Fuzzy Formal Concept Research Articles

Dynamic updating variable precision three-way concept method based on two-way concept-cognitive learning in fuzzy formal contexts

Cognitive learning and two-way learning are effective knowledge representations, which can simulate the human brain to learn concepts. The combination of both topics has achieved some results and improved conceptual evolution ability in fuzzy formal concept analysis (FFCA), but there are still some shortcomings: 1) FFCA does not consider the flexibility of concepts, which makes it difficult to select suitable concepts; 2) the existing necessary and sufficient concepts fail to learn directly from any information granules; 3) the cognitive learning mechanism ignores to integrate previously acquired knowledge into the present state in the process of dynamic concept learning. To tackle these issues, in this paper, we put forward a novel two-way concept-cognitive learning (TCCL) model based on three-way decision in fuzzy formal contexts. Firstly, we introduce the object and attribute operators to learn variable precision object induced three-way concept, where such concept has flexibility by adjusting thresholds. Then, to learn directly necessary and sufficient three-way concept from the given clues, we investigate a new TCCL model, which has low computation cost for concept learning. Furthermore, updating mechanism of three-way concept is discussed in dynamic learning environment. Finally, the conducted experiments explicate the effectiveness and feasibility of our proposed approach in the large-scale datasets.

Concept-drift detection index based on fuzzy formal concept analysis for fake news classifiers

Unpredictable changes in the underlying distribution of the streaming data over time are known as concept drift. The development of procedures and techniques for drift detection, interpretation, and adaptation is central to concept-drift research. Data research has demonstrated that machine learning in a concept-drift environment produces poor learning results if drift is not handled. This study focuses on defining the concept-drift detection index to predict when the performance of a machine learning model for text-stream classifiers is low. It proposes an index that relies on the Fuzzy Formal Concept Analysis theory. The index exploits the formal lattice to understand whether new incoming facts (e.g., news) are well represented in the training data used to build the machine-learning model. Fake news was deemed ideal for testing this new measure because its typical application scenario required handling a stream of unstructured content and concept-drift awareness. Experiments on three news datasets revealed a relevant correlation (i.e., 73.9 %, 80.8 %, and 81 %) between the Accuracy of Random Forest (RF), Naïve Bayes (NB), and Passive Aggressive (PA) models, respectively, and the proposed index. This strong correlation suggests that the new index can avoid incorrect classifications and help in retraining decisions.

Extracting Concepts From Fuzzy Relational Context Families

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Fuzzy relational formal concept analysis (FRCA)</i> mines collections of fuzzy concept lattices from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fuzzy relational context families</i> , which are special datasets made of fuzzy formal contexts and fuzzy relations between objects of different types. Mainly, FRCA consists of the following procedures: first, an initial fuzzy relational context family is transformed into a collection of fuzzy formal contexts; second, a fuzzy concept lattice is generated from each fuzzy formal context by using one of the techniques existing in the literature. The principal tools to transform a fuzzy context family into a set of fuzzy formal contexts are the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fuzzy scaling quantifiers</i> , which are particular fuzzy quantifiers based on the concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evaluative linguistic expression</i> . FRCA can be applied whenever information needs to be extracted from multirelational datasets including vagueness, and it can be viewed as an extension of both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">relational concept analysis</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fuzzy formal concept analysis</i> . This article contributes to the development of fuzzy relational concept analysis by achieving the following goals. First of all, we present and study a new class of fuzzy quantifiers, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t-scaling quantifiers</i> , to extract fuzzy concepts from fuzzy relational context families. Subsequently, we provide an algorithm to generate, given a t-scaling quantifier, a collection of fuzzy concept lattices from a special fuzzy relational context family, which is composed of a pair of fuzzy formal contexts and a fuzzy relation between their objects. After that, we introduce an ordered relation on the set of all t-scaling quantifiers, which allows us to discover a correspondence among fuzzy concept lattices deriving from different t-scaling quantifiers. Finally, we discuss how the results obtained for t-scaling quantifiers can be extended to the class of fuzzy scaling quantifies. Therefore, this analysis highlights the main differences between t-scaling and fuzzy quantifiers.

Attribute reduction and information granulation in Pythagorean fuzzy formal contexts

Pythagorean fuzzy set theory is one of the significant tools to deal with real-life problems which are prone to imprecision, partial truth or uncertainty. A Pythagorean fuzzy set reports the degree of truthness as well as falsity of a statement in order to illustrate the imprecision of that statement. Motivated by the resourcefulness of this theory, this paper is aimed to explore formal concept analysis in Pythagorean fuzzy environment. It defines Pythagorean fuzzy formal concept and Pythagorean fuzzy concept lattice associated with a Pythagorean fuzzy formal context. The proposed Pythagorean fuzzy formal concept is a duple whose first argument is (crisp) extension and second argument is Pythagorean fuzzy intension. Moreover, the join of different combinations of object concepts of a Pythagorean fuzzy formal context returns different Pythagorean fuzzy formal concepts. We also studied the knowledge reduction in Pythagorean fuzzy formal contexts in association with Pythagorean fuzzy concept lattice. The key ideas of attribute reduct, core and discernibility matrix for a Pythagorean fuzzy formal context are illustrated. Further, we merged the notions of information granulation and attribute reduction with Pythagorean fuzzy formal context. Various results of formal concepts and concept lattices are extended in Pythagorean fuzzy set theory. At last, an algorithm is developed which discovers non-redundant Pythagorean fuzzy formal concepts for a given Pythagorean fuzzy formal context. Eventually, an example is presented which elaborates the procedure of this algorithm.

Incremental concept-cognitive learning approach for concept classification oriented to weighted fuzzy concepts

Fuzzy formal concept analysis (FFCA) is generally used to describe the processes of concept-cognitive learning (CCL). However, for fuzzy formal contexts, each attribute has the same weight (i.e, the same degree of importance) before constructing fuzzy concepts, which limits mining interesting knowledge and affects its application promotion. On the other hand, this model is hard to resist the influence of noise hidden in data, which results in poor classification learning. Moreover, the existing incremental CCL algorithms still face some challenges that the previously acquired knowledge is not fully utilized to improve the classification accuracies for dynamic data. To address these issues, we introduce different weights into fuzzy formal contexts and propose a novel incremental CCL mechanism in dynamic environment. Firstly, weight values of attributes from different decisions based on fuzzy entropy are established to measure the significant degree of attributes. Then, to comprehensively explicate the hierarchical relationships of fuzzy concepts, we construct the weighted fuzzy concept lattice and the weighted fuzzy concept space. Secondly, we design an algorithm to update the weighted fuzzy concepts for facilitating concept classification. To overcome the individual cognitive limitation, we put forward the progressive weighted fuzzy concept to remove repeated information. Furthermore, the classification prediction label and dynamic updating mechanism after adding objects are systematically discussed. Finally, we perform an experimental evaluation on ten data sets which explicate the feasibility and efficiency of our proposed approach.

Attribute reduction in intuitionistic fuzzy formal concepts

Knowledge acquisition in intuitionistic fuzzy information systems is of importance because those fuzzy information systems are often encountered in many real-life problems. Formal concept analysis is a simple and effective tool for knowledge acquisition. However, there is still little work on introducing knowledge acquisition methods based on formal concept analysis into intuitionistic fuzzy information systems. This paper mainly extends the formal concept theory into intuitionistic fuzzy information systems. Firstly, two pairs of adjoint mappings are defined in intuitionistic fuzzy formal contexts. It is verified that both pairs of adjoint mappings form Galois connections. Secondly, two types of intuitionistic fuzzy concept lattices are constructed. After that, we also present the main theorems and propositions of the intuitionistic fuzzy concept lattices. Thirdly, we deeply discuss the attribute characteristics for type-1 generalized one-sided intuitionistic fuzzy concept lattice. Furthermore, a discernibility matrix-based algorithm is proposed for attribute reduction and the effectiveness of this algorithm is demonstrated by a practical example. The construction of intuitionistic fuzzy conceptS is meaningful for the complex and fuzzy information in real life.

Fuzzy formal concept analysis: approaches, applications and issues

Formal concept analysis (FCA) is today regarded as a significant technique for knowledge extraction, representation, and analysis for applications in a variety of fields. Significant progress has been made in recent years to extend FCA theory to deal with uncertain and imperfect data. The computational complexity associated with the enormous number of formal concepts generated has been identified as an issue in various applications. In general, the generation of a concept lattice of sufficient complexity and size is one of the most fundamental challenges in FCA. The goal of this work is to provide an overview of research articles that assess and compare numerous fuzzy formal concept analysis techniques which have been suggested, as well as to explore the key techniques for reducing concept lattice size. as well as we'll present a review of research articles on using fuzzy formal concept analysis in ontology engineering, knowledge discovery in databases and data mining, and information retrieval.

Fuzzy formal concept analysis: approaches, applications and issues

Formal concept analysis (FCA) is today regarded as a significant technique for knowledge extraction, representation, and analysis for applications in a variety of fields. Significant progress has been made in recent years to extend FCA theory to deal with uncertain and imperfect data. The computational complexity associated with the enormous number of formal concepts generated has been identified as an issue in various applications. In general, the generation of a concept lattice of sufficient complexity and size is one of the most fundamental challenges in FCA. The goal of this work is to provide an overview of research articles that assess and compare numerous fuzzy formal concept analysis techniques which have been suggested, as well as to explore the key techniques for reducing concept lattice size. as well as we'll present a review of research articles on using fuzzy formal concept analysis in ontology engineering, knowledge discovery in databases and data mining, and information retrieval.

Graded cubes of opposition in fuzzy formal concept analysis

We recently introduced special fuzzy quantifiers named quantifier-based operators to form extended fuzzy concept lattices and to construct graded squares, hexagons, octagons and decagons of oppositions. This article aims to extend our previous works by organizing quantifier-based operators in more general structures of oppositions: the so-called graded cubes of opposition and 5-graded cubes of opposition.

Covid-19 sentiments in smart cities: The role of technology anxiety before and during the pandemic

The spread of Covid-19 profoundly changed citizens' daily lives due to the introduction of new modes of work and access to services based on smart technologies. Although the relevance of new technologies as strategic levers for crisis resolution has been widely debated before the pandemic, especially in the smart cities' context, how individuals have agreed to include the technological changes dictated by the pandemic in their daily interactions remains an open question. This paper aims at detecting citizens' sentiment toward technology before and after the emergence of the Covid-19 pandemic using Fuzzy Formal Concept Analysis (FFCA) to analyze a large corpus of tweets. Specifically, citizens' attitudes in five cities (Berlin, Dublin, London, Milan, and Madrid) were explored to extract and classify the key topics related to the degree of confidence, familiarity and approval of new technologies. The results shed light on the complex technology acceptance process and help managers identify the potential negative effects of smart technologies. In this way, the study enhances scholars' and practitioners' understanding of the strategies for enabling the use of technology within smart cities to manage the transformations introduced by the health emergency and guide citizens’ behaviour.

Skyline refinement exploiting fuzzy formal concept analysis

PurposeThe study of the skyline queries has received considerable attention from several database researchers since the end of 2000's. Skyline queries are an appropriate tool that can help users to make intelligent decisions in the presence of multidimensional data when different, and often contradictory criteria are to be taken into account. Based on the concept of Pareto dominance, the skyline process extracts the most interesting (not dominated in the sense of Pareto) objects from a set of data. Skyline computation methods often lead to a set with a large size which is less informative for the end users and not easy to be exploited. The purpose of this paper is to tackle this problem, known as the large size skyline problem, and propose a solution to deal with it by applying an appropriate refining process.Design/methodology/approachThe problem of the skyline refinement is formalized in the fuzzy formal concept analysis setting. Then, an ideal fuzzy formal concept is computed in the sense of some particular defined criteria. By leveraging the elements of this ideal concept, one can reduce the size of the computed Skyline.FindingsAn appropriate and rational solution is discussed for the problem of interest. Then, a tool, named SkyRef, is developed. Rich experiments are done using this tool on both synthetic and real datasets.Research limitations/implicationsThe authors have conducted experiments on synthetic and some real datasets to show the effectiveness of the proposed approaches. However, thorough experiments on large-scale real datasets are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.Practical implicationsThe tool developed SkyRef can have many domains applications that require decision-making, personalized recommendation and where the size of skyline has to be reduced. In particular, SkyRef can be used in several real-world applications such as economic, security, medicine and services.Social implicationsThis work can be expected in all domains that require decision-making like hotel finder, restaurant recommender, recruitment of candidates, etc.Originality/valueThis study mixes two research fields artificial intelligence (i.e. formal concept analysis) and databases (i.e. skyline queries). The key elements of the solution proposed for the skyline refinement problem are borrowed from the fuzzy formal concept analysis which makes it clearer and rational, semantically speaking. On the other hand, this study opens the door for using the formal concept analysis and its extensions in solving other issues related to skyline queries, such as relaxation.

Graded polygons of opposition in fuzzy formal concept analysis

Quantifier-based operators are fuzzy quantifiers that are, similarly to the intermediate quantifiers, based on the evaluative linguistic expressions not small, very big and extremely big. This article focuses mainly on achieving two goals. Firstly, quantifier-based operators are introduced to create extended fuzzy concept lattices that capture more detailed information from datasets compared to the existing ones. Then, graded extensions of Aristotle's square, named polygons of opposition, are constructed using quantifier-based operators. Our results highlight new connections between three different research areas: the theory of evaluative linguistic expressions, fuzzy formal concept analysis, and the studies on Aristotle's square.1

Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis

Measuring semantic similarity/semantic relatedness is an important task in computational linguistic, natural language processing and ontology creation. In this paper, a new hybrid method using LSA and FFCA is proposed for computing the semantic-relatedness. Latent semantic analysis (LSA) is used to extract the attributes of the concepts and these attributes are further mapped to FFCA to compute semantic relatedness. The latent semantic analysis is used for finding the neighbouring words or attributes and their correlation value. The concepts and their attributes are mapped to FCA table and then to FFCA table by using the correlation value as membership. A fuzzy similarity measure is then used to compute the semantic relatedness between these concepts/words. The proposed method is evaluated on word similarity bench mark dataset WS-353 and found an accuracy of 0.85.

Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis

Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis

Reducing concept lattices by means of a weaker notion of congruence

Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based on the notion of congruence on lattices, with the goal of losing as less information as possible and being suitable for the reduction of concept lattices. We analyze how the equivalence classes obtained from a local congruence can be ordered. Moreover, different properties related to the algebraic structure of the whole set of local congruences are also presented. Finally, a procedure to reduce concept lattices by the new weaker notion of congruence is introduced. This procedure can be applied to the classical and fuzzy formal concept analysis frameworks.

Pharmacovigilance in the era of social media: Discovering adverse drug events cross-relating Twitter and PubMed

In pharmacovigilance, post-marketing surveillance is mainly supported by spontaneous reporting systems (SRS) collecting adverse drug events explicitly submitted by physicians alerted by their patients. Nowadays, this activity could leverage on mining opinions and experiences of individuals from social media by monitoring users’ posts citing symptoms, drugs, etc. The most critical problem is the reliability of the information sources. In order to address this challenge, the proposed method tries to cross-relate heterogeneous data sources with correspondingly different levels of trustworthiness. It filters out assertions quoted on social media on the basis of data validated by official information sources. The method adopts the Fuzzy Formal Concept Analysis (Fuzzy FCA) to evaluate the reliability of adverse drug events extracted on Twitter and PubMed. It keeps track of the difference between the co-citation frequencies by calculating a residual thresholdτ. The main outcome is that with τ in the range [−4,+4], 91% of drug and side effect correlations extracted from tweets can be considered reliable, according to the official site (we used http://sideeffects.embl.de).

A conversational recommender system for diagnosis using fuzzy rules

Graded implications in the framework of Fuzzy Formal Concept Analysis are used as the knowledge guiding the recommendations. An automated engine based on fuzzy Simplification Logic is proposed to make the suggestions to the users. Conversational recommender systems have proven to be a good approach in telemedicine, building a dialogue between the user and the recommender based on user preferences provided at each step of the conversation. Here, we propose a conversational recommender system for medical diagnosis using fuzzy logic. Specifically, fuzzy implications in the framework of Formal Concept Analysis are used to store the knowledge about symptoms and diseases and Fuzzy Simplification Logic is selected as an appropriate engine to guide the conversation to a final diagnosis. The recommender system has been used to provide differential diagnosis between schizophrenia and schizoaffective and bipolar disorders. In addition, we have enriched the conversational strategy with two strategies (namely critiquing and elicitation mechanism) for a better understanding of the knowledge-driven conversation, allowing user’s feedback in each step of the conversation and improving the performance of the method.

Fuzzy Implication and Functional Dependency on Formal Context

Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.

A New Methodology for Computing Semantic Relatedness: Modified Latent Semantic Analysis by Fuzzy Formal Concept Analysis

Semantic similarity is used to perceive the meaning of words in textual data and having several applications in the field of Computational linguistic and Natural language processing. Semantic similarity and semantic relatedness are interchangeable terms, in Semantic relatedness all types of semantic relationships are considered i.e. (has, part-of, contains etc.) whereas in semantic similarity only “is-a” type of relationship is used. Computing accurate similarity improves the efficiency of query processing and understanding of textual data more proficiently. In this work, a novel hybrid approach of corpus based and knowledge based method is proposed approach to compute the semantic relatedness among words. In this hybrid method, Latent semantic analysis is used to find the concepts and their correlation value and mapping is done for different words with the help of fuzzy formal concept analysis.To compute semantic relatedness on different words a fuzzy set similarity measure is used.The proposed approach has been evaluated on solar domain and attains improved results as compared to other baseline measures. This method can be used for any doamin as it is a generalized approach for similarity computation.

Hesitant fuzzy graphs, hesitant fuzzy hypergraphs and fuzzy graph decisions1

Up to now, there have been a lot of research results about multi-attribute decision making problems by fuzzy graph theory. However, there are few investigations about multi-attribute decision making problems under the background of indecisiveness. The main reason is that the difference of cognition and the complexity of thinking by decision makers, for the same question have different opinions. In this paper, we proposed a hesitant fuzzy hypergraph model based on hesitant fuzzy sets and fuzzy hypergraphs. At the same time, some basic graph operations of hesitant fuzzy hypergraphs are investigated and several equivalence relationship between hesitant fuzzy hypergraphs, hesitant fuzzy formal concept analysis and hesitant fuzzy information systems are discussed. Since granular computing can deal with multi-attribute decision-making problems well, we considered the hesitant fuzzy hypergraph model of granular computing, and established an algorithm of multi-attribute decision-making problem based on hesitant fuzzy hypergraph model. Finally an example is given to illustrate the effectiveness of the algorithm.