ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

Covering based intuitionistic fuzzy (IF) rough set is a generalization of granular computing and covering based rough sets. By combining covering based rough sets, IF sets and fuzzy rough sets, we introduce three classes of coverings based IF rough set models via IF$$\beta $$-neighborhoods and IF complementary $$\beta $$-neighborhood (IFC$$\beta $$-neighborhood). The corresponding axiomatic systems are investigated, respectively. In particular, the rough and precision degrees of covering based IF rough set models are discussed. The relationships among these types of coverings based IF rough set models and covering based IF rough set models proposed by Huang et al. (Knowl Based Syst 107:155–178, 2016). Based on the theoretical analysis for coverings based IF rough set models, we put forward intuitionistic fuzzy TOPSIS (IF-TOPSIS) methodology to multi-attribute decision-making (MADM) problem with the evaluation of IF information problem. An effective example is to illustrate the proposed methodology. Finally, we deal with MADM problem with the evaluation of fuzzy information based on CFRS models. By comparative analysis, we find that it is more effective to deal with MADM problem with the evaluation of IF information based on CIFRS models than the one with the evaluation of fuzzy information based on CFRS models.

The basic notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation. This paper proposes an intuitionistic fuzzy rough set (IFRS) model which is a combination of intuitionistic fuzzy set (IFS) and rough set. We approximate an IFS by using soft binary relations instead of fixed binary relations. By using this technique, we get two pairs of intuitionistic fuzzy (IF) soft sets, called the upper approximation and lower approximation with respect to foresets and aftersets. Properties of newly defined rough set model (IFRS) are studied. Similarity relations between IFS with respect to this rough set model (IFRS) are also studied. Finally, an algorithm is constructed depending on these approximations of IFSs and score function for decision-making problems, although a method of decision-making algorithm has been introduced for fuzzy sets already. But, this new IFRS model is more accurate to solve the problem because IFS has degree of nonmembership and degree of hesitant.

Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction

A novel intuitionistic fuzzy rough instance selection and attribute reduction with kernelized intuitionistic fuzzy C-means clustering to handle imbalanced datasets

This paper researched and constructed residuation implication operator of intuitionistic fuzzy T-norms.Based on this,the paper deducted the intuitionistic fuzzy rough sets model,and proved that the Pawlak rough sets,intuitionistic fuzzy sets,fuzzy rough sets,rough fuzzy sets and fuzzy T-norms rough sets were special cases of intuitionistic fuzzy rough sets.At last,some properties of intuitionistic fuzzy sets were presented and proved.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak's rough approximations have been made in the literature over these years. This paper proposes a general framework for the study of intuitionistic fuzzy rough approximation operators based on intuitionistic fuzzy triangle norm. In the constructive approach, a pair of lower and upper induced from intuitionistic fuzzy relation are defined. Basic properties of intuitionsitic fuzzy rough approximation operators are then examined. By introducing intuitionistic fuzzy residual implication, Further properties of intuitionistic fuzzy rough approximation operators are then investigated. we propose that classical rough set and fuzzy rough are special types of intuitionistic fuzzy rough set based on intuitionistic fuzzy triangle norm.

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods.

In this paper, we are concerned with a problem related to granular computing with game theoretic intuitionistic fuzzy rough sets(GTIFRS). The game theoretic intuitionistic fuzzy rough sets is defined over compatibility based intuitionistic fuzzy relation. The imprecise information obtained, is considered to be composed of intuitionistic fuzzy granules. The basis of granulation is splitting intervals into several sub-intervals. A competitive situation arises due to movement of granules which is controlled by threshold parameters.

An improved measure of similarity based on the Hamming distance for measuring the degree of similarity between intuitionistic fuzzy rough sets was proposed on the basis of analyzing the deficiency of the existing similarity measure method.This method solved the problem of inaccurate similarity measure by adding the hesitancy degree and weight.Firstly,a similarity measure method for the degree of similarity between two intuitionistic fuzzy rough elements was given,and several important characters of it were revealed.Furthermore,a similarity measure method based on the Hamming distance for the degree of similarity between intuitionistic fuzzy rough sets was presented.This method was proved to have the same characters.At last,this improved similarity measure method is confirmed to be more reasonable and effective by examples.

In view of the characteristics with big data, high feature dimension, and dynamic for a large-scale intuitionistic fuzzy information systems, this paper integrates intuitionistic fuzzy rough sets and generalized dynamic sampling theory, proposes a generalized attribute reduction algorithm based on similarity relation of intuitionistic fuzzy rough sets and dynamic reduction. It uses dynamic reduction sampling theory to divide a big data set into small data sets and relative positive domain cardinality instead of dependency degree as decision-making condition, and obtains reduction attributes of big intuitionistic fuzzy decision information systems, and achieves the goal of extracting key features and fault diagnosis. The innovation of this paper is that it integrates generalized dynamic reduction and intuitionistic fuzzy rough set, and solves the problem of big data set which cannot be solved by intuitionistic fuzzy rough set. Taking an actual data as an example, the scientificity, rationality and effectiveness of the algorithm are verified from the aspects of stability, diagnostic accuracy, optimization ability and time complexity. Compared with similar algorithms, the advantages of the proposed algorithm for big data processing are confirmed.

This paper has proposed a classification rule base mining algorithm combining the genetic algorithm and intuitionistic fuzzy-rough set for large-scale intuitionistic fuzzy information system. The algorithm has proposed innovatively the definitions and measurement metrics of completeness, interaction and compatibility describing the whole rule base, and constructed a multi-objective optimization model to optimize the population size of data sample, and used the intuitionistic fuzzy-rough set to reduce the attribute set of fuzzy information system, and used intuitionistic fuzzy similar class to extract large-scale intuitionistic fuzzy information system rules, and obtained an optimal rule base with the minimal size, configuration, generation time and storage space. A threshold control mechanism is used to evaluate the completeness, interaction and correlation of rule population and improves the robustness and flexibility of sample population optimization and rule base generation. The algorithm is verified by the real aircraft health data sets. The algorithm is validated by similar mature and effective algorithms in accuracy, time complexity using real data and has good robustness and adaptability to different size large-scale fuzzy information system.

Representations of L-fuzzy rough approximation operators

Recently, making decisions and analyzing data are getting more and more attention by taking advantage of rough set and intuitionistic fuzzy set theories. Additionally, it can be found that many works have been developed about intuitionistic fuzzy rough set approaches from different viewpoints. In this article, we introduce similarity degrees and four kinds of uncertainty measurement, called θ -conditional entropies, θ -similarity intuitionistic fuzzy accuracies, θ -similarity intuitionistic fuzzy roughness and θ -rough decision entropies in intuitionistic fuzzy decision tables. Also, we provide a novel method for classifying the objects’ intuitionistic fuzzy decision table. Moreover, we carefully discuss the lower approximation and upper approximation of a given set and classify their important properties based on the novel classes in the intuitionistic fuzzy decision table. Furthermore, an illustrated example is employed to demonstrate the conceptual arguments of these measurements based on different similarity degrees and similarity rates. From this, it can be found that the new measures are superior to the classical accuracy and roughness, and the method is valuable and useful in real life situations.