Incomplete Information Systems Research Articles

Improved rough approximations based on variable J-containment neighborhoods

Classic generalized rough set model in neighborhood systems provides a more general framework for depicting approximations, while it may meet the non-reflexive situations. Some scholars put forward different neighborhoods, such as adhesion neighborhoods (briefly, P_{j}-neighborhoods), containment neighborhoods (briefly, C_{j}-neighborhoods), and E_{j}-neighborhoods. However, not all of them are reflexive. Moreover, the granularity of P_{j}-neighborhoods and C_{j}-neighborhoods are too fine, and that of E_{j}-neighborhoods too coarse. To solve the problem, we aim to design a novel construction approach of neighborhoods, called variable j-containment neighborhoods (briefly, V_{j}^{beta }-neighborhoods), which satisfies the reflexivity and the granularity so flexible that the neighborhood space can adjust the granularity to meet the needs of problems. We generalize three kinds of rough approximations in V_{j}^{beta }-neighborhood spaces and discuss their properties. What’s more, we analyze the topology structures relying on V_{j}^{beta }-neighborhood spaces and compare our proposed approach with the existing approaches. By selecting the appropriate parameter beta, our neighborhood system is more flexible in adjusting the granularity to fit problem requirements. And illustrative examples demonstrate the advantages of the proposed rough set model to attribute reduction in incomplete information systems.

Collaborative Fuzzy Linguistic Learning to Low-Resource and Robust Decision System Based on Bounded Rationality

Low-resource languages are challenging to process intelligent decision systems due to limited data and resources. As an effective way of processing low-resource languages in intelligent decision systems, fuzzy linguistic approaches excel in transforming original uncertain linguistic information into highly structured data and learning valid decision rules between complex data structures. However, existing fuzzy linguistic methods may not fully capture realistic features of multi-attribute group decision-making (MAGDM), such as incomplete and hesitant linguistic expressions, stable information fusion, and bounded rationality of decision-makers (DMs). Therefore, it is necessary to develop a collaborative fuzzy language learning system based on bounded rationality, low-resource and robust decision-making. Specifically, we present a new multi-granularity (MG) group decision-making (GDM) scheme by using MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and PT (Prospect Theory) for incomplete hesitant fuzzy linguistic information systems (I-HFL-ISs), where MG GDM aims to discover knowledge from complex MAGDM problems with MG features. To achieve the above goal, we first introduce the concept of MG-I-HFL-ISs to represent incomplete, hesitant and imprecise linguistic evaluation information offered by multiple decision-makers (DMs). Then, we apply a valid transformation scheme to convert MG-I-HFL-ISs into MG-HFL-ISs, and use the MG probability rough set (PRS) to develop a series of MG-HFL-PRSs with the support of MULTIMOORA. Afterwards, an HFL MG GDM method is designed by integrating MULTIMOORA and PT for solving MAGDM problems with MG-I-HFL-ISs. The proposed method can effectively synthesize low-resource languages and mine useful decision-making knowledge. At last, a drug selection case and a simulated case are performed for showing the rationality of the designed HFL MG GDM scheme.

Attributes Reduction on SE-ISI Concept Lattice for an Incomplete Context Using Object Ranking

The formal concept of lattice plays a vital role in knowledge discovery. Reduction of the attribute has many applications in machine learning technology and data mining fields. In this paper, we introduce an object ranking concept to define a consistency set and the reduction of the attributes by structural features. An incomplete information system works on the three-way concepts using the SE-ISI Context. The granular was emphasized with join (meet) irreducible sets using the object ranking concepts. A dual operator is defined based on the object ranking concepts and its properties and conditions are verified. Hence, this elaborates on the four kinds of reduction of the attributes. The ordered pairs give the knowledge of the attributes that deal with the interval set of both the approximation of rough set theory concerning the objects. Therefore, the relationship between four kinds of reduction of the attribute was appropriate to access the consistency set using the object ranking concepts by some of the theorems and examples.

Incomplete intuitionistic fuzzy behavioral group decision-making based on multigranulation probabilistic rough sets and MULTIMOORA for water quality inspection

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs’ psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies.

A Novel Attribute Reduction Algorithm for Incomplete Information Systems Based on a Binary Similarity Matrix

With databases growing at an unrelenting rate, it may be difficult and complex to extract statistics by accessing all of the data in many practical problems. Attribute reduction, as an effective method to remove redundant attributes from massive data, has demonstrated its remarkable capability in simplifying information systems. In this paper, we concentrate on reducing attributes in incomplete information systems. We introduce a novel definition of a binary similarity matrix and present a method to calculate the significance of attributes in correspondence. Secondly, We develop a heuristic attribute reduction algorithm using a binary similarity matrix and attribute significance as heuristic knowledge. In addition, we use a numerical example to showcase the practicality and accuracy of the algorithm. In conclusion, we demonstrate through comparative analysis that our algorithm outperforms some existing attribute reduction methods.

Regret Theory-Based Three-Way Decision Method on Incomplete Multiscale Decision Information Systems With Interval Fuzzy Numbers

In realistic decision-making environments, human behaviors bring influences to various decision-making procedures, and classic multiattribute decision-making approaches based on utility decisions own some deviations from actual situations. The behavioral decision theory modifies classic decision-making theories to make the new method more applicable. Regret theory, as one of the important components in behavioral decision theories, has been widely used in theories and applications. Based on regret theory, we establish a generalized three-way decision method on incomplete multiscale decision information systems with interval fuzzy numbers. First, we select an incomplete optimal subsystem for the incomplete multiscale information system, and convert the multiscale evaluation information into an interval fuzzy number by using a linguistic term set. Second, based on the probability distribution of evaluation values and tradeoff factors, we propose a target-dependent approximation estimation method for the incomplete interval fuzzy subsystem. Then, the regret–rejoicing preferences between objects are obtained. Finally, a tripartition and ranking method based on a max-bipartition and preference index is established. Moreover, the incompleteness experiments show that the decision-making results of our method can still maintain more than 97% consistency in an incomplete information system with a missing rate of at most 20%. In addition, the parameter analysis shows that the proposed method maintains an accuracy rate of more than 98% and a classification error rate of no more than 0.6%.

Outlier detection for incomplete real-valued data based on inner boundary

Outlier detection is a process to find out the objects that have the abnormal behavior. It can be applied in many aspects, such as public security, finance and medical care. An information system (IS) as a database that shows relationships between objects and attributes. A real-valued information system (RVIS) is an IS whose information values are real numbers. A RVIS with missing values is an incomplete real-valued information system (IRVIS). The notion of inner boundary comes from the boundary region in rough set theory (RST). This paper conducts experiments directly in an IRVIS and investigates outlier detection in an IRVIS based on inner boundary. Firstly, the distance between two information values on each attribute of an IRVIS is introduced, and the parameter λ to control the distance is given. Then, the tolerance relations on the object set are defined according to the distance, by the way, the tolerance classes, the λ-lower and λ-upper approximations in an IRVIS are put forward. Next, the inner boundary under each conditional attribute in an IRVIS is presented. The more inner boundaries an object belongs to, the more likely it is to be an outlier. Finally, an outlier detection method in an IRVIS based on inner boundary is proposed, and the corresponding algorithm (DE) is designed, where DE means degree of exceptionality. Through the experiments base on UCI Machine Learning Repository data sets, the DE algorithm is compared with other five algorithms. Experimental results show that DE algorithm has the better outlier detection effect in an IRVIS. It is worth mentioning that for comprehensive comparison, ROC curve and AUC value are used to illustrate the advantages of the DE algorithm.

Logics for Temporal Information Systems in Rough Set Theory

The article discusses temporal information systems (TISs) that add the dimension of time to complete or incomplete information systems. Through TISs, one can accommodate the possibility of domains or attribute values for objects changing with time or the availability of currently missing information with time. Different patterns of flow of information give different TISs. The corresponding logics with sound and complete axiomatization are presented.

On numerical characterizations of the topological reduction of incomplete information systems based on evidence theory

Abstract Knowledge reduction of information systems is one of the most important parts of rough set theory in real-world applications. Based on the connections between the rough set theory and the theory of topology, a kind of topological reduction of incomplete information systems is discussed. In this study, the topological reduction of incomplete information systems is characterized by belief and plausibility functions from evidence theory. First, we present that a topological space induced by a pair of approximation operators in an incomplete information system is pseudo-discrete, which deduces a partition. Then, the topological reduction is characterized by the belief and plausibility function values of the sets in the partition. A topological reduction algorithm for computing the topological reducts in incomplete information systems is also proposed based on evidence theory, and its efficiency is examined by an example. Moreover, relationships among the concepts of topological reduct, classical reduct, belief reduct, and plausibility reduct of an incomplete information system are presented.

Maximal consistent block based optimal scale selection for incomplete multi-scale information systems

Maximal consistent block based optimal scale selection for incomplete multi-scale information systems

TFD-IIS-CRMCB: Telecom Fraud Detection for Incomplete Information Systems Based on Correlated Relation and Maximal Consistent Block

Telecom fraud detection is of great significance in online social networks. Yet the massive, redundant, incomplete, and uncertain network information makes it a challenging task to handle. Hence, this paper mainly uses the correlation of attributes by entropy function to optimize the data quality and then solves the problem of telecommunication fraud detection with incomplete information. First, to filter out redundancy and noise, we propose an attribute reduction algorithm based on max-correlation and max-independence rate (MCIR) to improve data quality. Then, we design a rough-gain anomaly detection algorithm (MCIR-RGAD) using the idea of maximal consistent blocks to deal with missing incomplete data. Finally, the experimental results on authentic telecommunication fraud data and UCI data show that the MCIR-RGAD algorithm provides an effective solution for reducing the computation time, improving the data quality, and processing incomplete data.

Attribute Reduction Algorithm for Incomplete Information Systems Based on Intuitive Fuzzy Pairs

Attribute Reduction Algorithm for Incomplete Information Systems Based on Intuitive Fuzzy Pairs

Method for three-way decisions using similarity in incomplete information systems

Method for three-way decisions using similarity in incomplete information systems

Three-way neighborhood based stream computing for incomplete hybrid information system

Stream computing paradigm focuses on efficiently knowledge updating when immigration and emigration occur simultaneously. Existing stream computing for reasoning with three-way decisions aims at symbolic and complete data. In contrast, the studies on more realistic cases of numerical and symbolic types with potentially incomplete data are preliminary. To efficiently cope with the concept uncertainty, a dynamic neighborhood stream three-way decisions algorithm for incomplete hybrid information systems (DNS3WD) is proposed. Following the setting of flowing into one object and flowing out of another, we dynamically generate all neighborhood classes and decision equivalence classes in the data streaming window. Finally, we deduce the principles of variations of conditional probabilities and update three-way regions accordingly. Theoretically, the time complexity of the non-incremental three-way decisions algorithm (NIH3WD) is about N times that of DNS3WD, where N is the size of the data streaming window. In addition, extensive comparisons against NIH3WD demonstrate that DNS3WD can efficiently leverage the previously acquired knowledge.

A method for incremental updating three-way decision with incomplete information system

In recent years, the three-way decisions theory has been developed in both theoretical and practical applications. In fact, data are often incomplete and often change over time. To solve this problem, a method of updating the three-way decisions in the dynamic incomplete information system is proposed. First, we consider the relationship between the change of conditional probabilities for the change of the three regions. Then, we consider the change of conditional probability when objects and attribute values of the object change. From that change, we propose a method for updating three-way decisions for two situations, namely, the objects vary, and the attribute values of an object vary. Finally, we give an example to illustrate this method.

Information structures in a multiset-valued information system with application to uncertainty measurement

Information system (IS) is a significant model in the field of artificial intelligence. Information structure is not only a research direction in the field of granular computing (GrC), but also an important method to study an IS. A multiset-valued information system (MVIS) refers to an IS where information values are multisets. A MVIS can be seen as a model that is the result of information fusion of multiple categorical ISs. This model helps deal with missing values in the dataset. This paper studies information structures in a MVIS on the view of GrC and consider their application for uncertainty measurement (UM). First of all, some notions of multisets and probability distribution sets (PDSs) are proposed. Naturally, relationships between multisets and PDSs are researched. Then, the concept of a MVIS based on the notion of multisets is given, and the internal structure of a MVIS is revealed by an incomplete information system (IIS). Furthermore, tolerance relations in a MVIS are defined by using Hellinger distance, and tolerance classes are obtained to construct the information structures of a MVIS. Considering the association of information structures, relationships between information structures are raised from the two aspects of dependence and separation. Moreover, some properties between information structures are provided by using information distance and inclusion degree. Finally, four UMs as the applications of information structures are investigated, and comprehensive experiments on several datasets demonstrate the feasibility and superiority of the proposed measures. These results will be helpful for establishing a framework of GrC in a MVIS and studying UM.

Soft ordered double quantitative approximations based three-way decisions and their applications

The classical theory of rough set was established by Pawlak, which mainly focusses on the approximation of sets characterized by a single equivalence relation over the universe. However, most of the current single granulation structure models cannot meet the user demand or the target of solving problems. Multigranulation rough sets approach can better deal with the problems, where data might be spread over various locations. In this article, we present the idea of soft preference and soft dominance relation for the development of soft dominance rough set in an incomplete information system. Subsequently, several important structural properties and results of the proposed model are carefully analyzed. After employing soft dominance based rough set approach to it for any times, we can only get six different sets at most in an incomplete information system. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Based on soft dominance relation, we introduce logical disjunction/conjunction soft dominance optimistic/pessimistic multigranulation decision theoretic rough approximations in an incomplete information. Meanwhile, to measure the uncertainty of soft dominance optimistic/pessimistic multigranulation decision theoretic rough approximation and some of their interesting properties are examined. Thereafter, a novel multi attribute with multi decision making problem approach based on logical disjunction/conjunction soft dominance optimistic/pessimistic multigranulation decision theoretic rough sets approach are developed to solve the selection of medicine to treat the coronavirus disease (COVID-19). The basic principle and the detailed steps of the decision making model (algorithms) are presented in detail. To demonstrate the applicability and potentiality of the proposed model, we present a practical example of a medical diagnosis is given to validate the practicality of the technique.

A prospect-regret theory-based three-way decision model with intuitionistic fuzzy numbers under incomplete multi-scale decision information systems

As a new data representation in the big data era, a multi-scale decision information system (MSDIS) realizes “multi-level, multi-angle and multi-view” evaluations in various problems. However, most of existing multi-scale data analysis models are built for complete information systems (CISs), whereas the research on incomplete multi-scale decision information systems (I-MSDISs) is not perfect. Additionally, the irrational behavior of one decision-maker (DM) often has an impact on decision outcomes. On this basis, this paper develops a prospect-regret theory-based three-way decision (3WD) model with intuitionistic fuzzy numbers (IFNs) under an I-MSDIS, which is abbreviated as PR-3WD-I-MSDIS. Specifically, we first select the optimal scale combination of I-MSDISs by the matrix theory to complete the information extraction of incomplete optimal sub-systems. Then, we further propose an attribute weight evaluation strategy under the incomplete optimal subsystem, which fully considers the neighborhood information of each object. Subsequently, the concept and calculation method of aggregated weighted fuzzy conditional probabilities are constructed from the perspective of intuitionistic fuzzy sets. Furthermore, a prospect-regret theory-based relative profit function is proposed, which sufficiently takes into account the loss and utility in decision-making processes. Finally, a novel three-way classification and ranking method is developed for solving incomplete multi-scale problems. The experimental results on real-world datasets demonstrate that the PR-3WD-I-MSDIS model achieves excellent performance.

A three-way decision approach with prospect-regret theory via fuzzy set pair dominance degrees for incomplete information systems

The generalized three-way decision (G3WD) theory is featured by a trisecting-acting-outcome paradigm. Experiments in psychology and economics have indicated that risky decision-making problems should take into account the psychological characteristic of agents. Moreover, the loss of information acts as a serious challenge in G3WD. Thus, exploring valid G3WD approaches that consider the mental state of decision-makers in incomplete information systems (IISs) is imperative. This paper explores a new three-way decision (3WD) approach that combines the prospect theory with the regret theory for IISs with the support of fuzzy set pair dominance degrees. First, the notion of fuzzy set pair dominance degrees to process evaluation information in IISs is put forward. Then, an approach that obtains objective reference points and determines the weighting function in the prospect theory is given by combining 3WD with the behavioral decision theory. In light of the prospect theory, a prospect value function is obtained, which is introduced into the regret theory to obtain two utility perception functions. As a consequence, a G3WD approach based on fuzzy set pair dominance degrees and the behavioral decision theory is constructed for IISs. By using two medical cases in the KEEL and UCI datasets, the superiority, effectiveness and stability of the constructed approach are verified via corresponding comparative and experimental analyses.

Three-Way Fuzzy Sets and Their Applications (II)

Recently, the notion of a three-way fuzzy set is presented, inspired by the basic ideas of three-way decision and various generalized fuzzy sets, including lattice-valued fuzzy sets, partial fuzzy sets, intuitionistic fuzzy sets, etc. As the new theory of uncertainty, it has been used in attribute reduction and as a new control method for the water level. However, as an extension of a three-way decision, this new theory has not been used in multi-criteria decision making (MCDM for short). Based on the previous work, in this paper, we present rough set models based on three-way fuzzy sets, which extend the existing fuzzy rough set models in both complete and incomplete information systems. Furthermore, the new models are used to solve the issue of MCDM. Firstly, three-way fuzzy relation rough set and three-way fuzzy covering rough set models are presented for complete and incomplete information systems. Because almost all existing fuzzy rough set models are proposed under complete information, the new proposed models can be seen as a supplement to these existing models. Then, a relationship between the three-way fuzzy relation rough set and the three-way fuzzy covering rough set is presented. Finally, a novel method for the issue of MCDM is presented under the novel three-way fuzzy rough set models, which is used in paper defect diagnosis.