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As a system reliability analysis technology, failure mode and effect analysis (FMEA) has been widely used in various industries to reduce the failure risk of products, systems, and services. In recent years, many researchers have found that this technology has limitations in failure mode assessment and failure mode prioritization in complex uncertain environment. In order to solve this problem, this article proposes a new FMEA model, which combines hesitant Pythagorean fuzzy sets (HPFSs) and ORESTE method. Specifically, HPFSs are used to describe the risk assessment information of experts. The ORESTE method is extended to determine the risk priority of the failure modes in FMEA. Moreover, the PIR structure of ORESTE is improved to reduce the subjective influence of experts. Finally, an example of risk assessment of intelligent aquaculture system is given to verify the applicability and effectiveness of the proposed FMEA model. The results show that the proposed FMEA model can not only accurately describe the hesitation and uncertainty of experts’ risk assessment information, but also obtain more suitable risk ranking of failure modes, based on which managers can further take corresponding preventive measures.

With the rise of emerging technology in the fourth industrial revolution, modern agricultural technologies are gradually adopted to increase the yield and efficiency. Meanwhile, they also may bring the negative effect to social and environment sustainable development. Ignoring the requirement of sustainability will have an impact on the development of the country and society. Besides, the uncertainty and multistakeholder on sustainable modern agricultural technology assessment (SMATA) have made this appraisal much more complex, including their entanglement with rapidly changing cultural norms and social relations. Thus, in order to address these concerns, this article develops a holistic multistakeholder transdisciplinary approach with supporting SMATA. More precisely, due to the uncertainty of environment and vague knowledge possessed by stakeholders, we first investigate the evaluation measure of SMATA by introducing $q$ -rung orthopair fuzzy set ( $q$ -ROFS). Second, group opinion of stakeholders is fused by developing a new transdisciplinary evaluation aggregation operator. Third, to achieve more robust weights of key factors, three extended best worst method models from three different comparative perspectives of $q$ -ROFS are established. The final weight of key factors is further obtained by utilizing the variable entropy method. Fourth, we design a new decision approach of SMATA by improving evaluation based on distance from average solution method. Finally, a modern agricultural project base of Xichang city in China is used to demonstrate the effectiveness and rationality of our proposed SMATA method, including the simulation experiments on sensitivity analysis and comparative analysis. These results provide some exploratory insight and guidelines of SMATA for government and organization.

Recently, frequent emergencies seriously impact the 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, the 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 paper 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 model to forecast the emergency materials demand by designing hybrid similarity between cases. Finally, we elaborate the application of time-varying intuitionistic fuzzy case-based reasoning model by using an example of forest fire and verify the validity of our proposed method.

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 non-membership and further impact 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 paper 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 firstly investigate the IVq-ROFS integral to aggregate continuous IVq-ROFSs by developing simplified interval-valued q-rung Orthopair fuzzy set (SIVq-ROFS). 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. Secondly, a new equivalence class method is constructed to support three-way decision. Thirdly, 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.

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.

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.

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.

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.