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Three-way decision is consistent with human cognitive processes and applied to different information systems. However, since the real world is more imprecision, hesitation, and ambiguity, experts can select interval fuzzy information to represent their evaluations. In the evaluation process, experts sometimes may not guarantee the interval fuzzy information satisfy the constraint between membership and nonmembership, which further impacts make decisions. Interval-valued $q$ -rung orthopair fuzzy set (IVq-ROFS) are proposed to improve the fault-tolerant ability and ensure the experts’ evaluation make sense. In this case, this article generalizes IVq-ROFS to three-way decision, which consists of the construction of three-way decision and the aggregation of interval continuity of IVq-ROFS. For considering the aggregation of interval continuity of IVq-ROFS, we first investigate the IVq-ROFS integral to aggregate continuous IVq-ROFSs by developing simplified interval-valued $q$ -rung orthopair fuzzy set. Particularly, in order to obtain integrable region, we design $\varepsilon$ -amendment to amend integral region of IVq-ROFS for removing unmeaning point in advance. To simplify the calculation, we further utilize Taylor series of the integral function to replace the complicated integral function. Second, a new equivalence class method is constructed to support three-way decision. Third, with the aid of the integral of IVq-ROFS and equivalence class method, we availably fuse the loss functions of the equivalence class and obtain the classifying rules of three-way decision by comparing the expected losses. Finally, we elaborate three-way decision by using a case of medical diagnosis about nephropathy and prove the validity of the investigated model. [ABSTRACT FROM AUTHOR]

Recently, frequent emergencies seriously impact people’s life and production. The timely emergency material can save more people. Hence, emergency material demand prediction is a core of emergency rescue. However, emergency is a continuous, uncertain evolution process. The emergency of different periods has various situations. The time-varying and uncertain characteristics of emergency have made this representation and prediction work much more complex. In order to address this concern, this article proposes a time-varying intuitionistic fuzzy set (TVIFS) to precisely depict the time-varying scenario and the uncertainty of emergencies. For utilizing the TVIFS of different time frames, we deeply explore the integral aggregation operator of TVIFS, which can take full account of decision hesitation and possible information. Due to the different time importance of different time frames, we investigate the integral of TVIFS with constant period weight in advance. Considering the time-varying period weight, the TVIFS integral with time-varying period weight is investigated. For the sake of calculation feasibility, inspired by the relationship between continuity and dispersion, we translate the TVIFS integral with variable period weight into the TVIFS integral with constant period weight. Furthermore, we develop time-varying intuitionistic fuzzy case-based reasoning (CBR) model to forecast the emergency materials demand by designing hybrid similarity between cases. Finally, we elaborate the application of time-varying intuitionistic fuzzy CBR model by using an example of forest fire and verify the validity of our proposed method. [ABSTRACT FROM AUTHOR]

Interval sets and hesitant fuzzy sets capture two types of hesitant situations and provide novel expression formats for decision makers. The authors propose a new hesitant fuzzy interval set and explore its information aggregation for multicriteria decision-making. An example is presented to elaborate on the performance of the approach. [ABSTRACT FROM AUTHOR]

Decision-theoretic rough sets (DTRSs) capture the decision semantics and can deduce three-way decisions with respect to the minimum expected risk. Considering the new evaluation format of hesitant fuzzy sets, we extend the range of applications of DTRSs to hesitant fuzzy information systems. In this case, the integrated approach by considering the interaction between information systems and loss functions becomes one of challenges. Different from the results reported in most of the existing papers, we combine the hesitant fuzzy information system and loss functions together via error analysis. In the hesitant fuzzy information system, a new binary relation is first defined by utilizing the normalization of hesitant fuzzy elements and the distance function. Then, the calculations of the similarity class and the conditional probability are discussed. With the aid of the error analysis method, we effectively aggregate the loss functions presented in the similarity class and determine the expected losses in the format of the intervals. Based on the possibility degree, we further explore the decision rules by comparing the expected losses. With the above analysis, we design a decision-making procedure of three-way decisions in a hesitant fuzzy information system. Finally, we elaborate the application of three-way decisions in hesitant fuzzy information systems by an example of the security evaluation of peer-to-peer lending platforms and validate our methods. [ABSTRACT FROM AUTHOR]

Three-way decisions play an important role in rough sets and decision theory. As a representative model, decision-theoretic rough sets (DTRSs) provide a sound interpretation of thresholds used in three-way decisions. This problem is associated with the determination of the loss function of DTRSs. In this paper, we investigate a novel way of determining the loss functions of DTRSs with relative values. More specifically, with the aid of analytic hierarchy process (AHP) method, the determination of loss functions is realized in the context of DTRSs. First, a hierarchical structure of DTRSs is constructed. Second, along the hierarchical structure, pairwise comparison matrices are analyzed in a top-down fashion. In light of the generic condition imposed on the loss functions of DTRSs, some constraints on relative values between loss functions are introduced. The relative ratios at each level are computed. Considering the consistency ratio (CR) of the reciprocal matrices, two mathematical programming approaches are developed by exploiting the flexibility of information granularity. Then, we design a decision procedure for the determination of loss functions and deduce three-way decisions. The loss functions are calculated by aggregating the relative ratios being available at each level. With regard to the loss functions, we finally compare the existing studies with the AHP method. We demonstrate that the relative value with AHP improves the restriction of the existing studies and exhibits a certain level of tolerance to inconsistency. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

In three-way group decision-making based on the minimum risk Bayesian decision theory, the consensus of basic loss function evaluation becomes its main core issue. However, if we only consider evaluation information consensus, it does not ensure the classification quality of three-way decisions. Thus, to balance the consensus and decision quality, we design a three-way group decision-making joint learning process via constructing a two-stage group consensus method. Inspired by supervised learning, Stage 1 establishes the minimum decision error optimization model (MDEOM) to learn the optimal parameters of three-way decisions and calculate decision loss reference values. Then, we design an algorithm to solve MDEOM based on particle swarm optimization (PSO) algorithm. In Stage 2, we calculate adjusted decision losses with the minimum decision loss difference consensus model (MDLDCM), which can guide the consensus adjustment of loss functions and improve the decision quality of three-way group decision making. Finally, some implications of three-way group decision making with the two-stage group consensus method are discussed by a series of experiments which prove the improvement effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]