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

The uncertainty of probabilistic rough sets in multi-granulation spaces

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.

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.

A regret theory-based multi-granularity three-way decision model with incomplete T-spherical fuzzy information and its application in forest fire management

Probabilistic rough sets define the lower and upper approximations and the corresponding three regions by using a pair of (α,β) thresholds. Many attempts have been made to determine or calculate effective (α,β) threshold values. A common principle in these approaches is to combine and utilize some intelligent technique with a repetitive process in order to optimize different properties of rough set based classification. In this article, we investigate an approach based on genetic algorithms that repeatedly modifies the thresholds while reducing the overall uncertainty of the rough set regions. A demonstrative example suggests that the proposed approach determines useful threshold values within a few iterations. It is also argued that the proposed approach provide similar results to that of some existing approaches such as the game-theoretic rough sets.

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.

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.

Quantitative rough sets based on subsethood measures

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.

Probabilistic rough set based on statistics and equivalence relations can provide membership, boundary approximations, subsets dependency, criterion dependency, three-way decision, and so forth. However, the probability is non-determinant due to randomness and users choices which is subjective in most cases. This research aims to provide determinant probabilities through relevant evidences on three-way decision, called evidential probabilities for rough set (EPRS) to consider the subjective criteria. In this article a research position highlights the boundary regions in terms of subjective criteria showing how subjective criteria may provide a means to narrow the uncertainty by projecting the boundary regions through user preferences in providing better decision precisions. The idea is also projected on prospect theory by showing the adaptable tuning of reference point through decision based subjective preferences. A case study about nations competitiveness is estimated through EPRS and shows the evidential probability can be identified in reality.

Neighborhood based decision-theoretic rough set models

Matrix approach to decision-theoretic rough sets for evolving data

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values' Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules w.r.t. AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods.

With the requirements of the power load predicting accuracy becoming higher and higher, and the actual power load is also a complex nonlinear system limited by various uncertain factors. Given only considering the influence of a single model on the load forecasting, the predicting accuracy is absolutely not high under the comprehensive effects of multiple factors. Ensuring to make the electrical model satisfy the requirements, there is access to improving the accuracy of load predicting results through analysis of the relationship between load and multiple factors in power load forecasting. This paper combines the rough set theory with information fusion, firstly a decision table of attributes is established on the basis of historical datum, for the purpose of simplifying the attribute index in mining to obtain important information. Following step is to rank the importance of the factors influencing the load according to the degree of effect, with grouping these sorted factors into attributes combination and using the same kind of load forecasting method to predict each combination's own results, and finally all groups of the predicting results are integrated by fusion, where then final predicting result can be obtained. The results of the algorithmic example show that groups of predicting results integrated based on information fusion theory are better than the results got through any casual single attribute combination. And fusion results are a combined action of a variety of related factors, enhancing the favorable trend, where at the same time it has reduced the uncertainty brought by multiple factor comprehensive effect. Based on information fusion the predicting results are helpful to reduce the prediction error, which is feasible and effective. With the explosive growth on the amount of in today's information age, the wave of data is coming, fast and furious. The era of big proposes a new challenge for the development in electricity industry. With the advance of electricity industry, intelligence, automation and interaction will bring many datum casing electrical big generation. Due to the numerous index of power load forecasting, different goals of all kinds of power load forecasting, even with the same kind of theory, the forecast model to predict no matter from the form, content or effect also vary widely. The load in the medium and long-term prediction of power system is greatly influenced by economy, society and meteorology factors and other uncertainties, etc. How to extract the key factor from multiple factors and reduce the results' uncertainty arising from the comprehensive effect of multiple factors, and improving the precision has been becoming a serious problem to be solved. Aiming at these problems, the paper based on the literature (8) proposing medium-and long- term load forecasting based on partial least squares regression analysis, an more optimized and advanced method is put forward to improve accuracy of prediction. The rough set theory and information fusion are introduced into the model, which respectively advance pre-processing and optimize the integration of multiple sets of results after prediction, in order to reduce uncertainty caused by varieties factors affecting and improve accuracy of forecasting results. II. THE ROUGH SET THEORY In the era of big data, on account of the characteristics on grid volume, which is large amount, variety type, and more speed, the traditional attribute simplified methods have been unable to complete the pre-processing on electrical big data. To this end the paper proposes a method on power big simplified processing based on cloud computing technology. The rough set theory which offers a new way for mining, is a new mathematical tool to deal with uncertain and imprecise problems. In this paper, rough sets method is used in power load forecasting to analyze the dependence of load on each factor and the importance of various properties in condition attribute set. In the decision system R={U, A}, the rough set divides A(attribute) into two categories C and D, where C is condition attribute, D is decision attribute, and U is domain. The ternary collection R={U,C,D} is known as a decision-making system. An important application of rough set in the analysis is to find the dependence among attributes from a known decision system R={U,C,D}. The dependency is defined as follows.

Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets