Formal Concept Research Articles

Single sample-oriented attribute reduction for rule learning with formal concept analysis

As an effective tool for data mining, formal concept analysis can yield interpretable decision rules using attribute reduction. Currently, existing reduction methods within the framework of formal concept analysis result in all samples sharing the same conditional attributes, thereby overlooking the distinctions between rules extracted from different samples. To address this problem, we present a novel attribute reduction method for single samples. For this purpose, a single sample-oriented reduction framework is established by incorporating a discernibility attribute vector and an algorithm for calculating reducts based on the matrix representation of the discernibility attribute vector. Furthermore, the process of obtaining a new reduct from the original reduct is discussed by considering incremental learning. Given that attributes included in reducts are crucial conditions for decision-making, intent-minimal granular rules are generated through attribute reduction, and a reduction-based method for measuring the completeness of the rule set is discussed. Finally, to accomplish the classification task, a minimal rule-based classification model (MRCM) is proposed. The experimental results show that the MRCM has the same classification ability as the unreduced rules, and the rules with higher completeness tend to exhibit better classification performance.

The Concept Of Amanah Metaphor In Accounting: Meaning, Guidelines, And Purposes

This paper aims to construct Amanah's (trustful) metaphor in accounting related to meaning, guidelines, and purpose. This research is a qualitative research with an interpretive paradigm which is analyzed using content analysis. Data obtained from structured interviews with 40 IAI (Indonesian Accountant Assosiation) member, the Holy Qur'an, Hadith, and other literature. The research results are in the form of the metaphorical concept of Amanah, which is interpreted by a human perspective in perceiving his duties as God's representative in the world. Accounting guidelines based on the metaphor of Amanah concept must be based on strong Aqidah, based on good morals, a responsibility to society and the Ummah, based on legal, financial processes, and behavioral aspects of each of their actions. Besides, it also purpose at hisful amwal, the existence of al kitabah, assisting decision making, calculating business zakat, determining and calculating profit sharing for the unionized party. These concept will change accountants' behavior to be more trustworthy and not materialistic because all of their work is intended only to get the pleasure of Allah.

Artistic Conception In Meticulous Flower-and-Bird Painting

Chinese painting has its own unique form of artistic conception, which aims to convey the inner emotions and spirits of different people. Although more and more people are fond of Chinese meticulous painting, their aesthetic views on it are also constantly improving, and they are increasingly emphasizing the spirit of Chinese meticulous flower and bird painting through the expression of their works. Chinese meticulous painting is an inheritance of China's excellent traditions, and the images displayed through the paintings can allow viewers to feel the true emotions of the creators. "Artistic conception" is the source of meticulous flower-and-bird painting art creation, the "soul" of flower-and-bird painting, and also the rich connotation of meticulous flower-and-bird painting art in various periods, and the key and core of creation. In spite of this importance, there are deficiencies in the analysis of artistic conception in contemporary meticulous flower-and-bird painting in the current literature. This study attempts to fill this gap by organizing and analyzing the relevant content of "artistic conception". This paper focuses on the artistic conception of Chinese meticulous flower-and-bird painting. Firstly, an overview of the artistic conception was provided, followed by an analysis of the constituent elements and expressive techniques of the artistic conception in Chinese meticulous painting. Finally, the artistic conception in the creation of Chinese meticulous flower and bird painting was conducted. The results of research and analysis show that the reality of Chinese contemporary meticulous flower-and-bird painting is not only a collection reflection of the essence of objective things, but also a creation of "the unity of mind and scene, the unity of meaning and context" that integrates with the author's personal feeling experience, and is a total embodiment of the combination of the viewer's inner expectation of artistic conception.

Fuzzy object-induced network three-way concept lattice and its attribute reduction

Concept cognition and knowledge discovery under network data combine formal concept analysis with complex network analysis. However, in real life, network data is uncertain due to some limitations. Fuzzy sets are a powerful tool to deal with uncertainty and imprecision. Therefore, this paper focuses on concept-cognitive learning in fuzzy network formal contexts. Fuzzy object-induced network three-way concept (network OEF-concept) lattices and their properties are mainly investigated. In addition, three fuzzy network weaken-concepts are proposed. As the real data is too large, attribute reduction can simplify concept-cognitive learning by removing redundant attributes. Thus, the paper proposes attribute reduction methods that can keep the concept lattice structure isomorphic and the set of extents of granular concepts unchanged. Finally, an example is given to show the attribute reduction process of a fuzzy network three-way concept lattice. Attribute reduction experiments are conducted on nine datasets, and the results prove the feasibility of attribute reduction.

Multidimensional Representation of Semantic Relations between Physical Theories, Fundamental Constants and Units of Measurement with Formal Concept Analysis

We propose several hierarchical graphs that represent the semantic relations between physical theories, their fundamental constants and units of measurement. We begin with an alternative representation of Zel’manov’s cube of fundamental constants as a concept lattice. We then propose the inclusion of a new fundamental constant, Milgrom’s critical acceleration, and discuss the implications of such analysis. We then look for the same fundamental constants in a graph that relates magnitudes and units of measurement in the International System of Units. This exercise shows the potential of visualizing hierarchical networks as a tool to better comprehend the symmetries, interrelations and dependencies of physical magnitudes, units and theories. New regimes of application may be deduced, as well as an interesting reflection on our ontologies and corresponding theoretical objects.

Exploring the 3-dimensional variability of websites' user-stories using triadic concept analysis

Configurable software systems and families of similar software systems are increasingly being considered by industry to provide software tailored to each customer's needs. Their development requires managing software variability, i.e. commonalities, differences and constraints. A primary step is properly analyzing the variability of software, which can be done at various levels, from specification to deployment. In this paper, we focus on the software variability expressed through user-stories, viz. short formatted sentences indicating which user role can perform which action at the specification level. At this level, variability is usually analyzed in a two dimension view, i.e. software described by features, and considering the roles apart. The novelty of this work is to model the three dimensions of the variability (i.e. software, roles, features) and explore it using Triadic Concept Analysis (TCA), an extension of Formal Concept Analysis. The variability exploration is based on the extraction of 3-dimensional implication rules. The adopted methodology is applied to a case study made of 65 commercial web sites in four domains, i.e. manga, martial arts sports equipment, board games including trading cards, and video-games. This work highlights the diversity of information provided by such methodology to draw directions for the development of a new product or for building software variability models.

Enhancing Interpretability in Medical Image Classification by Integrating Formal Concept Analysis with Convolutional Neural Networks.

In this study, we present a novel approach to enhancing the interpretability of medical image classification by integrating formal concept analysis (FCA) with convolutional neural networks (CNNs). While CNNs are increasingly applied in medical diagnoses, understanding their decision-making remains a challenge. Although visualization techniques like saliency maps offer insights into CNNs' decision-making for individual images, they do not explicitly establish a relationship between the high-level features learned by CNNs and the class labels across entire dataset. To bridge this gap, we leverage the FCA framework as an image classification model, presenting a novel method for understanding the relationship between abstract features and class labels in medical imaging. Building on our previous work, which applied this method to the MNIST handwritten image dataset and demonstrated that the performance is comparable to CNNs, we extend our approach and evaluation to histopathological image datasets, including Warwick-QU and BreakHIS. Our results show that the FCA-based classifier offers comparable accuracy to deep neural classifiers while providing transparency into the classification process, an important factor in clinical decision-making.

The Unique Formality in the Fabric Designs of the Iraqi Fashion House

This research addresses the topic of unique formality in the designs of the fashion house by employing symbols and colors in the elements executed on fashion fabrics for the Iraqi fashion house's runway shows, and the methods and techniques of their implementation, which distinguish the house from its counterparts.The research problem was identified through the following question: How can unique formality be achieved in the fabric designs of the Iraqi fashion house? The aim of the research was to study and analyze the concept of unique formality in the fabric designs of the Iraqi fashion house. The research discussed relevant literature, including the concept and importance of unique formality in fabrics, history and cultural heritage as sources for fashion design, and techniques for showcasing decorative designs in fashion fabrics. The research followed a descriptive analytical method, relying on theoretical framework indicators and expert opinions in analyzing sample models. The research concluded with several findings, the most significant of which are: the elements used greatly influence highlighting the unique formality of fashion fabric designs, and unique formality enhances the beauty and authenticity of fabric designs, reflecting cultural and heritage identity. The research also made several recommendations, the most important of which is to emphasize uniqueness in designs by matching the elements used with historical symbols, referencing original images in museums. Lastly, the research proposed further study on decorative display techniques for the Iraqi fashion house's designs.

МЕКТЕПКЕ ЧЕЙИНКИ МАТЕМАТИКАЛЫК БИЛИМ БЕРҮҮДӨ ЗАМАНБАП ТЕХНОЛОГИЯЛАРДЫ КОЛДОНУУ

The article is written based on current problem. In fact, there are no textbooks or manuals for the formation of elementary mathematical concepts in preschool education. We know the situation of teachers and students specializing in preschool education. In the article "Explanation and justification", "Using children's literature for the formation and consolidation of mathematical ideas" it shows the method of using strategic formation and consolidation of elementary mathematical ideas. For the strategy "Using children's literature for the formation and consolidation of mathematical concepts" I used the work of A. Osmonova "Aldar köse" (1st grade) is children's literature. The work was analyzed step by step, feedback was formed and addressed. The above-mentioned methods are the most important and necessary methods of preschool mathematical education. The article consists of introduction, main part and conclusion.

The Importance of Mathematical Ideas to Learning of Higher Algebra

This article discusses the importance of mathematical ideas in the learning of higher algebra. First of all, this article briefly introduces the core position of higher algebra in the field of mathematics. Then, this article analyzes the mathematical ideas behind these knowledge, such as abstract thinking, inductive classification, and returning. Application in algebra. Further, this article discusses the specific application of mathematical ideological methods in definition and concept formation, solving specific problems, etc., and shows its effects through case analysis. Finally, the article analyzes the impact of mathematical ideological methods on improving students' problem -solving ability, logical thinking and innovative ability.

A Formal Concept Analysis approach to hierarchical description of malware threats

The problem of intelligent malware detection has become increasingly relevant in the industry, as there has been an explosion in the diversity of threats and attacks that affect not only small users, but also large organisations and governments. One of the problems in this field is the lack of homogenisation or standardisation in the nomenclature used by different antivirus programs for different malware threats. The lack of a clear definition of what a category is and how it relates to individual threats makes it difficult to share data and extract common information from multiple antivirus programs. Therefore, efforts to create a common naming convention and hierarchy for malware are important to improve collaboration and information sharing in this field.Our approach uses as a tool the methods of Formal Concept Analysis (FCA) to model and attempt to solve this problem. FCA is an algebraic framework able to discover useful knowledge in the form of a concept lattice and implications relating to the detection and diagnosis of suspicious files and threats. The knowledge extracted using this mathematical tool illustrates how formal methods can help prevent new threats and attacks. We will show the results of applying the proposed methodology to the identification of hierarchical relationships between malware.

RETREATS AS INNOVATIVE FORM OF TOURISM DEVELOPMENT

This paper is focused on the research of formation of the retreats concept for young people in the conditions of health tourism development in Ukraine and Moldova. The article analyzes the basic concepts and types of classifications of retreats, examines the experience of European countries in the field of organizing retreats. The state and prospects of non-traditional forms of health tourism on the example of Ukraine are analyzed, as well as scientific research on the formation of the concept of retreats. As a result of the work was formed the concept of retreats on the basis of research conducted by survey method, it was found that the most popular type of retreat for young people is adventure retreat. For the purpose of research and analysis of new directions of tourism in Europe and in the world the Report of Global Wellness from Institute Grand View Research was examined, confirming the relevance and demand for new forms and types of health tourism. This research will contribute to the development of health tourism in Ukraine and the Republic of Moldova and the solution of the main problems identified in the official document of the Cabinet of Ministers of Ukraine "Strategy for the development of tourism and resorts in Ukraine until 2026" and also in Moldova in the National Tourism Development Program "Tourism 2026" for the years 2022-2026. Based on a comprehensive analysis, the concept of retreats for youth in the development of health tourism in Ukraine and Moldova was formed, which involves the organization of events aimed at stimulating adventure and active lifestyle, as well as promoting personal development and teamwork.

Bimorphisms and attribute implications in heterogeneous formal contexts

Formal concept analysis is a powerful mathematical framework based on mathematical logic and lattice theory for analyzing object-attribute relational systems. Over the decades, Formal concept analysis has evolved from its theoretical foundations into a versatile methodology applied across various disciplines. A heterogeneous formal context provides a feasible generalization of a formal context, enabling diverse truth-degrees of objects, attributes, and fuzzy relations. In our paper, we present extended theoretical results on heterogeneous formal contexts, including bimorphisms, Galois connections, and heterogeneous attribute implications. We recall the basic notions and properties of the heterogeneous formal context and its concept lattice. Moreover, we present extended results on bimorphisms and Galois connections in a heterogeneous formal context, including a self-contained proof of the main result. We include examples of introduced notions in heterogeneous formal contexts and two-valued logic. We propose the extension of attribute implications for heterogeneous formal contexts and explore their validity. By embracing heterogeneity in Formal concept analysis, we enrich its extended theoretical foundations and pave the way for innovative applications across diverse domains, including personal data protection and cybersecurity.

Paradoxical thinking as a way of solving theoretical problems

An awareness of the need for paradoxical justification of content thought first came to the Christian theologian Quintus Septimius Florence Tertulian, who lived in Carthage from 160 to 220 AD. In the controversy against abstract theoretical reason, he insisted on the importance of the “organic” practical reason, opposite to theoretical, the idea of which he associated with his paradoxical organization. The peculiarity is this organization of the mind that would allow it to avoid the emergence of problems in the form of a clash of opposing opinions, which Aristotle associated with the need for self-justification of its content. However, to bring it to the consciousness of the scientific community that self-justification of the conceivable follows be considered as a way of solving theoretical problems, requiring the exclusion of thinking from the logic of theoretical reasoning and reorienting it to a strict opposition to the Logos required the efforts of the geniuses of Antiquity and the Renaissance, as well as the best minds of the New time. In the process of searching for a mechanism for realizing self-justification, a paradox was considered a promising construct that posed the subject before the need to understand the object of comprehension based on simultaneously two incompatible, mutually justifying each other logician: the logic of his understanding that has become familiar and other logic into which thinking dissatisfied with its previous reasoning, literally “pushed out” the object of unrealized own cognitive efforts. Enrichment of thinking due to two opposing definitions of the concept object of comprehension ensured the acquisition of new knowledge, inaccessible each logically formed thinking separately and was achieved through the complementary dialogue of two logically incompatible logic justifications. The fundamental possibility of such a dialogue stimulated by the subject setting a task for himself as a situation requiring him to take a certain action in conditions where it is necessary to “find” something “unknown in principle”, the idea of which is what is “given” in a problem is based only on the awareness of the existence some unstructured set of empirical and devoid of any -certain contours and landmarks of its manifestations, which It is impossible to subsume it under any concept or any known theory. This led to the formulation of the “unknown in principle” into the concept of “unknown the “sought” that the task requires “to find.” In the face of uncertainty what needs to be “found”, what is sought is no longer the most “unknown in principle”, but the way of searching for it, resulting in the idea of this very unknown and the definition of its concept directly depend on what is found way of understanding it. Realization of mental action in conditions uncertainty of what is sought is carried out using operating component of thinking, which, using as its own means dialectical-logical concepts and triadic inferences, carries out a categorically unacceptable combination of opposing judgments. This connection, in accordance with the provision on “reflecting the properties of an object in principle of action”, leaves for the categorical component of thinking only a function of the source of the initial premises that are subject to reorganization. As a result of this reorganization, the idea of what needs to be “found” was gradually refined in the process of improving the search method, and its the concept reaches its utmost clarity only after the final complete search. The found method makes sense of the “unknown” sought” in the plane of problematic-dialogical reality, thereby revealing most its own content through a gradual transition from the definition the concept of thinking as “paradoxical”, given to it from a logical point of view, to the definition of his concept as “dialogical”, which corresponds to his natural design. In the process of making this transition the “unknown sought after” gradually becomes known due to the fact that it signs are combined in the process of this transition into a single thought based on which is the logic of the dialogue of two logics or dialogics. Picture of theory of thinking, built based on problem-dialogical it organization, involves the introduction of the concepts of “paradox”, “dialogic,” and “dialogical thinking” into its categorical system, starting with paradoxical design of the initial category with subsequent paradoxical formulation of its theoretical provisions in the form of species and subspecific dialectical-logical concepts, which will theoretically allow justifiably, using as psychological tools of thinking triadic inferences, to cognize the object of comprehension in all its completeness and internal inconsistency. Proposed theoretical understanding an object that is “unknown in principle” raises its understanding above the functional level of finding its place in a separate concept or paradigmatic model and opens up the prospect of objectification at the meta-paradigmatic level in a ompletely exhausted categorical methodological completeness.

Exploration of mathematical concepts in prayer and Mushofahah movements

Knowledge of integration between mathematics and religion is necessary to increase a Muslim's mastery of scientific treasures. This article describes several mathematical concepts contained in prayer movements and Mushofahah. This research is a qualitative descriptive research type of literature review. Data/information collection methods are carried out by observation and documentation. These two methods are used to collect information about mathematical concepts contained in prayer movements and Mushofahah, obtained from several primary and secondary sources in the form of the al-Qur’an, al-Hadith, books, and scientific journals as well as documentation of prayer movements and Mushofahah (shaking hands). The data analysis technique used is content analysis. The research results showed many daily life activities, including prayer and Mushofahah, concrete examples of the integration of mathematics and Islamic religion. These concepts include: In the prayer movement, there were number concepts, which included the addition and multiplication of integers, algebraic concepts in the form of sets, arithmetic sequences, and geometric concepts in the form of lines and angles. Meanwhile, in Mushofahah, there were factorial concepts, permutation concepts, and opportunities.

Class-Based Assessment Concepts: A Comprehensive Study

The assessment carried out by educators on students must be comprehensive and include cognitive, affective, and psychomotor aspects and cannot be looked at from one side only, besides that, it also has certain concepts. One form of the many assessment concepts that can be carried out by educators is class-based assessment. So the purpose of this study is to describe the Class-Based Assessment Concept. This research uses descriptive qualitative techniques with a literature study approach model. The results of the study show that the Class-Based Assessment Concept aims to find detailed information about student learning outcomes. And principled in validity, education, competency-oriented, fair, objective, open, sustainable, comprehensive, and meaningful. So with all that, if there are students who still have not finished their studies, remedial can be done which functions to heal, as well as adaptive, interactive, flexible principles, there is feedback, continuity, and availability in providing services. Then in developing the implementation the educator must explain the material again, students must study independently, then retest, give additional assignments, study groups with teacher guidance, and finally study groups with the guidance of students who have graduated from their studies.

Kant’s Thought Formation and the Role of the Mind: A Groundwork for Development

This paper argues that no form of meaningful development can be discussed without an incursion into the realm of consciousness, from which ideas emanate. This paper demonstrates that human civilization is driven by notions such as ideas, imaginations, concepts, plans, and projects which are germane to social development. An examination of Kant’s theory of concept formation reveals that though objects are given to us by means of sensibility, it is through the understanding that concepts arise. The mind therefore becomes the ‘breeding’ ground from which our ideas are generated and organized. In Kant’s analysis of the faculty of understanding, he noted that there are a priori pure intuitions and sets of categories such as Quality, Relation, Modality that organize particular sensations into unified objects of experience. This capacity of the mind enables it to produce or generate ideas within its own operations. Ideas generated are used to recreate our world. This paper provides a conceptual framework to explicate the foundation of development. Using the method of analysis, this essay concludes that the basis of development − social, economic, and cultural − is hinged on the nature and role of the mind.

Methodology for the formation of elementary quantitative concepts in preschoolers with intellectual disabilities

Methodology for the formation of elementary quantitative concepts in preschoolers with intellectual disabilities

Features of studying and implementing gamification technologies in the practice of teaching a foreign language

Importance. The development of gamification technologies in the practice of teaching activities is considered. The process of formation and development of gamification concepts in domestic and foreign education is analyzed, the main approaches to the specification of the term “gamification” are identified, it is emphasized that gamification, unlike many gaming practices, has a nonimitation nature, where, based on certain rules, an educational result is achieved.Materials and Methods. An overview of the results of foreign empirical studies of gamification is presented, the identified positive effects of technology application and promising directions of its study are shown.Results and Discussion. Structural and content types of gamification are identified, including the main elements and mechanisms of this pedagogical technology. The potential of pedagogical technology in the field of motivational orientation, involvement and immersion of students in the educational process is emphasized. The distinctive features and possible negative trends in the use of gamification in the educational process are identified.Conclusion. Gamification technologies make it possible to implement most didactic principles and implement sociocultural, communicative, self-development, therapeutic, correctional and entertaining pedagogical functions.

СУЧАСНИЙ СТАН НАУКОВОГО ДОСЛІДЖЕННЯ ТА ПЕРСПЕКТИВИ РОЗВИТКУ КРИМІНАЛЬНО-ПРАВОВОЇ БІОГРАФІСТИКИ В УКРАЇНІ

The article analyzes the current state of scientific research in criminal legal biography in Ukraine. The author defines criminal legal biography as a branch of biographical science which studies the peculiarities of formation, formation and development of fundamental criminal law doctrines, ideas, views and concepts of leading criminalists, taking into account their life biography, in particular, public, state, political, scientific and scientific-pedagogical activities. The author identifies the main areas of development of criminal law biography, in particular, writing dissertations, preparing monographic studies, compiling (organizing) editions of selected works and biographies (bibliographies) of leading criminalists. The first area in criminal law biography – conducting dissertation research on the criminal law (including criminological and criminal executive) heritage of prominent representatives of Ukrainian legal science. The second area in criminal legal biography – conducting monographic studies of the peculiarities of the formation and development of individual scientific schools in Ukrainian criminal law, criminology and criminal executive law. The third area in criminal legal biography is the compilation (arrangement) of publications (selected works, selected works, biographies (bibliographies), etc.) covering generalizations of the criminal legal (including criminological and criminal executive) heritage of certain leading representatives of Ukrainian legal science, in particular, containing both the full content and certain fragments of abstracts, articles, monographs, manuals, scientific and practical commentaries, textbooks, etc. The author outlines the prospects for the development of criminal law biography in Ukraine. Key words: biography, science, biographical method, law, research, criminal law heritage, doctrine, ideas, views, concepts, criminal law, criminology, criminal executive law.