Thresholds Determination for Probabilistic Rough Sets with Genetic Algorithms

The uncertainty of probabilistic rough sets in multi-granulation spaces

Three-way decision making approach to conflict analysis and resolution using probabilistic rough set over two universes

The rough set theory (RST) can deal with the approximations of an arbitrary subset of a universe by two definable subsets called, respectively, the lower and the upper approximations. Probabilistic rough sets (PRS) model is an extension of RST. In this paper, we propose a new matrix view of PRS and give the matrix representation of the lower and upper approximations of PRS. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under PRS. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

Quantitative rough sets based on subsethood measures

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.

Sentiment analysis, one of the most trending natural language processing tasks, is used to mine opinions or sentiments from a given text. Two significant challenges of sentiment analysis are 1) complexity in data pre-processing caused by the high dimensionality of textual data; 2) uncertainty in classifying sentiment polarities due to the ambiguity of natural languages. To address these issues, we propose a model using part-of-speech-based feature extraction to reduce dimensionality and game-theoretic rough sets (GTRS) to establish a balance between the accuracy and coverage trade-off. We evaluate this model with three different sizes of datasets (Yelp reviews, IMDB movie reviews, and Amazon product reviews). The experiment results show that the proposed model outperforms Pawlak’s rough set model and 0.5-probabilistic rough set model. In comparison with four traditional binary classification models (i.e., SVM, naïve Bayes, decision tree, and KNN), the proposed model also achieves higher accuracy rates. This research suggests that the proposed model is promising to deal with the complexity and uncertainty in sentiment analysis tasks.

In this paper, we study the application of fuzzy set theory, genetic algorithms and rough set theory techniques to the control of the rectifier. A fuzzy adaptive control scheme with the aid of rough set theory via genetic algorithms (GAs) finding the center parameters in place of the classical control is proposed. On the one hand, genetic algorithm gets optimal parameters of an accurate domain model, which tunes the scaling factors of fuzzy adaptive control but is hardly established in a non-liner system. On the other hand, fuzzy adaptive control deals with the dynamics and complexity of responses from rectifier of a HVDC system in the operation points, by adjusting its control parameters with the aid of rough tuner adaptively. Our study includes a brief introduction to fuzzy control and rough set algorithms, both theory and application. We also evaluate the performance of rough fuzzy control by simulation in the paper. The focus of our experiments is on the constant current control in rectifier side of HVDC system. The result shows there are many improvements offered by the fuzzy control scheme based on rough set theory in comparison with the only fuzzy control scheme in the rectifier side of HVDC system.

Soft rough fuzzy sets and soft fuzzy rough sets

In e-learning environment, optimal learning patterns are discovered for realising and understanding the effective learning styles. The value of uncertain and imprecise knowledge collected has to be categorised into classes known as membership grades. Rough set theory is potential in categorising data into equivalent classes and fuzzy logic may be applied through soft thresholds for refining equivalence relation that quantifies correlation between each class of elucidated data. In this paper, probabilistic variable precision fuzzy rough set technique (PVPFRST) is proposed for deriving robust approximations and generalisations that handles the types of uncertainty namely stochastic, imprecision and noise in membership functions. The result infers that the degree of accuracy of PVPFRST is 21% superior to benchmark techniques. Result proves that PVPFRST improves effectiveness and efficiency in identifying e-learners styles and increases the performance by 27%, 22% and 25% in terms of discrimination rate, precision and recall value than the benchmark approaches.

Smart tourism destinations are characterized by a pervasive presence of new technologies able to influence and improve the quality of tourist experiences. Understanding how tourists perceive and evaluate the assets and point of interests of a smart tourism destination is the first step for supporting decision makers and urban planners in making coherent and informed decisions aiming at improving the competitiveness of the destination. In this paper, we present a novel approach based on Granular Computing and Rough Set Theory for the analysis of the collective perception of a community of users with respect to points of interest (POI) in a smart tourism destination. The approach supports the classification of the POIs with respect to the tourists' perception by leveraging on the Three-way decision model and Probabilistic Rough Sets. The creation of multi-level granular structures representing the users' opinions is an added value of the approach when dealing with many POIs and large communities of tourists. An illustrative example related to the city of Salerno is reported to demonstrate the capability of the approach in supporting decision makers in the evaluation of tourist experiences.

This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF) probabilistic rough sets (MG-BVF-PRSs) models in multi-granulation BVF probabilistic approximation space over two universes. Four types of MG-BVF-PRSs are established, by the four different conditional probabilities of BVF event. For different constraints on parameters, we obtain four kinds of each type MG-BVF-PRSs over two universes. To find a suitable way of explaining and determining these parameters in each kind of each type MG-BVF-PRS, three-way decisions (3WDs) are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation BVF decision-theoretic rough set (MG-BVF-DTRS) approach. The main contribution of this paper is twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-BVF-PRS model over two universes. Another is to present an approach to select parameters in MG-BVF-PRS modeling by using the process of decision making under conditions of risk.

Matrix approach to decision-theoretic rough sets for evolving data

Rough sets, proposed by Pawlak and rough fuzzy sets proposed by Dubois and Prade were expressed with the different computing formulas that were more complex and not conducive to computer operations. In this paper, we use the composition of a fuzzy matrix and fuzzy vectors in a given non-empty finite universal, constitute an algebraic system composed of finite dimensional fuzzy vectors and discuss some properties of the algebraic system about a basis and operations. We give an effective calculation representation of rough fuzzy sets by the inner and outer products that unify computing of rough sets and rough fuzzy sets with a formula. The basis of the algebraic system play a key role in this paper. We give some essential properties of the lower and upper approximation operators generated by reflexive, symmetric, and transitive fuzzy relations. The reflexive, symmetric, and transitive fuzzy relations are characterized by the basis of the algebraic system. A set of axioms, as the axiomatic approach, has been constructed to characterize the upper approximation of fuzzy sets on the basis of the algebraic system.

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

Proposed a method of fault diagnosis for cold storage system, the method based on probabilistic rough set and support vector machine(SVM). Simplify the uncertain information by using probabilistic rough set of Bayes decision making. Design a multi-level classifier of SVM to fault diagnosis. Research the typical fault set of cold storage system with the proposed method. The results show the accuracy ability of fault diagnosis with the proposed method.