Research On Fault Diagnosis Method Based On Trapezoidal Fuzzy Numbers

Multi attribute decision-making is an important component of modern decisionmaking science and operations research,and its theoretical methods have wide applications in many fields of real life.The purpose of multi-attribute decision-making(MADM)is to comprehensively consider various factors that may be contradictory and incompatible,sort or select alternative plans based on multiple attributes,and find the most ideal solution.With the development of society,decision-making problems have become increasingly complex,making it impossible for a single decision-maker to consider all aspects of the problem.Therefore,how to make accurate and optimal choices for alternative plans in a fuzzy environment has received great attention from researchers in recent years.This article focuses on the problems of difficult calculation of expert weights,difficult quantification of evaluation information,and easy loss of decisionmaking information in fault diagnosis of mechanical manufacturing equipment.The following aspects have been studied.Aiming at multi attribute decision making problems with uncertain expert weights and attribute weights expressed as interval intuitionistic trapezoidal fuzzy numbers,a method for determining expert weights based on the combination of evaluation hesitation and group expert similarity was proposed.This method utilizes incomplete information of weights to establish Hamming distance models for individual decision matrices and comprehensive decision matrices.The expert weight based on distance measurement is obtained by solving the model,and the expert weight based on evaluation hesitation is obtained by relying on the hesitation information in the expert evaluation information.The expert weights are weighted based on the decision-maker’s attitude parameters,and then the TOPSIS model is used to rank the options.An example demonstrates the feasibility and effectiveness of this method.A new VIKOR decision-making method based on trapezoidal fuzzy numbers is proposed.Firstly,the expert weight is calculated using distance measure method,and the criterion weight is calculated using deviation maximization method.At first,a weighted average operator is added to the VIKOR method to aggregate the decision matrix into a comprehensive weighted decision matrix,and then the VIKOR model is used to solve the problem.At the same time,the method was applied to a practical example to illustrate the effectiveness and feasibility of the method.Finally,a comprehensive analysis of the method was conducted through sensitivity analysis and comparative tests.At the same time,this thesis also proposes Fermatean trapezoidal fuzzy numbers,compares Fermatean trapezoidal fuzzy numbers with intuitionistic trapezoidal fuzzy sets and Python trapezoidal fuzzy sets,focuses on multi-attribute decision-making based on Fermatean trapezoidal fuzzy sets,defines the basic operations of Fermatean trapezoidal fuzzy sets,and defines the score function and accurate function of Fermatean trapezoidal fuzzy sets based on Fermatean fuzzy sets.In addition,we established the Fermatean trapezoidal fuzzy number VIKOR method to solve multiple attribute decision-making problems.Finally,an illustrative case is used to demonstrate the feasibility and practicality of the method described.