Attribute reduction in generalized one-sided formal contexts

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.

Characterizing One-Sided Formal Concept Analysis by Multi-Adjoint Concept Lattices

Managing and extracting information from databases is one of the main goals in several fields, as in Formal Concept Analysis (FCA). One-sided concept lattices and multi-adjoint concept lattices are two frameworks in FCA that have been developed in parallel. This paper shows that one-sided concept lattices are particular cases of multi-adjoint concept lattices. As a first consequence of this characterization, a new attribute reduction mechanism has been introduced in the one-side framework.

Formal context reduction in deriving concept hierarchies from corpora using adaptive evolutionary clustering algorithm star

It is beneficial to automate the process of deriving concept hierarchies from corpora since a manual construction of concept hierarchies is typically a time-consuming and resource-intensive process. As such, the overall process of learning concept hierarchies from corpora encompasses a set of steps: parsing the text into sentences, splitting the sentences and then tokenising it. After the lemmatisation step, the pairs are extracted using formal context analysis (FCA). However, there might be some uninteresting and erroneous pairs in the formal context. Generating formal context may lead to a time-consuming process, so formal context size reduction is require to remove uninterested and erroneous pairs, taking less time to extract the concept lattice and concept hierarchies accordingly. In this premise, this study aims to propose two frameworks: (1) A framework to review the current process of deriving concept hierarchies from corpus utilising formal concept analysis (FCA); (2) A framework to decrease the formal context’s ambiguity of the first framework using an adaptive version of evolutionary clustering algorithm (ECA*). Experiments are conducted by applying 385 sample corpora from Wikipedia on the two frameworks to examine the reducing size of formal context, which leads to yield concept lattice and concept hierarchy. The resulting lattice of formal context is evaluated to the standard one using concept lattice-invariants. Accordingly, the homomorphic between the two lattices preserves the quality of resulting concept hierarchies by 89% in contrast to the basic ones, and the reduced concept lattice inherits the structural relation of the standard one. The adaptive ECA* is examined against its four counterpart baseline algorithms (Fuzzy K-means, JBOS approach, AddIntent algorithm, and FastAddExtent) to measure the execution time on random datasets with different densities (fill ratios). The results show that adaptive ECA* performs concept lattice faster than other mentioned competitive techniques in different fill ratios.

On Bonds for Generalized One-Sided Concept Lattices

The generalized one-sided concept lattices represent a generalization of the classical FCA method convenient for a hierarchical analysis of object-attribute models with different types of attributes. The mentioned types of object-attribute models are formalized within the theory as formal contexts of a certain type. The aim of this paper is to investigate some intercontextual relationships represented by the notion of bond. A composition of bonds is defined in order to introduce the category of formal contexts with bonds as morphisms. It is shown that there is a one-to-one correspondence between bonds and supremum preserving mappings between the corresponding generalized one-sided concept lattices. As the main theoretical result it is shown that the introduced category of formal contexts with bonds is equivalent to the category of complete lattices with supremum preserving mappings as morphisms.

Attribute reduction of SE-ISI concept lattices for incomplete contexts

Three-way concept analysis in incomplete contexts lays the theory dealing with the data in incomplete contexts, especially three kinds of partially known formal concepts including SE-ISI formal concept, ISE-SI formal concept and ISE-ISI formal concept. Generally speaking, not every attribute is essential in an incomplete context since the purpose of research is different. Thus, we propose four kinds of attribute reduction of SE-ISI concept lattices based on different criteria. Then, we discuss the relationships among the four kinds of attribute reduction, including the relationships among the consistent sets and relationships among the reducts. Finally, based on discernibility matrices and discernibility functions, the approaches to obtaining these attribute reduction are presented.

Impact of Local Congruences in Attribute Reduction

Local congruences are equivalence relations whose equivalence classes are convex sublattices of the original lattice. In this paper, we present a study that relates local congruences to attribute reduction in FCA. Specifically, we will analyze the impact in the context of the use of local congruences, when they are used for complementing an attribute reduction.