Fuzzy Concept Lattice Research Articles

Rule extraction based on linguistic-valued intuitionistic fuzzy layered concept lattice

As one of the research tools for data processing and knowledge discovery, concept lattice can effectively extract information. In daily life, due to the ambiguity and uncertainty of the decision environment, different experts may provide different evaluation information according to individual needs which may be expressed with linguistic values. In order to handle these problems, we study the rule extraction method of linguistic-valued intuitionistic fuzzy layered concept lattice. First, we propose a linguistic-valued intuitionistic fuzzy formal decision context based on the intuitionistic fuzzy lattice implication algebra, which can simultaneously process the obtained comparable and incomparable linguistic information from both positive and negative aspects. Furthermore, by setting different linguistic-valued trust degrees, we put forward the linguistic-valued hierarchical concept construction operator. On this basis, a linguistic-valued intuitionistic fuzzy layered concept lattice can be constructed to meet the requirements of different experts at different levels. And then through the relationship between the conditional concept and decision concept in the obtained concept set, we get a rule set of the formal decision context. Finally, we present a rule extraction method to help people make more reasonable decisions, combining the confidence and support degree of linguistic-valued intuitionistic fuzzy decision rules. And a practical example involving individual financial investment decision-making is used to verify the efficiency and applicability of the proposed approach.

Single-valued Plithogenic graph for handling multi-valued attribute data and its context

Recently, several researchers paid attention to dealing with uncertainty in data with neutrosophic attributes. In this process, a problem is addressed while dealing with contradiction and its impact on decision-making. It is considered as one of the major issues for data science researchers working in a three-way fuzzy concept lattice. To deal with this issue, the current paper tried to introduce the algebra of a single-valued Plithogenic graph and its visualization based on infimum and supremum. The proposed method is also demonstrated with an illustrative example for better understanding.

Variable-precision three-way concepts in L-contexts

The notion of fuzzy concept is proposed to deal with object-attribute data with L-values (where L is a truth-value structure). One disadvantage of fuzzy concept is that a fuzzy context contains a considerable number of fuzzy concepts. This makes it very time-consuming to generate a fuzzy concept lattice, and it is very difficult to find important concepts. In addition, the fuzzy concept shows great strictness when applying to crisp sets. To overcome these problems, we propose several new kinds of variable-precision concepts within L-contexts in this paper. First, we present two kinds of variable-precision two-way (VP2W) concepts: α-positive concept and β-negative concept. The family of each kind of VP2W concept forms a complete lattice. Next, considering both the positive and negative parts, we investigate two kinds of variable-precision three-way (VP3W) concepts: (α,β)-object-induced three-way concept and (α,β)-attribute-induced three-way concept. The family of each kind of VP3W concept forms a complete lattice. Then, we study the relationships between VP2W concepts and VP3W concepts. The results show that VP3W concept lattices can be directly generated by VP2W concept lattices. Finally, the experiments are preformed to verify the effectiveness of our model.

Research on the Intelligent Fault Diagnosis of Medical Devices Based on a DEMATEL-Fuzzy Concept Lattice

Hospitals’ daily operations have become increasingly dependent on medical devices. However, the occurrence of faults is inevitable. Therefore, it is crucial for hospitals to make timely fault diagnoses and enact the corresponding measures and improvements. This paper proposes a novel concept lattice method for the intelligent diagnosis of medical device faults. To minimize the influence of uncertain factors, fuzzy sets are used to accurately express relationships between concepts. First, the occurrence frequency and severity of each fault type are extracted based on the collected information. Then, the fuzzy formal context of occurrent faults and known faults can be constructed. Next, the corresponding fuzzy concept lattice is established and visualized using a Hasse diagram. Finally, the similarity between the concept lattices is calculated and used for fault diagnosis. Here, the weight factors are determined using the decision-making trial and evaluation laboratory (DEMATEL) method. A comparative analysis is performed to show that the proposed method uses simple calculations and is highly accurate.

Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degree

As an important expanded of the classical formal concept, the three-way formal concept analysis integrates more information with the three-way decision theory. However, to the best of our knowledge, few scholars have studied the intuitionistic fuzzy three-way formal concept analysis. This paper proposes an intuitionistic fuzzy three-way formal concept analysis model based on the attribute correlation degree. To achieve this, we comprehensively analyze the composition of attribute correlation degree in the intuitionistic fuzzy environment, and introduce the corresponding calculation methods for different situations, as well as prove the related properties. Furthermore, we investigate the intuitionistic fuzzy three-way concept lattice ((IF3WCL) of object-induced and attribute-induced. Then, the relationship between the IF3WCL and the positive, negative and boundary domains in the three-way decision are discussed. In addition, considering the final decision problem of boundary objects, the secondary decision strategy of boundary objects is obtained for IF3WCL. Finally, a numerical example of multinational company investment illustrates the effectiveness of the proposed model. In this paper, we systematically study the IF3WCL, and give a quantitative analysis method of formal concept decision along with its connection with three-way decision, which provides new ideas for the related research.

Hesitant Fuzzy Concept Lattice and its Application

The hesitant fuzzy set (HFS) can reflect the hesitation and uncertainty of decision-makers for the reason that it uses some possible values instead of a certain value. Considering that there is still no research on concept lattice or fuzzy formal concept analysis (FFCA) in a hesitant fuzzy environment, in this paper, we propose the definition and the related theory of hesitant fuzzy concept lattice. Firstly, we propose the hesitant fuzzy formal concept analysis theory and study the definition of hesitant fuzzy concept lattice. Secondly, we provide two effective reduction methods of hesitant fuzzy formal context and discuss the differences of them. Thirdly, we propose an incremental construction algorithm to construct the hesitant fuzzy concept lattice. After that, we study the similarity calculation method of hesitant fuzzy concepts. Finally, we design a practical application to validate the hesitant fuzzy concept lattice theory, which is proven to be correct and effective.

Generation of proto-fuzzy concepts from fixpoints of fuzzy closure operators

It is well known in Formal Concept Analysis that computation of all formal concepts from data table with graded attributes can be reduced to the problem of computing fixpoints of two fuzzy closure operators, ↑↓ and ↓↑. It is also true that as the size of datasets grows, the fuzzy concepts generated from fuzzy context become larger in number. Therefore for large and complex datasets, it is very hard to deal with such a large number of fuzzy concepts. To handle large and complex datasets, several alternative approaches were proposed to the fuzzy concept lattice theory by researchers. The fuzzy concepts introduced by Kridlo et al (2008) are known as proto-fuzzy concepts. In point of view of applications in different domain, significance of proto-fuzzy concepts is very much effective. But as far as our knowledge is concerned, there is no general method to generate proto-fuzzy concepts. In this paper, we present an algorithm for finding proto-fuzzy concepts directly from the input data. The algorithm we present generates proto-fuzzy concepts form the fixpoints of the fuzzy closure operators, ↑↓ and ↓↑.

基于直觉模糊概念格的新型病毒分类方法

基于直觉模糊概念格的新型病毒分类方法

Knowledge structure preserving fuzzy attribute reduction in fuzzy formal context

Attribute reduction is an important and even crucial pre-processing step in knowledge achievement. Existing fuzzy attribute reduction methods in Formal Concept Analysis tend to remove the redundant attributes that preserve the invariability of algebraic structures, and thus might distort the knowledge structures underlying fuzzy formal contexts. To avoid the issue, this paper presents a fuzzy attribute reduction approach of preserving the invariability of knowledge structure, and discusses some properties of fuzzy attribute reduct under the choice of hedges. We also propose an algorithm for computing fuzzy attribute reduct using Łukasiewicz adjoint operators and hedge. Compared with the previous approaches, our approach is based on the widely accepted framework, fuzzy concept lattice with hedge, and has the capability of producing a vector, specifying a significance degree for each attribute.

Unlabelled text mining methods based on two extension models of concept lattices

Concept lattice is a useful tool for text extraction. The common text clustering method fails to generate hierarchical relationships among categories and realize soft clustering simultaneously, while the concept lattice ignores the negative correlation between an object subset and an attribute subset. Motivated by the problems, we propose unlabelled text mining methods based on fuzzy concept lattice and three-way concept lattice. Firstly, we excavate hierarchical text categories to construct a classification system based on fuzzy concept lattice, and the labelled samples are obtained by the word matching method. Then, we construct a three-way concept lattice to get positive and negative classification rules based on the labelled samples, and the classifier is constructed to predict the new samples. Finally, Sogou laboratory news corpus is used to evaluate the efficiency of text clustering and classification methods. The results demonstrate that the improved clustering method has a higher average cluster goodness than earlier procedures and the classification model based on three-way concept lattice achieves a higher accuracy.

A method of multimedia teaching evaluation based on fuzzy linguistic concept lattice

With the development of multimedia technology, multimedia based teaching has become a popular style for educations. However, multimedia teaching evaluation performance is not an easy task as it involves human decision making which is imprecise, vague and uncertain. In order to acquire the effect of multimedia teaching in incomplete formal context, this paper mainly focuses on an algorithm of rule extraction based on incomplete multi-expert fuzzy linguistic formal decision context. Specifically, we propose a kind of fuzzy linguistic concept lattice combining with fuzzy linguistic information in uncertainty linguistic environment. The corresponding confidence level, the support degree of linguistic decision rules in fuzzy linguistic decision concept are discussed. Based on fuzzy linguistic formal context, we construct a multi-expert fuzzy linguistic concept lattice to handle multi-expert linguistic evaluation information. To address the scenario that the experts’ weights are unknown, we present a maximization deviation method in multi-expert fuzzy linguistic formal context through the distance of linguistic evaluation matrix. Furthermore, we develop a linguistic aggregation operator of multi-expert fuzzy linguistic concept lattice to obtain the association rules. A novel linguistic completing method using similarity and average difference is proposed to deal with the information missing problem, which can make the linguistic evaluation information more compact and the decision results more reasonable. We validate the effectiveness and practicability of our method via an intuitive example of multimedia teaching evaluation.

The construction of fuzzy concept lattice based on weighted complete graph

The construction of fuzzy concept lattice based on weighted complete graph

Complex multi-fuzzy context analysis at different granulation

The m-p olar fuzzy graph representation of concept lattice gives a way to deal with its periodic changes at a given phase of time. One of the suitable examples is opinion of reviewers towards acceptance and rejection of a manuscript used to change several times for a given journal. Dealing with these types of m-polar complex fuzzy attributes is a crucial task for the data analytic researchers. The first problem arises with its precise mathematical representation and second with its algebraic processing for knowledge discovery tasks. In this regard, the calculus of complex multi-fuzzy set and its granulation is introduced for handling complex multi-fuzzy context and its graphical traversal. The information obtained from the proposed methods is also analyzed with recently introduced mathematical model on m-polar fuzzy set as well as complex fuzzy concept lattice.

Single-valued neutrosophic context analysis at distinct multi-granulation

In the current era, most of the researchers addressed an issue while dealing with uncertainty and indeterminacy that exists in fuzzy attributes. It becomes more complex when indeterminacy exists independently when compared to acceptation and rejection part. Due to which, some of the researchers tried to develop a three-way fuzzy concept lattice using neutrosophic set for characterization of uncertainty based on its acceptation, rejection, and uncertain parts, independently. In this process, a problem was addressed while processing the neutrosophic context based on user-required subset of attributes. It takes more time to extract interesting pattern from a given neutrosophic context having a large number of attributes. One of the solutions is to decompose the neutrosophic context via a defined multi-granulation for the truth, falsity and indeterminacy, membership values. To accomplish this task, a method is proposed in this paper using the computing paradigm of granular computing and applied lattice theory with an example.

Multi-Granulation-Based Graphical Analytics of Three-Way Bipolar Neutrosophic Contexts

Recently, a three-way fuzzy concept lattice and its graphical structure analytics has given a mathematical way to deal with cognitive concept learning based on its truth, false, and uncertain regions, independently. In this process, a major problem was addressed while existence of bipolar information in a three-way decision space. To address this problem, the current paper aimed at introducing bipolar neutrosophic graph representation of concept lattice and its granular-based processing for cognitive concept learning. In addition, the proposed method is illustrated with an example for better understanding. Cognitive computing provides a way to mimic with human brain and its uncertainty beyond the binary values. To characterize these types of bipolar attributes based on its acceptation, rejection, and uncertain part, the three-way bipolar neutrosophic context and its concept lattice is introduced in this paper. In addition, another method is proposed to extract some of the bipolar cognitive concepts based on user required bipolar truth, bipolar indeterminacy, and falsity membership values, independently. This paper provides a graphical structure visualization of the three-way bipolar information at user defined granules. It is also shown that the extracted information from both of the proposed methods are concordant with each other. It is also shown that, the proposed method provides an adequate way to model the three-way bipolar cognitive concepts when compared to other available approaches. This paper introduces a method to model the three-way bipolar cognitive context using the properties of bipolar neutrosophic graph and its lattice structure. The line diagram is drawn based on their lower neighbors within O(|C| n2 m3) time complexity. In addition, another method is proposed to refine the three-way bipolar neutrosophic cognitive concepts at user defined granulation within O(n6) or O(m6) time complexity with an illustrative example. However, the proposed method is unable to measure the changes in the three-way bipolar neutrosophic cognitive concepts at the given phase of time. Due to that, the author will focus on resolving this issue of bipolar neutrosophic context in near future.

Fuzzy Parameterized Complex Multi-Fuzzy Soft Expert Set Theory and Its Application in Decision-Making

Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set ( F P - CMFSES ), and investigate part of its fundamental properties. This F P - CMFSES model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among F P - CMFSES and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making.

Granular-based decomposition of complex fuzzy context and its analysis

The mathematical paradigm of complex fuzzy concept lattice gives a platform to analyze the complex fuzzy attributes. The problem is addressed by several reviewers about applications of complex fuzzy concept lattice and its decomposition at user-required information granules. To resolve this problem, one of the methods is introduced using the chosen subset of attributes and properties of granulation defined for amplitude and phase term, independently. One of the real-life applications is also given for analyzing the potential manuscripts for the publications in journal based on changes in reviewer feedback at given phase of time.

Green Credit Product Design Based on Fuzzy Concept Lattice

In recent years, China's rapid development has brought severe environmental problems. We need to vigorously support the development of green credit and strive to innovate green credit products. Aiming at the diversity and ambiguity of green credit evaluation indicators, we propose a green credit product design method based on fuzzy concept lattice. Firstly, we improve the theory of fuzzy formal concept analysis and design a construction algorithm based on non-repetitive attribute set. Secondly, the reference information about green industries from different sources is added into a fuzzy formal context, and then the fuzzy concept lattice structure is generated by the construction algorithm based on non-repetitive attribute set. Thirdly, we propose a clustering method which considers the weights of attributes to reduce the size of the fuzzy concept lattice, and we use the relaxation error to evaluate the performance of the fuzzy concepts. Finally, we design some green credit products according to the results of the methods proposed in this paper, which are proved to be correct and effective.

A novel fuzzy rule extraction approach using Gaussian kernel-based granular computing

In this paper, we present a novel fuzzy rule extraction approach by employing the Gaussian kernels and fuzzy concept lattices. First we introduce the Gaussian kernel to interval type-2 fuzzy rough sets to model fuzzy similarity relations and introduce a few concepts and theorems to improve the classification performance with fewer attributes accordingly. Based on this idea, we propose a novel attribute reduction algorithm, which can achieve better classification performance of deducing reduction subset of fewer attributes, and this will be used in the subsequent decision rule extraction. Then we justify the necessary and sufficient conditions of our fuzzy rule extraction approach through three implicit rule theorems and present a novel fuzzy decision rule extraction algorithm using fuzzy concept lattices and introduce the concepts of frequent nodes and candidate 2-tuples to our pruning strategy. Also, comparative performance experiments are carried out on the UCI datasets, and the results of both reduction subset size and classification ability show the advantages of our algorithm.

Bipolar $$\delta$$δ-equal complex fuzzy concept lattice with its application

Recently, bipolar as well as vague concept lattice visualization is introduced for precise representation of inconsistency and incompleteness in data sets based on its acceptation and rejection part simultaneously. In this process, a problem is addressed while measuring the periodic fluctuation in bipolar information at the given phase of time. This changes in human cognition used coexist often in our daily life where the sentiments (i.e., love or hatred) for anyone may change several times from morning to evening office time. In this case precise representation of this type of bipolar information and measuring its pattern is a major issue for the researchers. To deal with this problem, the current paper proposes three methods for adequate representation of bipolar complex data set using the calculus of complex fuzzy matrix, $$\delta$$-equality and the calculus of granular computing, respectively. Hence, the proposed method provides an umbrella way to navigate or decompose the bipolar complex data sets and their semantics using an illustrative example. The results obtained from the proposed methods are also compared to validate the results.