Attribute reduction of data with error ranges and test costs

The cost-sensitive approximation of neighborhood rough sets and granular layer selection

Neighborhood rough sets (NRS) are the extended model of the classical rough sets. The NRS describe the target concept by upper and lower neighborhood approximation boundaries. However, the method of approximately describing the uncertain target concept with existed neighborhood information granules is not given. To solve this problem, the cost-sensitive approximation model of the NRS is proposed in this paper, and its related properties are analyzed. To obtain the optimal approximation granular layer, the cost-sensitive progressive mechanism is proposed by considering user requirements. The case study shows that the reasonable granular layer and its approximation can be obtained under certain constraints, which is suitable for cost-sensitive application scenarios. The experimental results show that the advantage of the proposed approximation model, moreover, the decision cost of the NRS approximation model will monotonically decrease with granularity being finer.

Three-way decisions with decision-theoretic rough sets based on covering-based q-rung orthopair fuzzy rough set model

Based on decision theory rough sets (DTRSs), three-way decisions (TWDs) provide a risk decision method for solving multi-attribute decision making (MADM) problems. The loss function matrix of DTRS is the basis of this method. In order to better solve the uncertainty and ambiguity of the decision problem, we introduce the q-rung orthopair fuzzy numbers (q-ROFNs) into the loss function. Firstly, we introduce concepts of q-rung orthopair fuzzy β-covering (q-ROF β-covering) and q-rung orthopair fuzzy β-neighborhood (q-ROF β-neighborhood). We combine covering-based q-rung orthopair fuzzy rough set (Cq-ROFRS) with the loss function matrix of DTRS in the q-rung orthopair fuzzy environment. Secondly, we propose a new model of q-ROF β-covering DTRSs (q-ROFCDTRSs) and elaborate its relevant properties. Then, by using membership and non-membership degrees of q-ROFNs, five methods for solving expected losses based on q-ROFNs are given and corresponding TWDs are also derived. On this basis, we present an algorithm based on q-ROFCDTRSs for MADM. Then, the feasibility of these five methods in solving the MADM problems is verified by an example. Finally, the sensitivity of each parameter and the stability and effectiveness of these five methods are compared and analyzed.

Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model

On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions.

Rough sets and Laplacian score based cost-sensitive feature selection

Cost-sensitive feature selection learning is an important preprocessing step in machine learning and data mining. Recently, most existing cost-sensitive feature selection algorithms are heuristic algorithms, which evaluate the importance of each feature individually and select features one by one. Obviously, these algorithms do not consider the relationship among features. In this paper, we propose a new algorithm for minimal cost feature selection called the rough sets and Laplacian score based cost-sensitive feature selection. The importance of each feature is evaluated by both rough sets and Laplacian score. Compared with heuristic algorithms, the proposed algorithm takes into consideration the relationship among features with locality preservation of Laplacian score. We select a feature subset with maximal feature importance and minimal cost when cost is undertaken in parallel, where the cost is given by three different distributions to simulate different applications. Different from existing cost-sensitive feature selection algorithms, our algorithm simultaneously selects out a predetermined number of “good” features. Extensive experimental results show that the approach is efficient and able to effectively obtain the minimum cost subset. In addition, the results of our method are more promising than the results of other cost-sensitive feature selection algorithms.

Interval-Valued Neutrosophic Soft Rough Sets

We first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets (IVIF-soft rough sets).