Formal Decision Contexts Research Articles

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.

Concurrent concept-cognitive learning model for classification

Concept-cognitive learning (CCL) concerns the manner in which to incorporate new information into itself by mimicking human cognitive processes. Numerous CCL systems have been proposed to meet different requirements based on formal concept analysis. However, most of these can only operate effectively on small-scale datasets and lack classification ability. To overcome these two challenges, based on a regular formal decision context and multi-thread technique, a new concurrent CCL model is proposed in this study as an extension of classical CCL. More precisely, to enhance computational efficiency, a new concurrent learning framework is designed and its corresponding learning algorithms at the initial concept construction and CCL stages are developed. We propose a concurrent incremental learning technique by continuously accommodating newly added data to meet the requirements of classification tasks. Finally, experiments on various datasets, including real-world and synthetic data, demonstrate that the proposed concurrent method can achieve comparable classification effectiveness and significantly improve the concept learning performance simultaneously.

Local attribute reductions of formal contexts

Attribute reductions is an important topic in formal concept analysis. The existing attribute reduction approaches are dominated by global reductions and there is very limited investigation on local reductions. This paper is devoted to the study of decision rule specific reduction for formal decision context and concept specific reduction for formal context. The notion of decision rule specific reduction is proposed and the related reduction methods are presented. The relationships between existing reduction approaches and decision rule specific reduction approaches are analyzed. Accordingly, we make an analysis of attributes based on three-way classification by using reductions. Furthermore, the notion of concept specific reduction for formal context is proposed and the concept specific reduction methods are examined. The relationship between concept specific reduction and decision rule specific reduction is surveyed.

The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context.

Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.

Attribute reduction and rule acquisition of formal decision context based on object (property) oriented concept lattices

The study of concept lattices, property oriented concept lattices and object oriented concept lattices provides complementary conceptual structures, which can be used to search, analyze and extract information from data sets. This paper is devoted to the study of rule acquisition and attribute reduction of formal decision context. Based on object oriented concepts and property oriented concepts, the notions of object oriented decision rules and property oriented decision rules are proposed. By using some equivalence relations on the set of extents of the related conditional concept lattices and decision concept lattices, the rule acquisition methods are presented. The attribute reduction approaches for formal decision context to preserve the object oriented decision rules and property oriented decision rules are put forward by using discernibility attributes.

A fast attribute reduction method for large formal decision contexts

Attribute reduction in formal decision contexts is an important issue in formal concept analysis, which can help us to discover the knowledge hidden in formal decision contexts. However, most reduction methods in formal decision contexts are very time-consuming due to two main problems. The first is that one needs to construct a discernibility matrix after generating all the formal concepts of formal decision contexts. This is not an easy task because it requires much more storage space and computation time. Another problem is that most reduction methods are based on the Boolean reasoning and the computational complexity of which is exponential in the worst case. To overcome these problems, we propose a new attribute reduction method for formal decision contexts in this paper. A more simplified discernibility matrix which does not need to generate all the formal concepts is first constructed. It shows that the storage space and computation time are far less than the original method. Furthermore, different from the Boolean reasoning method, an approximation algorithm for obtaining a minimum reduct in formal decision contexts based on graph theory is designed. Finally, experiments are carried out to verify the effectiveness of the proposed method. The results, on 22 large data sets, demonstrate that the proposed method not only produces smaller subset of attributes but also has better performance in both storage space and speed.

A graph approach for knowledge reduction in formal contexts

Knowledge reduction in formal concept analysis (FCA) is an important procedure for knowledge processing and data analysis. Currently, the knowledge reduction in FCA based on granular computing (GrC) provides another way to analyze and represent the structure of concept lattices. However, the granular reduction method is based on Boolean reasoning and thus is an NP-hard problem. It is therefore natural to develop some heuristic methods to deal with this problem especially for the large data. In this paper, a new framework based on graph theory is used to study the granular reduction in FCA. A graph representation for the granular reduction is first investigated. The results in this paper show that the granular reduction computation in FCA can be translated into a graph optimization problem. Two new heuristic graph-based algorithms for the granular reduction in formal contexts and formal decision contexts are then respectively presented. Furthermore, numerical experiments are conducted to evaluate the effectiveness of the proposed methods.

Rule acquisition and optimal scale selection in multi-scale formal decision contexts and their applications to smart city

In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward three new types of rules: decision association rules, non-redundant decision association rules and simplest decision association rules. Then, we analyze the relationship among these three types of rules, and develop methods to acquire them from single-scale formal decision contexts. Some numerical experiments are also conducted to compare the performance of the method of acquiring the simplest decision association rules with that of the existing one of acquiring the non-redundant decision rules. Moreover, the new three types of rules are employed to introduce three types of consistencies in multi-scale formal decision contexts. In addition, the notion of an optimal scale is defined by each type of consistency, and how to select an optimal scale is investigated as well. Finally, two applications in smart city for the proposed rule acquisition and optimal scale selection methods are applied to smart city.

Attribute Reduction in Property Oriented Concept Lattices of Formal Contexts and Formal Decision Contexts

This paper studies notions and approaches to attribute reduction in property oriented concept lattices of formal contexts and formal decision contexts based on congruence relations. Firstly, dependence space based on the property oriented concept lattice is researched to obtain the relationship among property oriented concept lattices and the corresponding congruence relations. Then notions of attribute reduction is defined for formal contexts and decision contexts to find minimal attribute subsets which can preserve all congruence classes determined by the original attribute set, and also keep all property oriented extents and their original hierarchy in the property oriented concept lattice. Finally, approaches of discernibility matrix are presented to calculate all attribute reducts.

Comparison of reduction in formal decision contexts

In formal concept analysis, many reduction methods have recently been proposed for formal decision contexts, and each of them was to reduce formal decision contexts with a particular purpose. However, little attention has been paid to the comparison of their differences from various aspects. In fact, this problem is very important because it can provide evidence to select an appropriate reduction method for a given specific case. To address this problem, our study mainly focuses on clarifying the relationship among the existing reduction methods in formal decision contexts. Firstly, we give a rule-based review of the existing reduction methods, revealing the type of rules that each of them can preserve. Secondly, we analyze the relationship among the consistencies introduced by the existing reduction methods. More specifically, Wei's first consistency (see [39]) is stronger than others, while her second one is weaker than the remainder except Wu's consistency (see [43]). Finally, we make a comparison of the existing reductions, concluding that Li's reduction (see [14]) maintaining the non-redundant decision rules of a formal decision context is coarser than others. The results obtained in this paper are beneficial for users to select an appropriate reduction method for meeting their requirements.

Attribute reduction in inconsistent formal decision contexts based on congruence relations

In this paper, notions and methods of attribute reduction are investigated for an inconsistent formal decision context. Based on congruence relations defined on the object power set, we first introduce notions of distribution attribute reduct and maximum distribution attribute reduct for an inconsistent formal decision context, and discuss their relations in detail. We then define discernibility matrices and discernibility functions associated with the proposed attribute reducts, from which we can calculate all attribute reducts. Finally, we compare the proposed consistent sets with four types of consistent sets in previously published papers. The results show that a distribution consistent set belongs to any of those four types of consistent sets. Therefore, it has all the properties of those four types of consistent sets.

An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices

AbstractRule acquisition is one of the main purposes in the analysis of formal decision contexts. Up to now, there have been several types of rules in formal decision contexts. However, these existing rules were investigated independently and are, to some extent, unsatisfactory for making better decision analysis since some of them (e.g. decision implications) are computationally expensive and others (e.g. decision rules and granular rules) are short of compactness. Motivated by these problems, minimal closed label concept lattice is defined to present limitary decision implications, which not only are easier to be extracted than decision implications, but also have more concise premises than decision rules and granular rules. Moreover, we discuss the pairwise inclusion and inference relationships among limitary decision implications, decision implications, decision rules and granular rules. Finally, some numerical experiments are conducted to demonstrate that the proposed limitary decision implications a...

Analysis of interval-valued decision formal contexts

This study investigates a novel approach to knowledge reduction in interval-valued decision formal contexts. Applying rule acquisition, we formulate a new framework of knowledge reduction for interval-valued decision formal contexts and the presented framework can be applicable to any interval-valued decision formal contexts. Based on this reduction method, more compact decision rules that can imply all of those derived from the initial interval-valued decision formal contexts in the form of implication rules are obtained. Furthermore, a corresponding reduction method is developed by constructing a discernibility matrix and its associated Boolean function.

A comparative study of multigranulation rough sets and concept lattices via rule acquisition

Recently, by combining rough set theory with granular computing, pessimistic and optimistic multigranulation rough sets have been proposed to derive “AND” and “OR” decision rules from decision systems. At the same time, by integrating granular computing and formal concept analysis, Wille’s concept lattice and object-oriented concept lattice were used to obtain granular rules and disjunctive rules from formal decision contexts. So, the problem of rule acquisition can bring rough set theory, granular computing and formal concept analysis together. In this study, to shed some light on the comparison and combination of rough set theory, granular computing and formal concept analysis, we investigate the relationship between multigranulation rough sets and concept lattices via rule acquisition. Some interesting results are obtained in this paper: (1) “AND” decision rules in pessimistic multigranulation rough sets are proved to be granular rules in concept lattices, but the inverse may not be true; (2) the combination of the truth parts of an “OR” decision rule in optimistic multigranulation rough sets is an item of the decomposition of a disjunctive rule in concept lattices; (3) a non-redundant disjunctive rule in concept lattices is shown to be the multi-combination of the truth parts of “OR” decision rules in optimistic multigranulation rough sets; and (4) the same rule is defined with a same certainty factor but a different support factor in multigranulation rough sets and concept lattices. Moreover, algorithm complexity analysis is made for the acquisition of “AND” decision rules, “OR” decision rules, granular rules and disjunctive rules.

On inference rules in decision formal contexts

On inference rules in decision formal contexts

On inference rules in decision formal contexts

Rule acquisition is one of the main purposes in the analysis of decision formal contexts. In general, the number of implications in a decision formal context is an exponential increase to the scale of the database. So, it is important to introduce effective inference rules between implications for eliminating as many superfluous implications as possible. This study puts forward a criterion called ‘strongness’ to assess the effectiveness of inference rules in terms of eliminating superfluous implications. We define a new inference rule in decision formal contexts and prove that the proposed inference rule is stronger than the existing one. Furthermore, we figure out the exact number of the superfluous implications that we can additionally remove by using the proposed inference rule compared with the existing one.

Rule-preserved object compression in formal decision contexts using concept lattices

Rule acquisition is one of the main purposes in the analysis of formal decision contexts. In general, given a formal decision context, some of its objects may not be essential to the rule acquisition. This study investigates the issue of reducing the object set of a formal decision context without losing the decision rule information provided by the entire set of objects. Using concept lattices, we propose a theoretical framework of object compression for formal decision contexts. And under this framework, it is proved that the set of all the non-redundant decision rules obtained from the reduced database is sound and complete with respect to the initial formal decision context. Furthermore, a complete algorithm is developed to compute a reduct of a formal decision context. The analysis of some real-life databases demonstrates that the proposed object compression method can largely reduce the size of a formal decision context and it can remove much more objects than both the techniques of clarified context and row reduced context.

Construction of a Unified Model for Formal Contexts and Formal Decision Contexts

This paper mainly constructs a unified model for formal contexts, consistent formal decision contexts and inconsistent formal decision contexts based on object oriented concept lattices, which is called a consistent approximate representation space. Congruence relations are first introduced into formal contexts and then relationships between congruence relations and the corresponding object oriented concept lattices are developed. Finally, consistent approximate representation space is defined for a formal context, which is a quadruple (U ,A ,R ,R'). It is verified that if we give R different meanings, then we obtain the corresponding formal context, consistent formal decision context and inconsistent formal decision context with respect to object oriented concept lattices. Therefore, the quadruple ( ,A ,R ,R') is a unified model for formal contexts and formal decision contexts.

Attribute reduction based on maximal rules in decision formal context

AbstractOne of the key issues in the theory of concept lattices is to extract the useful rules from the decision formal context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision formal context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision formal context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.

Rule acquisition and complexity reduction in formal decision contexts

In this paper, we introduce the notion of formal decision context as an extension of formal contexts by employing the notion of decision information table. We use formal concept analysis to formulate an approach to extract “if–then” rule from formal decision contexts. We also construct a knowledge-lossless method for complexity reduction in formal decision contexts so that the maximum rules extracted from the reduced formal decision contexts are identical to that extracted from the initial decision formal contexts. More specifically, we develop the discernibility matrix and the discernibility function in formal decision contexts to compute all of the attribute reductions without loss of knowledge.