Incomplete Information Table Research Articles

Two kinds of average approximation accuracy

AbstractRough set theory places great importance on approximation accuracy, which is used to gauge how well a rough set model describes a target concept. However, traditional approximation accuracy has limitations since it varies with changes in the target concept and cannot evaluate the overall descriptive ability of a rough set model. To overcome this, two types of average approximation accuracy that objectively assess a rough set model’s ability to approximate all information granules is proposed. The first is the relative average approximation accuracy, which is based on all sets in the universe and has several basic properties. The second is the absolute average approximation accuracy, which is based on undefinable sets and has yielded significant conclusions. We also explore the relationship between these two types of average approximation accuracy. Finally, the average approximation accuracy has practical applications in addressing missing attribute values in incomplete information tables.

A three-way decision model on incomplete single-valued neutrosophic information tables

In this paper, we focus on the three-way decision model on incomplete single-valued neutrosophic information tables. Firstly, we define the minimum and maximum similarity measures between single-valued neutrosophic numbers (SVNNs) which may contain unknown values. On this basis, the notion of θ-weak similarity measure is given. Then, we introduce the conception of an incomplete single-valued neutrosophic information table (ISVNIT). For an incomplete single-valued neutrosophic information table, a new similarity relation is proposed based on the θ-weak similarity measure. Some properties are also studied. By using Bayesian decision theory and this similarity relation, we construct a three-way decision model on an ISVNIT. Finally, an example of choosing product service providers is explored to illustrate the rationality and feasibility of the proposed model. We also discuss the influence of parameters in the model on decision results.

General three-way decision models on incomplete information tables

In this paper, we propose general three-way decision models on incomplete information tables. First, for an incomplete information table, we give an axiomatic definition of similarity degree functions on a single attribute. By use of extended aggregation functions, similarity degree functions on an attribute set are also proposed. Then we define a new kind of similarity class of objects and study its properties. On the basis of this similarity class, general three-way decision models based on two evaluation functions and one evaluation function on incomplete information tables are established, respectively. In addition, we study the properties of these general three-way decision models. Finally, we compare the general model based on one evaluation function and a pair of thresholds with four existing models. The results show that the four existing models can be regarded as special cases of this general model, which illustrates the rationality of the new proposed models.

Attribute Reduction of Coal Mine Fire Incidents Based on Finding Maximum Mutual Information

There are many redundant attributes for the original data of the emergency system with uncertainty and data loss, and the existing incomplete information system attribute reduction algorithms have the disadvantages of high time complexity and completeness of the reduction result, an attribute reduction method for incomplete emergencies based on finding the maximum mutual information is proposed. Firstly, the original data of the emergency was preprocessed, and the situation and the consequences were regarded respectively as conditional attributes and decision attributes, thereby an incomplete decision information table was constructed; then, according to the characteristic that the mutual information of the conditional attribute set and the decision attribute is equal to the information entropy of the decision attribute in the consistency incomplete information system, the attribute reduction algorithm based on finding the maximum mutual information was obtained; finally, this method was used to reduce the attribute of coal mine fire data and compared it with other three methods. The results indicate that this method can effectively reduce the redundant attributes of coal mine fire emergencies, and can ensure that the reduction results have strong completeness when the algorithm time is low, thus decision-making for the emergency department is provided.

Incrementally updating approximations based on the graded tolerance relation in incomplete information tables

The incremental learning methods based on rough set theory are effective in acquiring knowledge in dynamically changing information tables. In this paper, we focus on the effective acquisition of decision rules by incrementally updating approximations when an incomplete information table changes. First of all, we present a four-step model to obtain three-way decision rules in an incomplete information table based on the graded tolerance relation. The first step presents the graded tolerance relation between objects. The second step calculates the degrees of objects belonging to approximations by using fuzzy logic operators. Besides, we propose a relation matrix to calculate the degrees efficiently. The third step gets three-way approximations by applying a pair of thresholds to the degrees. The fourth step obtains three-way decision rules based on the descriptions of objects. According to the four-step model, we find the notion of approximations plays an essential role in rule acquisition. Incrementally updating approximations are an effective method to obtain decision rules when an incomplete information changes. Accordingly, we study the incrementally updating approximations by incrementally updating the relation matrix when changing attributes, objects, and the attribute value of an object. Finally, experimental results illustrate that the incremental methods are more effective than non-incremental methods.

Rule induction based on rough sets from information tables having continuous domains

Information tables having continuous domains are handled by neighborhood rough sets. Two approximations in complete information tables are extended to handle incomplete information. Consequently, four approximations are obtained: certain and possible lower ones and certain and possible upper ones without computational complexity. These extended approximations create the same results as the ones from possible world semantics by using possible indiscernibility relations. Therefore, the extension is justified. In complete information tables two types of single rules that an object supports are obtained: consistent and inconsistent ones. The single rule has low applicability. To increase applicability, a series of single rules are brought into one combined rule with an interval value. In incomplete information tables four kinds of single rules are obtained. From them, four kinds of combined rules are obtained: certain and consistent, possible and consistent, certain and inconsistent, and possible inconsistent ones. A combined rule has higher applicability than the single rules from which it is assembled.

Three-way decision based on improved aggregation method of interval loss function

Given a hybrid incomplete information table consisting both of the incomplete information table and loss function, the loss function of each object is denoted as an interval. The loss function of similarity class is defined as the aggregation of interval loss functions of all objects in its similarity class. However, existing optimistic aggregation method utilizes the union of interval loss functions of all objects in similarity class, which make the length of the aggregated interval loss function too broad. Pessimistic aggregation method utilizes the intersection of interval loss functions of all objects in similarity class, which make the length of the aggregated interval loss function too narrow. In order to get reasonable aggregated interval loss function, we propose a new aggregation method based on the principle of justifiable granularity, which make the length of the aggregated interval loss function neither too broad nor too narrow. That is, the aggregation result includes the interval loss functions of all objects in similarity class as much as possible and the aggregation result is as specific as possible. Based on the proposed aggregation method, we propose a new three-way decision model. Examples and experimental results demonstrate the effectiveness of the proposed method.

Structured approximations as a basis for three-way decisions in rough set theory

A major application of rough set theory is concept analysis for deciding if an object is an instance of a concept based on its description. Objects with the same description form an equivalence class and the family of equivalence classes is used to define rough set approximations. When deriving the decision rules from approximations, the description of an equivalence class is the left-hand-side of a decision rule. Therefore, it is useful to retain structural information of approximations, that is, the composition of an approximation in terms of equivalence classes. However, existing studies do not explicitly consider the structural information. To address this issue, we introduce structured rough set approximations in both complete and incomplete information tables, which serve as a basis for three-way decisions with rough sets. In a complete table, we define a family of conjunctively definable concepts. The structured three-way approximations are three structured positive, boundary and negative regions given by three sets of conjunctively definable concepts. By adopting a possible-world semantics, we introduce the notion of conjunctively definable interval concepts in an incomplete table, which is used to construct the structured three-way approximations. The internal structure of structured approximations contributes to sound semantics of rough set approximations and is directly and explicitly related to three-way decision rules.

On rule acquisition in incomplete multi-scale decision tables

Granular computing and acquisition of IF-THEN rules are two basic issues in knowledge representation and data mining. A rough set approach to knowledge discovery in incomplete multi-scale decision tables from the perspective of granular computing is proposed in this paper. The concept of incomplete multi-scale information tables in the context of rough sets is first introduced. Information granules at different levels of scales in incomplete multi-scale information tables are then described. Lower and upper approximations with reference to different levels of scales in incomplete multi-scale information tables are also defined and their properties are examined. Optimal scale selection with various requirements in incomplete multi-scale decision tables are further discussed. Relationships among different notions of optimal scales in incomplete multi-scale decision tables are presented. Finally, knowledge acquisition in the sense of rule induction in consistent and inconsistent incomplete multi-scale decision tables are explored.

Data Recovery Method for Seafood Quality Safety System Based on Rough Set Theory

To solve the seafood quality and safety information table missing data problem, a method for filling missing data based on rough set was proposed. This method first determine whether there is missing data in information table, if there is, then the information table is divided into two parts, one for the complete information table, and the other part is totally incomplete information table, and then complete the information sheet structure similar matrix to calculate the attributes importance, then calculate the number of missing attributes in incomplete information table, and the calculated results conjunctive operation to fill the missing data. If it is not, then output directly. Numerical examples show that the method can be used filling the missing data in seafood quality and safety information table effectively.

Decision-theoretic Rough Sets in Incomplete Information System

Decision-theoretic rough sets in two kinds of incomplete information systems are discussed in this paper. One is for the classical decision attribute and the other for the fuzzy decision attribute. In complete information system, the universe is partitioned with the equivalence relation. Given a concept, we get a pair of approximations of the concept using rough set theory, and the universe can be partitioned into three regions for making a decision. An incomplete information table can be expressed as a family of complete information tables. The universe is partitioned by the equivalence relation for each complete information table. The probability of each object belonging to the concept can be calculated in a completion from incomplete information system, and then the total probability of the object belonging to the concept can be obtained. Decision rules are derived using total probability instead of conditional probability in decision-theoretic rough sets. Finally, the universe is divided into three regions according to the total probability. A similar approach to fuzzy incomplete information system is examined and the universe is also divided into three regions.

Knowledge Reduction in Random Incomplete Decision Tables via Evidence Theory

Statisticians and database users often encounter the problem of missing or imprecise data obtained by a random experiment. Such a data set is called a random incomplete information table. In this paper, we study knowledge reduction in random incomplete information tables and random incomplete decision tables by using a hybrid model based on the rough set theory and the Dempster-Shafer theory of evidence. The concepts of random belief reducts and random plausibility reducts in random incomplete information tables and random incomplete decision tables are introduced. The relationships among the lower approximation reduct, the upper approximation reduct, the random belief reduct, the random plausibility reduct, and the classical reduct in random incomplete decision tables are examined.

An interval set model for learning rules from incomplete information table

A novel interval set approach is proposed in this paper to induce classification rules from incomplete information table, in which an interval-set-based model to represent the uncertain concepts is presented. The extensions of the concepts in incomplete information table are represented by interval sets, which regulate the upper and lower bounds of the uncertain concepts. Interval set operations are discussed, and the connectives of concepts are represented by the operations on interval sets. Certain inclusion, possible inclusion, and weak inclusion relations between interval sets are presented, which are introduced to induce strong rules and weak rules from incomplete information table. The related properties of the inclusion relations are proved. It is concluded that the strong rules are always true whatever the missing values may be, while the weak rules may be true when missing values are replaced by some certain known values. Moreover, a confidence function is defined to evaluate the weak rule. The proposed approach presents a new view on rule induction from incomplete data based on interval set.

Rule Extracting based on MCG with its Application in Helicopter Power Train Fault Diagnosis

In order to extract decision rules for fault diagnosis from incomplete historical test records for knowledge-based damage assessment of helicopter power train structure. A method that can directly extract the optimal generalized decision rules from incomplete information based on GrC was proposed. Based on semantic analysis of unknown attribute value, the granule was extended to handle incomplete information. Maximum characteristic granule (MCG) was defined based on characteristic relation, and MCG was used to construct the resolution function matrix. The optimal general decision rule was introduced, with the basic equivalent forms of propositional logic, the rules were extracted and reduction from incomplete information table. Combined with a fault diagnosis example of power train, the application approach of the method was present, and the validity of this method in knowledge acquisition was proved.

Incomplete Information Tables and Rough Classification

The rough set theory, based on the original definition of the indiscernibility relation, is not useful for analysing incomplete information tables where some values of attributes are unknown. In this paper we distinguish two different semantics for incomplete information: the “missing value” semantics and the “absent value” semantics. The already known approaches, e.g. based on the tolerance relations, deal with the missing value case. We introduce two generalisations of the rough sets theory to handle these situations. The first generalisation introduces the use of a non symmetric similarity relation in order to formalise the idea of absent value semantics. The second proposal is based on the use of valued tolerance relations. A logical analysis and the computational experiments show that for the valued tolerance approach it is possible to obtain more informative approximations and decision rules than using the approach based on the simple tolerance relation.