Decui Liang

Triangular fuzzy decision-theoretic rough sets

Based on decision-theoretic rough sets (DTRS), we augment the existing model by introducing into the granular values. More specifically, we generalize a concept of the precise value of loss function to triangular fuzzy decision-theoretic rough sets (TFDTRS). Firstly, ranking the expected loss with triangular fuzzy number is analyzed. In light of Bayesian decision procedure, we calculate three thresholds and derive decision rules. The relationship between the values of the thresholds and the risk attitude index of decision maker presented in the ranking function is analyzed. With the aid of multiple attribute group decision making, we design an algorithm to determine the values of losses used in TFDTRS. It is achieved with the use of particle swarm optimization. Our study provides a solution in the aspect of determining the value of loss function of DTRS and extends its range of applications. Finally, an example is presented to elaborate on the performance of the TFDTRS model.

Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets

Three-way decisions with decision-theoretic rough sets (DTRSs) provide a new methodology to confront risk decision problems. The risk is associated with the loss function of DTRSs. Under the intuitionistic fuzzy environment, we combine the loss functions of DTRSs with intuitionistic fuzzy sets (IFSs). Considering the new evaluation format of loss function with intuitionistic fuzzy numbers (IFNs), we propose a naive model of intuitionistic fuzzy decision-theoretic rough sets (IFDTRSs) and elaborate its relevant properties in advance. At this point, a critical issue is the determination of three-way decisions. In the frame of IFDTRSs, we then explore deriving three-way decisions for single-period decision making. Based on the positive and negative characteristics of IFNs, we design three strategies to address IFNs and derive corresponding three-way decisions. Meanwhile, we compare the three strategies and summarize their own applicabilities. In order to accommodate multi-period scenarios, we further extend IFDTRSs to the multi-period situation. With the aid of the results of the single period decision making, we analyze three aggregation operations of IFDTRSs for multi-period information, which are DIFWA, DIFPA and DIFOA, respectively. By comparing these operations, an algorithm for deriving three-way decisions in multi-period decision making is designed. These results help us to make a reasonable decision in the intuitionistic fuzzy environment. Finally, an example is presented to elaborate on three-way decisions with IFDTRSs.

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

Decision-theoretic rough sets (DTRS) are a representative rough set model. The loss function is a pivotal ingredient of DTRS, which is associated with the decision makers evaluation. Considering the value of loss function with the imprecise evaluation, interval-valued DTRS (IVDTRS) and its mechanism in this paper are explored. First, we construct a basic model of IVDTRS. The comparison between DTRS and IVDTRS is discussed. In the frame of IVDTRS, we then focus on deriving three-way decisions with the aid of two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively. The certain ranking method converts an interval value into single and derives decision rules under a certain risk attitude of decision maker; the degree of possibility ranking method assumes the flexibility of interval and utilizes the preference between interval values. All the combinations and their prerequisites are summarized, in which we obtain two types of decision rules. Based on the above analysis, we further propose an optimization method for three-way decisions with IVDTRS, which is designed to minimize the overall uncertainty based on the Shannon entropy. We also compare these methods based on standard data sets. Finally, the criteria for choosing a suitable method to three-way decisions with IVDTRS are generated. These results can support decision making in the uncertain environment.

Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making

Graphical abstractDisplay Omitted HighlightsWe provide a method of the determination of the two types of parameters used in the DTRS.The application of DTRS is extended to the scenarios of qualitative evaluation.An algorithm is designed to improve the inconsistency of multi-attribute group decision making under linguistic assessment. Based on decision-theoretic rough set model of three-way decisions, we augment the existing model by introducing linguistic terms. Considering the two types of parameters being used in the three-way decisions with linguistic assessment, a certain type of novel three-way decisions based on the Bayesian decision procedure is constructed. In this way, three-way decisions with decision-theoretic rough sets are extended to the qualitative environment. With the aid of multi-attribute group decision making, the values of these parameters are determined. An adaptive algorithm supporting consistency improvement of multi-attribute group decision making is designed. Then, we optimize the scales of the linguistic terms with the use of particle swarm optimization. The values of these parameters of three-way decisions are aggregated when proceeding with group decision making. Finally, the proposed model of three-way decisions with linguistic assessment is applied to the selection process of new product ideas.

THREE-WAY GOVERNMENT DECISION ANALYSIS WITH DECISION-THEORETIC ROUGH SETS

By considering the risks in policy making procedure, a three-way decision approach based on the decision-theoretic rough set model is adopted to risk government decision-making. A three-way decision is made based on a pair of thresholds on conditional probabilities. A positive rule makes a decision of executing, a negative rule makes a decision of non-executing, and a boundary rule makes a decision of deferment. The loss functions are used to calculate the required two thresholds to describe the decision risk with the Bayesian decision procedure. A case study of government petroleum risk investment demonstrates the proposed method.

A Novel Risk Decision Making Based on Decision-Theoretic Rough Sets Under Hesitant Fuzzy Information

Decision-theoretic rough sets (DTRSs) play a crucial role in risk decision-making problems. With respect to the minimum expected risk, DTRSs deduce the rules of three-way decisions. Considering the new expression of evaluation information with hesitant fuzzy sets (HFSs), we introduce HFSs into DTRSs and explore their decision mechanisms. More specifically, we take into account the losses of DTRSs with hesitant fuzzy elements and propose a new model of hesitant fuzzy decision-theoretic rough sets (HFDTRSs). Some properties of the expected losses and their corresponding scores are carefully investigated under the hesitant fuzzy information. Three-way decisions and the associated cost of each object are further derived. With the above analysis, a novel risk decision-making method with the aid of HFDTRSs is developed. Besides the three-way decisions with DTRSs, the method investigates the ranking and resource allocation by utilizing the associated costs of alternatives and multiobjective 0-1 integer programming. Our study also offers a solution in the aspect of determining losses of DTRS and extends the range of applications.

Three-way group decisions with decision-theoretic rough sets

GDM-based three-way decisions as an extension model of DTRSs is proposed.GDM provides a new semantic interpretation for three-way decisions.Our method explains the imprecise origin of the existing literatures. On consideration of the effectiveness of group decision making (GDM) in practical complex decision problems, we introduce GDM into three-way decisions with decision-theoretic rough sets (DTRSs) and propose GDM-based three-way decisions. GDM-based three-way decisions extend the range of applications of three-way decisions with DTRSs and provide a novel interpretation of the determination of loss functions. Based on DTRSs, we firstly focus on analyzing the determination for the loss functions under the GDM environment. With the aid of the principle of justifiable granularity, we adopt the important and majority suggestions of experts to measure each loss function, which supports a coherent way of designing information granules in presence of numerics. In this case, the loss functions are determined in the form of interval-valued information granule. By using the interval comparison method, we further deduce the three-way decisions and design a corresponding decision procedure of GDM-based three-way decisions. Then, an example of strategy supply selection is given to elaborate the GDM-based three-way decisions. Finally, we validate the performance of our proposed method by experimental analysis.

The New Extension of TOPSIS Method for Multiple Criteria Decision Making with Hesitant Pythagorean Fuzzy Sets

Abstract Pythagorean fuzzy sets (PFSs) as a new generalization of fuzzy sets (FSs) can handle uncertain information more flexibly in the process of decision making. In our real life, we also may encounter a hesitant fuzzy environment. In view of the effective tool of hesitant fuzzy sets (HFSs) for expressing the hesitant situation, we introduce HFSs into PFSs and extend the existing research work of PFSs. Concretely speaking, this paper considers that the membership degree and the non-membership degree of PFSs are expressed as hesitant fuzzy elements. First, we propose a new concept of hesitant Pythagorean fuzzy sets (HPFSs) by combining PFSs with HFSs. It provides a new semantic interpretation for our evaluation. Meanwhile, the properties and the operators of HPFSs are studied in detail. For the sake of application, we focus on investigating the normalization method and the distance measures of HPFSs in advance. Then, we explore the application of HPFSs to multi-criteria decision making (MCDM) by employing the technique for order preference by similarity to ideal solution (TOPSIS) method. A new extension of TOPSIS method is further designed in the context of MCDM with HPFSs. Finally, an example of the energy project selection is presented to elaborate on the performance of our approach.

Three-Way Decisions in Dynamic Decision-Theoretic Rough Sets

In the previous decision-theoretic rough sets DTRS, its loss function values are constant. This paper extends the constant values of loss functions to a more realistic dynamic environment. Considering the dynamic change of loss functions in DTRS with the time, an extension of DTRS, dynamic decision-theoretic rough sets DDTRS is proposed in this paper. An empirical study of climate policy making validates the reasonability and effectiveness of the proposed model.

Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information

Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the area of risk decision-making. When we confront the complicated and uncertain environment, one of challenges is to estimate the loss function of DTRSs. As a new generalization of fuzzy sets, dual hesitant fuzzy sets (DHFSs) can handle uncertain information more flexibly in the process of decision making and give a new measure for the determination of loss functions of DTRSs. To have more interesting results in the context of three-way decisions, we introduce the new hesitant format of DHFSs into DTRSs and explore a new three-way decision model. Firstly, we take into account the loss functions of DTRSs with dual hesitant fuzzy elements (DHFEs) and propose a dual hesitant fuzzy DTRS model. In order to satisfy the preconditions of three-way decisions, we analyze the normalized principle of loss functions under the dual hesitant fuzzy environment. Meanwhile, some properties of the expected losses are carefully investigated. Then, we further design two approaches for deriving three-way decisions with the new DTRS model, i.e., Method 1 and Method 2, which mainly relies on the comparisons among the expected losses. Method 1 is a general method based on the scores and the accuracies of DHFEs. Method 2 is a ranking method of possibility degrees with a stochastic strategy and enriches the comparisons among the expected losses. Finally, the assessment of emergency blood transshipment is used to illustrate and compare these proposed methods.