Note on formal contexts of generalized one-sided concept lattices

Generalized one-sided concept lattices represent one of the conceptual data mining methods, suitable for an analysis of object-attribute models with the different types of attributes. It allows to create FCA-based output in form of concept lattice with the same interpretation of concept hierarchy as in the case of classical FCA. The main aim of this paper is to investigate relationship between formal contexts and generalized one-sided concept lattices. We show that each one uniquely determines the other one and we also derive the number of generalized one-sided concept lattices defined within the given framework of formal context. The order structure of all mappings involved in some Galois connections between a power set and a direct product of complete lattices is also dealt with. Keywords: Galois connection, generalized one-sided concept lattice, formal context

Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices

In this paper we describe possible interpretation and reduction of fuzzy attributes in Generalized One-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization of Formal Concept Analysis (FCA) suitable for analysis of datatables with different types of attributes. FCA as well as generalized one-sided concept lattices represent conceptual data miningmethods. With growing number of attributes the interpretation of fuzzy subsets may become unclear, hence another interpretation of this fuzzy attribute subsets can be valuable. The originality of the presented method is based on the usage of one-sided concept lattices derived from submodels of former object-attribute model by grouping attributes with the same truth value structure. This leads to new method for attribute reduction in GOSCL environment

Distributed Computation of Generalized One-Sided Concept Lattices on Sparse Data Tables

In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets

Supplier selection based on multi-criterial AHP method

This paper describes a case-study of supplier selection based on multi-criterial Analytic Hierarchy Process (AHP) method.It is demonstrated that using adequate mathematical method can bring us “unprejudiced” conclusion, even if the alternatives (suppliercompanies) are very similar in given selection-criteria. The result is the best possible supplier company from the viewpoint of chosen criteriaand the price of the product

On Bonds for Generalized One-Sided Concept Lattices

The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms

On Bonds for Generalized One-Sided Concept Lattices

The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms

A Modular Approach to the Teaching of Mathematical Content at Technical Universities

A new approach to dividing the mathematical content into partial modules is presented. This allows to compose subjects with mathematical content from such partial modules and flexibly adapt these subjects to the needs of specific study programs at technical universities. The consistent and systematic implementation of this approach in a typical learning management system is described in detail. This approach means significant changes in the massive (or bulk) delivery of knowledge using available information technologies. The main benefits of the presented system consist in the increase the resulting level of knowledge of students along with their satisfaction with the results and the form of their study. The most important changes arising from our approach are the following. First, the study process became distributed in space and in time. Second, it can be piecewise continuous in time, and, since all students can study at their own pace, it runs in multiple individual time scales. The most important change, however, is the shift of the paradigm the educational process from transmissive “teach–learn” to active “study”

A Modular Approach to the Teaching of Mathematical Content at Technical Universities

A new approach to dividing the mathematical content into partial modules is presented. This allows to compose subjects with mathematical content from such partial modules and flexibly adapt these subjects to the needs of specific study programs at technical universities. The consistent and systematic implementation of this approach in a typical learning management system is described in detail. This approach means significant changes in the massive (or bulk) delivery of knowledge using available information technologies. The main benefits of the presented system consist in the increase the resulting level of knowledge of students along with their satisfaction with the results and the form of their study. The most important changes arising from our approach are the following. First, the study process became distributed in space and in time. Second, it can be piecewise continuous in time, and, since all students can study at their own pace, it runs in multiple individual time scales. The most important change, however, is the shift of the paradigm the educational process from transmissive “teach–learn” to active “study”

On concept reduction based on some graph properties

International audienceThe theory of concept lattices represents a well established and widely used conceptual data-mining method. Considering additional information represented by a graph structure on a set of objects, we propose a reduction of concepts. Using graph-theoretical point of view on FCA together with simple probabilistic arguments we derive the mean value of the cardinality of the reduced hierarchical structure

Implementation of Agile Methodologies in an Engineering Course

At present, a new generation of students is studying at universities with their specific abilities and skills. In addition to hard skills, potential employers also require significantly developed soft skills from their employees. The school, and not just the university, is entering this process in a different position than in the past due to the changing requirements placed on it. Activities in the school environment must adapt to emerging trends. This article explains how present-day requirements on graduates and specifics of the new generation of students challenge the approach to education. In order to increase the efficiency and attractiveness of the educational process, the SCRUM framework has been implemented into course Mathematics 1. The re-designed course was implemented and validated by an experimental group of students in the academic year 2019/2020. Two questionnaire analyses and a comparison of learning outcomes were conducted to find out the answers to research questions. The results of students indicate that agile methodologies are useful for increasing the efficiency of the educational process. The paper offers our proposal for the introduction of agile methodology into the educational process and our first-hand experience with this way of teaching and its impact on the studying results of the experimental group and, last but not least, suggestions for possible improvements