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

Complex and noisy financial eco-system requires reliable models and proven techniques to predict the market movements and investor decisions. This study uses competent soft computing techniques: rough set theory (RST) and formal concept analysis (FCA) to study the investors' preferences, behavioural drivers and their actual behaviour in Gold-ETF (G-ETF) market. G-ETF, though a safe-haven and an alternate for reducing portfolio risks, inherits all complexities of financial markets. The employed RST helps in generating decision rules; and FCA to identify key factors affecting investment decision. This study is first of its kind, as integration of the foresaid techniques was not employed to study financial behaviour, earlier. The study has analysed 250 responses of G-ETF investors, in 12 listed G-ETFs, to conclude with a rich insight on the investment decisions discretised by different decision rules, strongly recommending the combined use of RST and FCA for data driven decisions.

Basic relationships between Rough Set Theory (RST) and Formal Concept Analysis (FCA) are discussed. Differences between the “partition oriented” RST and the “order oriented” FCA concerning the possibility of knowledge representation are investigated. The fundamental connection between RST and FCA is that the knowledge bases of RST and the scaled many-valued contexts of FCA are shown to be nearly equivalent.

<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.

Rough set theory is an important tool to deal with imprecise, uncertainty and fuzzy information, and has gained great success in machine learning, data mining and intelligent data analysis. When it was proposed, many researchers worked on it in different views such as constructive methods, algebraic methods, formal concept analysis, and etc. We analyze it in view of entropy theory, and present a new concept - knowledge entropy. We discuss properties of it and apply it to discuss basic concepts in rough set theory. From the analysis, we construct a mapping between knowledge entropy theory and rough set theory, and we also hope to find effective algorithms by the application of it.

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.

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.

Three-way reduction for formal decision contexts

Graded polygons of opposition in fuzzy formal concept analysis

Formal contexts is a common framework for rough set theory and formal concept analysis, and some rough set models in formal contexts have been proposed. In this paper, based on the theory of abstract approximation spaces presented by Cattaneo [1], a Brouwer orthocomplementation on the set of objects of a formal context is presented, as a result, a pair of new lower and upper rough approximation operators is introduced. Comparison between the new approximation operators and the existing approximation operators is made, and two necessary and sufficient conditions about equivalence of the operators are obtained. Relationships and algebraic structures among the definable subsets of these approximation operators are investigated.

The paper examines Formal Concept Analysis (FCA) and Rough Set Theory (RST) against the background of the theory of finite approximations of continuous topological spaces. We define the operators of FCA and RST by means of the specialisation order on elements of a topological space X which induces a finite approximation of X. On this basis we prove that FCA and RST together provide a semantics for tense logic S4.t. Moreover, the paper demonstrates that a topological space X cannot be distinguished from its finite approximation by means of the basic temporal language. It means that from the perspective of topology S4.t is a better account of approximate reasoning then unimodal logics, which have been typically employed.

Creative knowledge discovery—finding useful, previously unknown links between concepts—is a vital tool in unlocking the economic and social value of the vast range of networked data and services that is now available. We define "standard" knowledge discovery as the search for explanatory and predictive patterns in a specific domain, usually with a large volume of data. In contrast, creative knowledge discovery is concerned with the creation of new (and effective) patterns—either by generalization of existing patterns or by analogy to patterns in other domains. An important precondition for creative knowledge discovery is that we understand the relations within the data. Fuzzy formal concept analysis is a powerful approach that enables us to find embedded structure in data and to extract novel concepts that can be used in subsequent processing such as creative knowledge discovery. This paper outlines a fast algorithm for computing fuzzy formal concepts and provides a brief illustration of the use of fuzzy formal concept analysis in creative knowledge discovery.

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints.

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.

Three-way conflict analysis: A unification of models based on rough sets and formal concept analysis

Convergence of information and communication on technology changed the life of a common man over the last few years. At the same time it increases threats to a common man. In order to overcome these situations lots of research is carried out in the direction network and internet security. In addition identification of various attacks is of great challenge before taking any security measures. Identification of phishing attacks such as fake e-mails or websites is one such critical attack in internetworking. It is an illegal trick game that collects personal information from a legitimate user. The fake e-mails or website looking like a true one and even in the web pages where users are asked to send their personal information may look like a legitimate. Identification of such websites, e-mails is one of great challenge today. To this end, in this paper, we propose a model for identification of phishing attacks and chief attributes that make an object phishing object using rough set and formal concept analysis. The concept is explained with an illustration and followed by a case study. The results obtained show the viability of the proposed research.