Fuzzy multiple attribute decision making method of interval valued intuitionistic trapezoidal
|School||Qufu Normal University|
|Keywords||Interval-valued intuitionistic trapezoidal fuzzy number Multi-attribute decisionmaking Integrated operator TOPSIS Projection model Deviation|
With the rapid development of economic, the modern society is gradually showing atrend of informatization and globalization, and the social competition is more intense. Theproblems that need to be resolved are increasingly complex. It is insufficient to meet therequirements of the complex and ever-changing modern society relying solely on intuition andexperience to complete the decision making. So it is of great importance to establish a system,scientific, rational and effective decision making theory and method. Due to the frequentlyenhanced of the complexity and uncertainty of social, as well as the diversity and ambiguity ofthe human mode of thinking, the decision problems are presents complexity and diversifytrends. Aiming at the problem, the fuzzy multi-attribute decision making appeared. UsingInterval-valued intuitionistic trapezoidal fuzzy numbers can consider the fuzzy information ina variety of circumstances, reflect the uncertainty of the decision making information and trulyexpress the intention of decision makers. The systemic and in-depth study of interval-valuedintuitionstic trapezoidal fuzzy multi-attribute decision making theory and method not only canenrich and improve the fuzzy multi-attribute decision making theory and method with acertain academic values, but also provide a scientific theory, reduce the burden of decisionmaking, and improve decision making efficiency and quality to solve many complex decisionproblems in reality.In this thesis, the theory and methods of fuzzy multi-attribute decision based oninterval-valued intuitionistic trapezoidal fuzzy numbers are introduced. And these methods areused to solve specific decision problems for the field of education.Firstly, this thesis introduced the theoretical basis of fuzzy multi-attribute decisionmaking and the interval-valued intuitionistic trapezoidal fuzzy numbers, including the generaldescription and solving process of fuzzy multi-attribute decision making problems, as well asthe definition, algorithms and sorting methods of interval intuition trapezoidal fuzzy numbers,so as to provide adequate preparation for the future research of fuzzy multi-attribute decisionmaking method based on interval-valued intuitionistic trapezoidal fuzzy numbers. Secondly,the integrated operators of decision making based on intuitionistic fuzzy information areexplored. The definitions of the ordered weighted arithmetic average operator and the orderedweighted geometric averaging operator are constructed according to the weighted arithmetic average operator and the weighted geometric average operator of interval-valued intuitionistictrapezoidal fuzzy numbers, the definitions of the blend ordered weighted arithmetic averageoperator and the blend ordered weighted geometric averaging operator are expounded, andthen the fundamental theorems of integrated operators are given. In addition, by using the twoinformation aggregation operators, the decision making model is established and a specificcollege assessment analysis example is given to verify its effectiveness. Then, the distanceformula, positive and negative ideal solution and the projection formula of interval-valuedintuitionistic trapezoidal fuzzy numbers are defined, and the TOPSIS method and theprojection model are extended to the form of intuition trapezoidal fuzzy numbers. Also thelimitations of TOPSIS method and projection model are analyzed, and a new interval-valuedintuitionistic trapezoidal fuzzy decision method is described to improve the TOPSIS methodand the projection model. The instance of teacher assessment analysis demonstrates theeffectiveness and feasibility of the method. Finally, aiming at the multi-attribute decisionmaking problems, which the information on attribute weights are unknown and the attributevalues are interval-valued intuitionistic trapezoidal fuzzy numbers, this thesis obtained themethod of calculated weight according to the distance formula of interval-valued intuitionistictrapezoidal fuzzy numbers and the ideology of maximum deviation. And then the model ofinterval-valued intuitionistic trapezoidal fuzzy decision making can be established and aspecific analysis example is given.