Computing Crisp Bisimulations for Fuzzy Structures

Fuzzy structures such as fuzzy automata, fuzzy transition systems, weighted social networks and fuzzy interpretations in fuzzy description logics have been widely studied. For such structures, bisimulation is a natural notion for characterizing indiscernibility between states or individuals. There are two kinds of bisimulations for fuzzy structures: crisp bisimulations and fuzzy bisimulations. While the latter fits to the fuzzy paradigm, the former has also attracted attention due to the application of crisp equivalence relations, for example, in minimizing structures. Bisimulations can be formulated for fuzzy labeled graphs and then adapted to other fuzzy structures. In this article, we present an efficient algorithm for computing the partition corresponding to the largest crisp bisimulation of a given finite fuzzy labeled graph. Its complexity is of order $O((m\log{l} + n)\log{n})$, where $n$, $m$ and $l$ are the number of vertices, the number of nonzero edges and the number of different fuzzy degrees of edges of the input graph, respectively. We also study a similar problem for the setting with counting successors, which corresponds to the case with qualified number restrictions in description logics and graded modalities in modal logics. In particular, we provide an efficient algorithm with the complexity $O((m\log{m} + n)\log{n})$ for the considered problem in that setting

Bisimulations for Kripke models of Fuzzy Multimodal Logics

The main objective of the dissertation is to provide a detailed study of several different types of simulations and bisimulations for Kripke models of fuzzy multimodal logics. Two types of simulations (forward and backward) and five types of bisimulations (forward, backward, forward-backward, backward-forward and regular) are presented hereby. For each type of simulation and bisimulation, an algorithm is created to test the existence of the simulation or bisimulation and, if it exists, the algorithm computes the greatest one. The dissertation presents the application of bisimulations in the state reduction of fuzzy Kripke models, while preserving their semantic properties. Next, weak simulations and bisimulations were considered and the Hennessy-Milner property was examined. Finally, an algorithm was created to compute weak simulations and bisimulations for fuzzy Kripke models over locally finite algebras

Fazi relacijske jednačine i nejednačine i njihova primena u analizi podataka

The subject of this thesis is the development of algorithms for computing the greatest solutions to systems of fuzzy relational equations and inequalities and application of these solutions in the analysis of one-mode and multi-mode fuzzy social networks. In addition, some problems of finding structural similarities (regular equivalences) between the actors of various networks have been considered, and have been employed for determination of connected positions in these networks

Increasing the Ethnic and Cultural Diversity of Virtual Classrooms

In recent years, there has been a rise in interest in receiving an education online. Learning that may be done outside of the traditional classroom setting, such as via the use of the internet, has gained significance as a result of the COVID-19 pandemic. As more and more education is made available online, it is imperative that educators find ways to create online environments that not only instill a sense of belonging but also make learning an enjoyable experience for all students. This requires consideration of how to encourage a diverse range of cultural perspectives inside an online learning environment. Learning may be significantly improved via the use of virtual environments by encouraging a diverse range of cultural expressions. On the contrary, it could be challenging to discover effective methods that can be used to enhance cultural variety in non-traditional educational settings. Competence in teaching that is culturally sensitive is essential for educators. Educators are better equipped and given the authority to innovate when they have a solid understanding of the aims of culturally responsive education. This ensures that their online classrooms are accepting of students from a wide range of cultural backgrounds