By combining covering based rough sets, fuzzy rough sets, and multigranulation rough sets, we introduce covering based multigranulation fuzzy rough set models by means of fuzzy
β
-neighborhoods. We ...investigate axiomatic characterizations of covering based optimistic, pessimistic and variable precision multigranulation fuzzy rough set models. We propose coverings based
α
-optimistic (pessimistic) multigranulation fuzzy rough sets and
D
-optimistic (pessimistic) multigranulation fuzzy rough sets from fuzzy measures. We examine the relationships among these kinds of coverings based fuzzy rough sets. Finally, we apply the proposed models to solve problems for multi-criteria group decision-making.
Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on affective, cognitive, and social processes employed by humans ...for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions.
The model of covering-based fuzzy rough sets (CFRSs) can be regarded as a hybrid one by combining covering-based rough sets with fuzzy sets. In this paper, based on fuzzy neighborhoods, we propose ...two types of covering-based variable precision fuzzy rough sets (CVPFRSs) via fuzzy logical operators, i.e., type-I CVPFRSs and type-II CVPFRSs. Then, several basic properties of the two types of CVPFRSs are discussed. In addition, by virtue of the idea of PROMETHEE II methods, we construct a novel method to multi-attribute decision-making (MADM) in the context of medical diagnosis based on the proposed rough approximation operators. Finally, a test example for illustrating the proposed method is given. Meanwhile, a comparative analysis and an experimental evaluation are further discussed to interpret and evaluate the effectiveness and superiority of the proposed method. The proposed rough set model not only extends the theory of CFRSs, but also provides a new perspective for MADM with fuzzy evaluation information.
Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is ...proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.
This paper proposes a method of quality for the uneven removal caused by the change of the radius of curvature in the aspheric surface polishing and finishing. This method uses a polishing disk and a ...bonnet as polishing devices, two kinds of aspheric parts as workpieces with a concave surface and a convex surface respectively. By deriving the model of pressure and velocity at different positions, the equation between dwell time and curvature radius on the elliptical generatrix of aspheric workpiece could be obtained from the famous Preston equation on polishing material removal. According to the dwell time on the different path points, the movement of the robot could be controlled. In this way, only the dwell time of the path points on the elliptical generatrix needs to be calculated, rather than the entire aspheric surface. By measuring the values of surface roughness in the polishing of concave and convex aspheric surfaces, the experimental results verify that the method could improve the processing efficiency.
Overrunning spring clutches are widely used as essential transmission devices, and the occurrence of abnormal noise can lead to a decline in their performance. This study investigates the dynamic ...aspects of abnormal noise in engineering applications, including its causes, influencing factors, and suppression methods. Audio processing algorithms are employed to analyze the audio associated with abnormal noise, and the Fourier Motion Blur algorithm is applied to process video images of the springs. By combining the motion blur curve with the noise spectrum curve, the source of the abnormal noise is identified as friction-induced vibrations in the spring. Theoretical modeling and calculations are carried out from a dynamic perspective to validate that the phenomenon of abnormal noise in the clutch is a result of self-excited friction vibration caused by the stick–slip phenomenon. Based on theoretical analysis and practical engineering, surface texturing is added to the center shaft of the spring seat, optimizing the system as an overdamped system to suppress self-vibration. Utilizing CFD simulation analysis, the simulation results are used to improve the texturing parameters and further optimize the texturing shape, resulting in an optimal parallelogram surface texture structure. Experimental validation confirms that the improved overrunning spring clutch completely eliminates abnormal noise during overrunning operation. Therefore, this paper contributes to the understanding of the dynamic issues associated with abnormal noise in overrunning spring clutches, confirming that the mechanism for abnormal noise generation is friction-induced self-excitation vibration, and demonstrating that surface texture optimization methods effectively suppress the occurrence of abnormal noise.
For complex decision-making problems, the joint evaluation of multiple experts is indispensable for efficiently addressing them. Therefore, multi-attribute group decision-making (MAGDM) problems have ...become popular in recent decades, however the development of MAGDM problems in the environment of probabilistic linguistic term sets (PLTSs) is not mature. To this end, the paper aims to study group consensus under PLTSs. Specifically, since some existing distance measures do not meet the basic principle of distance measures, and some ones can not measure the distance between PLTSs of different lengths, a new distance measure is defined to eliminate these two drawbacks. In the consensus reaching process, most of common orientation rules choose to change all evaluation information of experts, which is actually hard in reality. For the sake of guaranteeing the original information as much as possible with consensus reaching, the attribute discriminant value is proposed via using the idea of sequential three-way decision (STWD). Then, an STWD-based group consensus method is constructed under PLTSs, namely PLTS-STWD. Meanwhile, dynamic modification parameters are developed associated with attribute discriminant values. Afterwards, the regret-rejoice function is employed to rank all alternatives. Finally, the constructed method is applied to a realistic case and compared with other consensus methods to verify its effectiveness and feasibility.
Covering based multigranulation rough fuzzy set, as a generalization of granular computing and covering based rough fuzzy set theory, is a vital tool for dealing with the vagueness and ...multigranularity in artificial intelligence and management sciences. By means of neighborhoods, we introduce two types of coverings based (optimistic, pessimistic and variable precision) multigranulation rough fuzzy set models, respectively. Some axiomatic systems are also obtained. The relationships between two types of coverings based (optimistic, pessimistic and variable precision) multigranulation rough fuzzy set models are established. Based on the theoretical discussion for the covering based multigranulation rough fuzzy set models, we present an approach to multiple criteria group decision making problem. These two types of basic models and the procedure of decision making methods as well as the algorithm for the new approach are given in detail. By comparative analysis, the ranking results based on two different models have a highly consensus. Although there exist some different ranking results on these two methods, the optimal selected alternative is the same.
As a highly prevalent disease, the liver disease is usually diagnosed by testing with several aspects. Due to different accuracies of tests, the obtained results may be different, which may lead to ...potential errors in diagnosis results. Meanwhile, the psychological behavior and the psychological preference of a decision maker (DM) have a significant influence on decision-making results. Thus, we aim to propose a three-way decision (TWD) approach based on the regret theory (RT) in a multi-scale decision information system (MSDIS), which is named a TWD-R approach. First, by defining a dominating relation and a dominated relation based on the regret-rejoice value of each alternative under each attribute, a novel conditional probability calculation approach is proposed. Second, an objective approach for calculating relative utility functions is proposed to avoid the influence originated from the subjectivity. Third, the key steps and the algorithm of the TWD-R approach are summed up. Finally, the rationality, validity and superiority of the proposed approach are investigated by two cases and some experimental analyses.
The thermal fatigue behavior of 441 ferritic stainless steel was investigated in air and synthetic automotive exhaust gas by the cyclic tests under 100°C–800°C and 900°C conditions. After the ...fracture failure, the microstructure, oxide film, and precipitated phases were analyzed using optical microscopy, X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. In both atmospheres, increasing the maximum temperature from 800°C to 900°C results in lower strength and fatigue life and higher elongation and grain size. At the same maximum temperature, the thermal fatigue life of the specimen is lower in the synthetic exhaust gas than in the air. Both the higher maximum temperature and the synthetic exhaust gas facilitate fatigue failure. The failure mechanism is discussed according to the grain size, thermal stress, high-temperature oxidation rate, and the precipitation of secondary phases. Some precipitated carbides play an important role in the rapid fatigue failure of specimens in the synthetic exhaust gas.
