-valued dependencies, and the reduction of features and elimination of redundant objects in empirical data.
Current work focuses on balanced systems of relational equations, intuitionistic fuzzy relations, and the analysis of complex dependencies in data using logical-algebraic and cognitive approaches.
Contact: zmatusiewicz@wsiz.edu.pl
The department also develops mathematical models that can program the behavior of so-called rational agents modeled after swarms, such as swarms of bees or ants. In game theory, a rational agent is a person, a company, or even a software program that, from all possible actions available to perform a given task, can select the optimal outcome, thereby continuing the behavior of its predecessors
Contact: aschumann@wsiz.edu.pl
We encourage you to read the Report on Artificial Intelligence in the Work of Academic Teachers
Journal:
Scientific research projects
The ESG Imperative for the Project Management World: An Alliance to Develop and Support Change Makers (ESG4PMChange)
Team:
Joanna Wójcik, Ph.D – Chair of Cognitive Science and Mathematical Modelling
Joanna Świętoniowska, Ph.D – Chair of Management
International cooperation:
University of Novi Sad (leader, Serbia),UITM, University of Bologna (Italy), PMI Chapters (Serbia, Italy, Poland), EnergyNet (Serbia), Revas (Poland), Future Food Institute (Italy)
The project focuses on integrating environmental, social, and corporate governance (ESG) principles into project management to develop a new professional profile: the ESG project manager. As part of the initiative, a competency model, training programs, and the ESG4PMChange Hub digital educational platform will be developed. The goal is to strengthen the capacity of academic staff and practitioners to implement ESG strategies in business and social projects. UITM is responsible for coordinating the research and developing the certification system.
Sustainable Project Management through PM² (SPM²)
Team:
Joanna Wójcik, Ph.D – Chair of Cognitive Science and Mathematical Modelling
Joanna Świętoniowska, Ph.D – Chair of Management
International cooperation:
University of Novi Sad (leader, Serbia), UITM, PANEPISTIMIO THESSALIAS (Greece), European Academy (Lithuania), ADVISE INSTITUTE (Serbia), PM² Alliance (Belgium), Scientific Events – PM² Center (Greece)
The project aims to develop an integrated methodology and educational ecosystem for sustainable project management based on the PM² methodology. The project’s activities will include the creation of an SPM² guide, a curriculum, and a digital resource center, as well as a framework for micro-qualifications and competency certification. The project involves universities, industry organizations, and experts to promote sustainable practices in project management and integrate them into higher education and vocational training programs. UITM is responsible for coordinating research and developing the certification system.
Supporting the green and digital transitions through education and innovation in Eastern Europe, Central Asia, and Asia (GreenTech Horizons)
Team:
Joanna Wójcik, Ph.D – Chair of Cognitive Science and Mathematical Modelling
Joanna Świętoniowska, Ph.D – Chair of Management
International cooperation:
University of Novi Sad (leader, Serbia), UITM , Riga Technical University (Latvia), Kaunas University of Technology (Lithuania), University of Split (Croatia), European Academy (Latvia), Universities in Azerbaijan, Kazakhstan, and Mongolia.
The project supports the green and digital transformation in the Eastern Neighbourhood and Central Asia regions through the development of competencies, curricula, and e-learning. It includes an analysis of labor market needs, the development of a competency framework and a competency-based teaching model, as well as the piloting of courses and MOOCs at eight universities. WSIiZ is responsible for developing business content and training for academic staff. The goal is to strengthen the potential of universities and the labor market toward sustainable development and innovation.
Inspiring innovation, upholding ethics
Team:
Małgorzata Rataj, Ph.D – Chair of Cognitive Science and Mathematical Modelling
Iryna Berezowska, Ph. D– Chair of Cognitive Science and Mathematical Modelling
International cooperation:
Lviv Polytechnic National University
Charles University, Czech Republic
The research focuses on the need to better understand the use of generative artificial intelligence in academic settings and to support its strategic and ethical integration into higher education. The current challenge is that, although students use generative AI tools to some extent, their engagement with these tools during their studies is often sporadic and lacks sufficient support. For example, an EDUCAUSE study (2025) reports that 68% of respondents observe higher use of AI among students than among faculty, while institutions focus more on training faculty than students (EDUCAUSE, 2024). Universities currently offer only a limited amount of structured guidance and methodological support. At the same time, there are examples of best practices, but these should be further developed and systematized, taking into account the needs of various fields of study and local contexts. The project aims to promote the informed and responsible use of artificial intelligence, create specialized methodological materials, and strengthen students’ digital competencies (EDUCAUSE, 2024).
Scientific research projects financed from the Ministry:
Fuzzy sets and their application in real-world modeling
Project Manager:
Zofia Matusiewicz, Ph.D zmatusiewicz@wsiz.edu.pl
The project aims to analyze the concept of balanced fuzzy sets, including those based on existing set extensions. One of the main objectives is to describe the various operators of these sets and their properties. Research on balanced fuzzy sets aims to open up new possibilities for the practical application of this theory in various fields. Fuzzy sets are a useful tool in situations where data is incomplete, ambiguous, or subject to a certain degree of uncertainty. In addition to studying various operators and properties of balanced fuzzy sets, the project aims to open the door to potential applications in various fields, such as decision-making systems, control, and data analysis. In summary, the main objective of the project is to investigate the concept of balanced fuzzy sets and their potential applications, which may provide a new perspective on flexible modeling of reality under conditions of uncertainty and data ambiguity.
