Multiple Attribute Group Decision-Making Methods Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Partitioned Bonferroni Mean Aggregation Operators

Online Teaching Quality Evaluation of Business Statistics Course Utilizing Fermatean Fuzzy Analytical Hierarchy Process with Aggregation Operator

Due to the full-scale outbreak of COVID-19, many universities have adopted the way of online teaching to ensure the orderly development of teaching plans and teaching contents. However, whether online and offline teaching can develop homogeneously and how to ensure the teaching effect is a major challenge for colleges and universities. Therefore, it is urgent to construct a reasonable index system and evaluation approach for the quality of network teaching. Combined with the influencing factors and characteristics of online teaching, this study first puts forward a multi-index evaluation index system and then proposes a novel evaluation method for online teaching based on the analytical hierarchy process (AHP) and Dombi weighted partitioned Muirhead Mean (PMM) operator under Fermatean fuzzy (FF) environment. This presented method not only adapts to changeable evaluation information but also handles the elusive interrelationships among indexes, realizing the flexibility and comprehensiveness both in form and in the polyaddition process. The applicability and feasibility of this presented method are then discussed through the practical online teaching quality evaluation of a business statistics course case, and a group of tentative about the sensitivity analysis and comparative analysis further demonstrates the effectiveness and flexibility of the proposed method.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Extended VIKOR-QUALIFLEX Method Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Information for Multiple Attribute Decision-Making with Unknown Attribute Weight

Considering the advantages of trapezoid fuzzy two-dimensional linguistic variables (TrF2DLVs), which can not only accurately describe the qualitative evaluation but also use qualitative linguistic variables (LVs) to describe the confidence level of this evaluation in the second dimension, this paper proposes a novel method based on trapezoidal fuzzy two-dimensional linguistic information to solve multiple attribute decision-making (MADM) problems with unknown attribute weight. First, a combination weight model is constructed, which covers a subjective weight determination model based on the proposed trapezoidal fuzzy two-dimensional linguistic best-worst method (TrF2DL-BWM) and an objective weight determination model based on the proposed CRITIC method. Then, in order to accurately rank the alternatives, an extended VIKOR-QUALIFLEX method is proposed, which can measure the concordance index of each ranking combination by means of group utility and individual maximum regret value of each evaluation alternative. Finally, a practical problem of lean management assessment for industrial residential projects is solved by the proposed method, and the effectiveness and advantages of the method are demonstrated by comparative analysis and discussion.

Control of Robot Arm Motion Using Trapezoid Fuzzy Two-Degree-of-Freedom PID Algorithm

Symmetries play very important in the dynamics of robot systems. The relevant control of robot arm motion with fault diagnosis including the optimized fuzzy algorithm based on the error rate adjustment P, I, D value (Fuzzy PID algorithm) model relies on symmetry principles. A robot is a kind of mechanical device that can program and perform certain operations and mobile tasks under automatic control. The manipulator is a very complex multi-input multi-output non-linear system and the main actuator of the robot. This paper focuses on the design of a control algorithm for a two-degree-of-freedom (2-DOF) manipulator. First, the mathematical model of a 2-DOF articulated manipulator is established, that is, the functional relationship between the input driving force vector and the output rotation angle vector of a 2-DOF manipulator. Then, a set of trajectory planning algorithms are designed by using gradient model control, which can calculate the trajectory of the end-effector of a 2-DOF manipulator according to the user’s task requirements. The experimental results verify the effectiveness of the proposed algorithm.

Grey Fuzzy Multiple Attribute Group Decision-Making Methods Based on Interval Grey Triangular Fuzzy Numbers Partitioned Bonferroni Mean

Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

Health Management Decision of Sensor System Based on Health Reliability Degree and Grey Group Decision-Making

Metal Oxide Semiconductor (MOS) gas sensor has been widely used in sensor systems for the advantages of fast response, high sensitivity, low cost, and so on. But, limited to the properties of materials, the phenomenon, such as aging, poisoning, and damage of the gas sensitive material will affect the measurement quality of MOS gas sensor array. To ensure the stability of the system, a health management decision strategy for the prognostics and health management (PHM) of a sensor system that is based on health reliability degree (HRD) and grey group decision-making (GGD) is proposed in this paper. The health management decision-making model is presented to choose the best health management strategy. Specially, GGD is utilized to provide health management suggestions for the sensor system. To evaluate the status of the sensor system, a joint HRD-GGD framework is declared as the health management decision-making. In this method, HRD of sensor system is obtained by fusing the output data of each sensor. The optimal decision-making recommendations for health management of the system is proposed by combining historical health reliability degree, maintenance probability, and overhaul rate. Experimental results on four different kinds of health levels demonstrate that the HRD-GGD method outperforms other methods in decision-making accuracy of sensor system. Particularly, the proposed HRD-GGD decision-making method achieves the best decision accuracy of 98.25%.