Finding Fuzzy Concepts for Creative Knowledge Discovery

<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.

Graded polygons of opposition in fuzzy formal concept analysis

Fuzzy Formal Concept Analysis (FFCA) is a robust mathematical tool for analyzing data, particularly where uncertainty or fuzziness is inherent. FFCA is utilized across various domains, including data mining, information retrieval, and knowledge representation. However, fuzzy concepts extraction is a crucial yet computationally intensive task. This paper addresses the challenge of time efficiency in extracting single-sided fuzzy concepts from large datasets. A parallel algorithm is proposed to reduce computational time and optimize resource utilization, thus enabling the scalable analysis of expanding datasets. By computing fuzzy concepts across multiple threads in parallel, each thread processes an attribute independently to extract fuzzy concepts, which are then merged in the final step. The proposed algorithm extracts fuzzy-crisp concepts, which are more concise than other types of fuzzy concepts. Experiments were conducted to evaluate the performance of the proposed parallel algorithm against existing sequential methods. Experimental results demonstrate significant gains in computational efficiency, with the algorithm achieving an average time reduction of 68% compared to the attribute-based algorithm and up to 83%-time reduction compared to the fuzzy CbO algorithm across various types of datasets, including binary, quantitative, and fuzzy.

Similarity Reasoning in the presence of vague information is becoming fundamental in several research areas and, in particular, in the Semantic Web. Fuzzy Formal Concept Analysis (FFCA) is a generalization of Formal Concept Analysis (FCA) for modeling uncertainty information. Although FFCA has become very interesting for supporting different activities for the development of the Semantic Web, in the literature it is usually addressed at a technical level and intended for a restricted audience. This paper proposes a similarity measure for FFCA concepts. The key notions underlying the proposed approach are presented informally, in order to reach a broad audience of readers.

Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis

Conceptual-driven classification for coding advise in health insurance reimbursement

Semantic Web provides a knowledge-based environment that enables information to be shared and retrieved effectively. In this research, we propose the Scholarly Semantic Web for the sharing, reuse and management of scholarly information. To support the Scholarly Semantic Web, we need to construct ontology from data which is a tedious and difficult task. To generate ontology automatically, Formal Concept Analysis (FCA) is an effective technique that can formally abstract data as conceptual structures. To enable FCA to deal with uncertainty in data and interpret the concept hierarchy reasonably, we propose to incorporate fuzzy logic into FCA for automatic generation of ontology. The proposed new framework is known as Fuzzy Formal Concept Analysis (FFCA). In this paper, we will discuss the Scholarly Semantic Web, and the ontology generation process from the FFCA framework. In addition, the performance of the FFCA framework for ontology generation will also be evaluated and presented.

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

Fuzzy formal concept analysis is concerned with formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given and a given property is a matter of degree in a scale L (generally [0,1]). However, the extent to which object o has property a may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale L rather than a precise value. Such formal contexts naturally lead to interval-valued formal concepts. The aim of the paper is twofold. We provide a sound minimal set of requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Godel implication is proposed for building the complete lattice of all interval-valued formal concepts.

This work describes a system for supporting the user in the discovery of semantic web services, taking into account personal requirements and preference. Goal is to model an ad-hoc service request by selecting conceptual terms rather than using strict syntax formats. Through a concept-based navigation mechanism indeed, the user discovers conceptual terminology associated to the web resources and uses it to generate an appropriate service request which syntactical matches the names of input/output specifications. The approach exploits the fuzzy formal concept analysis for modeling concepts and relative relationships elicited from web resources. After the request formulation and submission, the system returns the list of semantic web services that match the user query.

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

The global influence of Big Data is not only growing but seemingly endless.\nThe trend is leaning towards knowledge that is attained easily and quickly from\nmassive pools of Big Data. Today we are living in the technological world that\nDr. Usama Fayyad and his distinguished research fellows discussed in the\nintroductory explanations of Knowledge Discovery in Databases (KDD) predicted\nnearly two decades ago. Indeed, they were precise in their outlook on Big Data\nanalytics. In fact, the continued improvement of the interoperability of\nmachine learning, statistics, database building and querying fused to create\nthis increasingly popular science- Data Mining and Knowledge Discovery. The\nnext generation computational theories are geared towards helping to extract\ninsightful knowledge from even larger volumes of data at higher rates of speed.\nAs the trend increases in popularity, the need for a highly adaptive solution\nfor knowledge discovery will be necessary. In this research paper, we are\nintroducing the investigation and development of 23 bit-questions for a\nMetaknowledge template for Big Data Processing and clustering purposes. This\nresearch aims to demonstrate the construction of this methodology and proves\nthe validity and the beneficial utilization that brings Knowledge Discovery\nfrom Big Data.\n

The aim of the paper is to provide a framework for the automatic generation of topic-based user interfaces for video lectures in MOOCs. The proposed approach leverages on Fuzzy Formal Concept Analysis and Semantic Technologies, which allow the definition of solutions for supporting learners to navigate the fragments of one or more video lectures, by selecting the topics of interest. The exploitation of a Semantic Web vocabulary, namely SKOS, to model topics, and their relationships, enables the interconnection of different video lectures, also belonging to different MOOCs. The high interoperability allowed by Semantic Web technologies enables the integration of different and heterogeneous MOOC Platforms, as well as other Open Repositories. This aspect fosters the capability of learners to self-regulate and to enhance their learning paths in new forms of learning experiences based on exploration.

Destination Management Organisations (DMOs) are driving the sustainability transformation at territorial level. The novel adoption of Fuzzy Formal Concept Analysis to analyse a census survey (n = 109) of Italian DMOs highlights the potential of FFCA to uncover nuanced patterns of sustainability implementation that remain hidden using more conventional methods: the co-existence of operational tourism flows management and strategic efforts aimed at advancing sustainability. This represents not only a methodological innovation and a valuable path to process categorical data from survey designs, but also a novel practice-oriented insight for destination managers aiming at implementing sustainability practices.

This paper describes a system for supporting the user in the discovery of semantic Web services, taking into account personal requirements. Goal is to model an ad-hoc service request by filtering semantic specifications rather than the exploitation of strict syntax formats. Adaptive agent-based techniques help the user to compose his Web service request, exploiting the semantic annotation of the browsed Web resources. This annotation reflects concepts or ontological terms that are relevant for the user services request formulation. Once the request is formulated, the system returns the list of semantic Web services that match the query input and output concepts.