Interval-valued Fuzzy Information Systems Research Articles

An overlap function-based three-way intelligent decision model under interval-valued fuzzy information systems

One of the expression forms of uncertain information are interval-valued fuzzy information systems (IFISs). Whereas, psychological experiments show that psychological behaviors of decision maker (DM) affect the decision results under uncertain information. Consequently, the main research objectives of this paper are two-fold: 1. To study how to portray the influence of psychological behaviors on decision-making under IFISs, so that the decision-making process is more realistic. 2. To investigate how to efficiently solve decision-making problems in the context of IFISs. Three-way decision (3WD) theory and fuzzy rough sets (FRSs) are effective tools for solving uncertain information. For that reason, this paper develops a 3WD model based on prospect theory (PT) under IFISs, which can provide the best decision action for objects from a viewpoint of optimization. First, an attribute-oriented interval fuzzy set is introduced, which establish a bridge between the state sets in 3WD and the reference points in PT. Furthermore, conditional probability of an object is reasonably estimated by interval-valued fuzzy rough sets (IVFRSs). Meanwhile, an attribute-oriented relative value model is proposed, which can get the prospect values of an object under each action. Second, an intelligent 3WD model is developed from a viewpoint of information granularity. Finally, through the search of the existing literature, relevant research data is obtained, and then case research method, qualitative and quantitative combination method, control variable method are adopted in turn to design the case study, comparative and experimental analyses. In short, the developed model not only expands the development of related theories, 3WD, PT, FRSs, but also offers new methods for solving the decision-making problems under IFISs, which has important practical guidance significance.

Incremental feature selection approach to interval-valued fuzzy decision information systems based on [formula omitted]-fuzzy similarity self-information

The relative decision self-information is a crucial evaluation function of feature selection in information system. It encapsulates classification information in upper and lower approximations and pays attention to the boundary region of samples. Nevertheless, with the frequent replacement of data, the static feature selection neglects the previous information of samples, which diminishes the computational efficiency. With the purpose of adapting to the evolution of the era, incremental learning is widely exerted in the field of data mining. In combination with incremental technique, it is not cumbersome to update the reduct in time. Enlightened by this, our work focuses on the mechanism of incremental feature selection due to the variation of objects in IvFDIS. Firstly, we construct λ-fuzzy similarity relation and introduce λ-fuzzy similarity self-information into IvFDIS based on relative decision self-information. Besides, with the assistance of matrix operation, we recommend static feature selection according to λ-fuzzy similarity self-information. Furthermore, two relevant incremental algorithms involving the insertion and removal of objects in IvFDIS are made a research. Finally, some comparative experiments are conducted on twelve public data sets to certify the validity of our incremental algorithms. Experimental results show that comparable to three tested algorithms, the proposed incremental algorithms lessen the computation time greatly, and they select fewer features in most instances without decreasing classification accuracy in IvFDIS.

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

On variable-precision-based rough set approach to incomplete interval-valued fuzzy information systems and its applications

With respect to multiple attribute group decision making problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of interval-valued uncertain linguistic variable. In this paper, we introduce the idea of variable precision into the incomplete interval-valued fuzzy information system and propose the theory of variable precision rough sets over incomplete interval-valued fuzzy information systems. Then, we give the properties of rough approximation operators and study the knowledge discovery and attribute reduction in the incomplete interval-valued fuzzy information system under the condition that a certain degree of misclassification rate is allowed to exist. Furthermore, a decision rule and decision model are given. Finally, an illustrative example is given and compared with the existing methods, the practicability and effectiveness of this method are further verified.

Probabilistic decision making based on rough sets in interval-valued fuzzy information systems

At present, the representative and hot research is three-way decision based on rough set theory. In addition, this topic has been applied in wide variety of specific. In the article, we aim to discuss the rough set method of decision theory in the background of interval-valued fuzzy information systems (IVFIS). First, the main work is to transform the IVFIS into two kinds of approximate spaces by the defined relations, which are fuzzy approximation space and interval-valued fuzzy approximation space, respectively. Simultaneously, fuzzy probability and IVF probability are considered in the whole process. Second, we study two kinds of decision-theoretic rough set methods by combining the Bayesian decision process. Finally, based on the above decision-making models, some illustrative examples about the credit evaluation of enterprises are introduced to deal with the real value and interval-valued data. These results show that the rough set method of decision theory we proposed has wider applications than decision-theoretic rough sets (DTRS).

Rule Extraction Based on Interval-Valued Rough Fuzzy Sets

A model of interval-valued rough fuzzy set combining interval-valued fuzzy set and rough set is investigated in this paper. Firstly, considering the deficiency of general sorting method between any interval-valued fuzzy numbers, an improved sorting method and a pair of new approximation operators about minimum and maximum are presented. Based on the improved operators, a model of interval-valued rough fuzzy set is established. At last, by using the modified model of interval-valued rough fuzzy set, a method of knowledge discovery in interval-valued fuzzy information systems is investigated.

Rough set theory for the incomplete interval valued fuzzy information systems

Considering the incompleteness and uncertainty of information systems, this paper combines the incomplete information systems with interval-valued fuzzy sets, and defines the incomplete interval-valued fuzzy information systems. The basic rough set theory for incomplete interval-valued fuzzy information systems is also discussed in this paper.

Information granularity in interval-valued intuitionistic fuzzy information systems

Interval-valued intuitionistic fuzzy information system is able to be more comprehensively,detailedly and visually depict and characterize the decision-making information than the general information system,so reaseaching its research uncertainty is of great importance.With the help of information granularity,this paper characterized the uncertainty of the interval-valued intuitionistic fuzzy information system.It constructed intersection,union,subtraction and complement four operators among granular structures,introduced three new partial order relations in interval-valued intuitionistic fuzzy information systems and established the relationships among them.It defined an interval-valued intuitionistic fuzzy information granularity and an axiomatic approach to interval-valued intuitionistic fuzzy information granularity in interval-valued intuitionistic fuzzy information systems.Finally,it investigated the properties of interval-valued intuitionistic fuzzy information granularity.

Graded dominance interval-based fuzzy objective information systems

Dominance interval-based fuzzy objective information systems are generalized models of single-valued fuzzy information systems. By introducing a graded dominance relation to dominance interval-valued fuzzy objective information systems, we establish a graded dominance interval-valued rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the graded dominance interval-valued relation. Furthermore, in order to simplify knowledge representation and extract nontrivial simpler graded dominance interval fuzzy decision rules, we propose two attribute reduction approaches to eliminate the redundant condition attributes that are not essential from the viewpoint of graded dominance interval-valued fuzzy decision rules. These results are helpful for decision-making analysis in dominance interval-valued fuzzy objective information systems.

Rule extraction based on granulation order in interval-valued fuzzy information system

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. This paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Two different approximation methods are then defined. Two algorithms based on the two approximation methods, called MRBFA and MRBBA are proposed for rule extraction. The two algorithms are evaluated by a housing database from UCI. The experimental results show that MRBFA and MRBBA achieve better classification performances than the method based on attribute reduction.

Positive approximation and converse approximation in interval-valued fuzzy rough sets

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. Thus, this paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Positive and converse approximations in interval-valued fuzzy rough sets are then defined, and their important properties are discussed. Two algorithms based on positive and converse approximations, namely, mine rules based on the positive approximation (MRBPA) and mine rules based on the converse approximation (MRBCA), are proposed for rule extraction. The two algorithms are evaluated by several data sets from the UC Irvine Machine Learning Repository. The experimental results show that MRBPA and MRBCA achieve better classification performances than the method based on attribute reduction.

New roughness measures of the interval-valued fuzzy sets

In the paper ( Gong, Sun, & Chen, 2008; Han, Chen, & Chen, 2008), by combining the rough set theory with the interval-valued fuzzy set theory, Gong and Han proposed the concept of the interval-valued rough fuzzy sets and studied a parameters-related roughness measure of the interval-valued fuzzy sets in an approximation space, respectively. Since the measure inherited from Banerjee’s about the fuzzy sets in Banerjee and Pal (1996), it inevitably holds some similar undesirable properties. In this paper, we first remark some defects about the above mentioned measure, and then give a new roughness measure–rough entropy of the interval-valued fuzzy sets in an approximation space by using the information entropy theory, and demonstrate the difference between the two measures by a simple illustration example. Furthermore, in respect that the two measures mentioned above both strongly depend on parameters, we propose a parameter-free roughness measure of the interval-valued fuzzy sets in an approximation space based on the notions of the average mass assignment and average membership function of an interval-valued fuzzy set, adhering to the idea of parameter-free roughness measure of the fuzzy sets proposed in Huynh and Nakamori (2005). Some related properties about the new measure are discussed. Finally, we discuss how use the new measure to evaluate the rough approximation quality of classification in an interval-valued fuzzy decision information system.

Fuzzy rough set theory for the interval-valued fuzzy information systems

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory, i.e., the interval-valued fuzzy rough set model is presented based on the interval-valued fuzzy information systems which is defined in this paper by a binary interval-valued fuzzy relations R ∈ F ( i ) ( U × U ) on the universe U . Several properties of the rough set model are given, and the relationships of this model and the others rough set models are also examined. Furthermore, we also discuss the knowledge reduction of the classical Pawlak information systems and the interval-valued fuzzy information systems respectively. Finally, the knowledge reduction theorems of the interval-valued fuzzy information systems are built.

Rough set theory for the interval-valued fuzzy information systems

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. This paper deals with an interval-valued fuzzy information system by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory and discusses the basic rough set theory for the interval-valued fuzzy information systems. In this paper we firstly define the rough approximation of an interval-valued fuzzy set on the universe U in the classical Pawlak approximation space and the generalized approximation space respectively, i.e., the space on which the interval-valued rough fuzzy set model is built. Secondly several interesting properties of the approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak approximation space and the generalized approximation space are investigated. Thirdly we discuss the attribute reduction of the interval-valued fuzzy information systems. Finally, the methods of the knowledge discovery for the interval-valued fuzzy information systems are presented with an example.