Interval-valued Fuzzy Rough Set 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.

Technical attribute prioritisation in QFD based on cloud model and grey relational analysis

Promptly development of new products can be achieved through quality function deployment (QFD) process, which is critical to companies’ survival. Since the multi-criteria decision-making problem involved in QFD, a novel method integrating cloud model and grey relational analysis is put forward in this paper. Taking into account the subjectivity and ambiguity in linguistic evaluations, some scholars utilise fuzzy theory, rough theory, interval-valued fuzzy-rough sets and MCDM methods to improve traditional QFD. However, much priori information requirements, inability to handle subjectivity and randomness, and lack of mechanism to overcome small sample size problem are some inevitable drawbacks in these methods. To solve these deficiencies, a hybrid methodology is proposed in this paper, integrating the fortes of cloud model in processing ambiguity and randomness, and the merits of grey relational analysis in overcoming small sample size error as well as revealing the inner correlations. The comparative analysis of different approaches as well as the sensitivity analysis of criteria weights is implemented to prove the stability of the novel method. The results obtained in this paper shows that the proposed method can be a practical tool for improving the efficiency and accuracy of traditional QFD in reality management.

Interval-valued dual hesitant fuzzy rough set over two universes and its application

Interval-valued dual hesitant fuzzy rough set over two universes and its application

Topological structures of interval-valued hesitant fuzzy rough set and its application

Interval-valued hesitant fuzzy rough set, defined by Zhang et al. (55), is an extension of hesitant fuzzy rough sets, interval- valued fuzzy rough sets and fuzzy rough sets. For further studying the theories and applications of interval-valued hesitant fuzzy rough sets, in this paper, we mainly investigate the topological structures of interval-valued hesitant fuzzy rough sets. Firstly, the concept of interval-valued hesitant fuzzy topological spaces is introduced by us. Then relationships between interval-valued hesitant fuzzy rough approximation spaces and interval-valued hesitant fuzzy topological spaces are further established. It is proved that the set of all lower approximation sets based on an interval-valued hesitant fuzzy reflexive and transitive approximation space forms an interval-valued hesitant fuzzy topology; and conversely, for an interval-valued hesitant fuzzy rough topological space, there exists an interval-valued hesitant fuzzy reflexive and transitive approximation space such that the topology in the interval- valued hesitant fuzzy rough topological space is just the set of all lower approximation sets in the interval-valued hesitant fuzzy reflexive and transitive approximation space. That is to say, there exists a one-to-one correspondence between the set of all interval-valued hesitant fuzzy reflexive and transitive approximation spaces and the set of all interval-valued hesitant fuzzy rough topological spaces. Finally, a practical application is provided to illustrate the validity of the interval-valued hesitant fuzzy rough set model.

Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models.

Generalized Interval-Valued Fuzzy Rough Set and its Application in Decision Making

This paper presents a general study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. In the constructive approach, by employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Then properties of generalized interval-valued fuzzy rough approximation operators are discussed. Furthermore, connections between special types of interval-valued fuzzy relations and properties of generalized interval-valued fuzzy approximation operator are also established. In the axiomatic approach, generalized interval-valued fuzzy rough approximation operators are defined by axioms. We prove that different axiom sets can characterize the essential properties of generalized interval-valued fuzzy rough approximation operators. Also the composition of two approximation spaces is explored. Finally, a practical application is provided to illustrate the efficiency of the generalized interval-valued fuzzy rough set model.

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.

Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion

Knowledge-based modeling is a trend in complex system modeling technology. To extract the process knowledge from an information system, an approach of knowledge modeling based on interval-valued fuzzy rough set is presented in this paper, in which attribute reduction is a key to obtain the simplified knowledge model. Through defining dependency and inclusion functions, algorithms for attribute reduction and rule extraction are obtained. The approximation inference plays an important role in the development of the fuzzy system. To improve the inference mechanism, we provide a method of similarity-based inference in an interval-valued fuzzy environment. Combining the conventional compositional rule of inference with similarity based approximate reasoning, an inference result is deduced via rule translation, similarity matching, relation modification, and projection operation. This approach is applied to the problem of predicting welding distortion in marine structures, and the experimental results validate the effectiveness of the proposed methods of knowledge modeling and similarity-based inference.

Attributes Reduction Based on Interval-Valued Fuzzy Rough Sets

Aims: This paper provides a systematic study on attribute reduction with interval-valued fuzzy rough sets. Study Design: The interval-valued fuzzy rough sets are an important improvement of traditional rough set model to deal with both fuzziness and vagueness in data which the traditional one cannot handle. Place and Duration of Study: The existing researches on interval-valued fuzzy rough sets mainly focus on the establishment of lower and upper approximation operators by using constructive and axiomatic approaches. Less effort has been put on the attributes reduction of databases based on interval-valued fuzzy rough sets. Methodology: After introducing some concepts and theorems of attributes reduction with interval-valued fuzzy rough sets, we study the structure of the attributes reduction with interval-valued fuzzy rough sets and present an algorithm by using discernibility matrix to find all the attributes reductions with interval-valued fuzzy rough sets. Results: Finally, we propose an example to demonstrate our idea and method in this paper. Conclusion: With these discussions we construct a basic foundation for attributes reduction based on interval-valued fuzzy rough sets.

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.

On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse

This paper proposes a general study of ( I , T ) -interval-valued fuzzy rough sets on two universes of discourse integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. Some primary properties of interval-valued fuzzy logical operators and the construction approaches of interval-valued fuzzy T -similarity relations are first introduced. Determined by an interval-valued fuzzy triangular norm and an interval-valued fuzzy implicator, a pair of lower and upper generalized interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy relation on two universes of discourse is then defined. Properties of I -lower and T -upper interval-valued fuzzy rough approximation operators are examined based on the properties of interval-valued fuzzy logical operators discussed above. Connections between interval-valued fuzzy relations and interval-valued fuzzy rough approximation operators are also established. Finally, an operator-oriented characterization of interval-valued fuzzy rough sets is proposed, that is, interval-valued fuzzy rough approximation operators are characterized by axioms. Different axiom sets of I -lower and T -upper interval-valued fuzzy set-theoretic operators guarantee the existence of different types of interval-valued fuzzy relations which produce the same operators.

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.