Bipolar fuzzy graph representation of concept lattice (original) (raw)
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Interval-valued fuzzy graph representation of concept lattice
2012
Formal Concept Analysis (FCA) with fuzzy setting has been successfully applied by researchers for data analysis and representation. Reducing the number of fuzzy formal concepts and their lattice structure are addressed as a major issues. In this study, we try to link between interval-valued fuzzy graph and fuzzy concept lattice to overcome from the issue. We show that proposed method reduces the number of fuzzy formal concepts and their lattice structure while preserving specialized and generalized concepts. Proposed ...
Knowledge representation using interval-valued fuzzy formal concept lattice
Formal concept analysis (FCA) is a mathematical framework for data analysis and processing tasks. Based on the lattice and order theory, FCA derives the conceptual hierarchies from the relational information systems. From the crisp setting, FCA has been extended to fuzzy environment. This extension is aimed at handling the uncertain and vague information represented in the form of a formal context whose entries are the degrees from the scale [0, 1]. The present study analyzes the fuzziness in a given many-valued context which is transformed into a fuzzy formal context, to provide an insight into generating the fuzzy formal concepts from the fuzzy formal context. Furthermore, considering that a major problem in FCA with fuzzy setting is to reduce the number of fuzzy formal concepts thereby simplifying the corresponding fuzzy concept lattice structure, the current paper solves the problem by linking an interval-valued fuzzy graph to the fuzzy concept lattice. For this purpose, we propose an algorithm for generating the interval-valued fuzzy formal concepts. To measure the weight of fuzzy formal concepts, an algorithm is proposed using Shannon entropy. The knowledge represented by formal concepts using interval-valued fuzzy graph is compared with entropy-based-weighted fuzzy concepts at chosen threshold.
The study of the L-fuzzy concept lattice.
The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to an example that has been studied by other methods.
Fuzzy formal concept analysis: approaches, applications and issues
Computer Science and Information Technologies
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 infor...
Formal Context Analysis is a mathematical theory that enables us to find concepts from a given set of objects, a set of attributes and a relation on them. There is a hierarchy of such concepts, from which a complete lattice can be made. In this paper we present a generalization of these ideas using fuzzy subsets and fuzzy implications defined from lower semicontinuous t-norms which, under suitable conditions, also results in a complete lattice.
Construction of the L-fuzzy concept lattice
Fuzzy Sets and Systems, 1998
We propose two processes to obtain L-fuzzy concepts based on finite L-fuzzy contexts and the theory of Cousot and Cousot [Pacific J. Math. 82 (1979) 43]. The first algorithm calculates the L-fuzzy concepts derived from an L-fuzzy set and the second one constructs the whole L-fuzzy concept lattice. We also represent graphically the L-fuzzy concept lattice.
The embedding of the formal concept analysis into the L-Fuzzy concept theory.
In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal concept theory where we have constructed the L-Fuzzy concept lattice.
Three-way fuzzy concept lattice representation using neutrosophic set
International Journal of Machine Learning and Cybernetics, 2016
Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neutrosophic set. For this purpose a method is proposed to generate the component wise three-way formal fuzzy concept and their hierarchical order visualization in the fuzzy concept lattice using the properties of neutrosophic graph, neutrosophic lattice, and Gödel residuated lattice with an illustrative example.
Interpretation of Fuzzy Attribute Subsets in Generalized One-Sided Concept Lattices
Journal of information and organizational sciences, 2013
In this paper we describe possible interpretation and reduction of fuzzy attributes in GeneralizedOne-sided Concept Lattices (GOSCL). This type of concept lattices represent generalization ofFormal 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 originalityof 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.