Method Research For Multiple Attribute Decision Making With Interval Numbers Based On Decision Maker’s Preferences

Due to the complexity of the decision-making environment and the decision maker’spreferences and other irrational factors, decision-making information is alwaysuncompleted. Therefore, forming a kind of uncertainty decision-making problems—intervalmultiple attribute decision making. Prospect theory is a new development of decisiontheory and supplements the expected utility theory, which can explain many phenomenathat utility theory can not explain. At the same time, how to combine prospect theory andinterval multiple attribute decision making well and reflect decision maker’s preferences isa problem that decision theory need to be solved.In this dissertation, on the basis of domestic and foreign research, summarize decisionmaker’s behavioral factors characteristic and the law of decision maker’s preferencesaccording to prospect theory and extract the behavioral variables. On the basis of existedinterval multiple attribute decision making models and algorithms, introduce or increase thebehavioral variable of decision maker’s preferences, form a series of interval multipleattribute decision making models and algorithms that have new behavioral variable. Finally,test the feasibility and effectiveness of the new model through the case studies.The main innovation of this dissertation has the following three aspects:(1) By using the relative dominance, possible degree, intermediate values and othermethods to achieve the idea of defuzzification in the analysis progress of Interval MultipleAttribute Decision.(2）Developing the field of research of the prospect theory from a single property tothe study of interval multiple attribute decision making.(3) Appling value function and decision-weighting function of the prospect theory tothe method of determining the weights and integration methods in interval multipleattribute decision making.The main contributions of this dissertation in the following areas:(1) Based on decision-makers’preference, the standard method of interval numbers ispresented. Aimed at interval numbers, this method conform to the psychologicalcharacteristics of decision makers. Besides this method can keep the integrity of originalinformation, the difference among the property index and decision-makers’preference have been considered. It also reflects the fact of the different cost pays for the different startingindex. Both positive and reverse index are positive indexs.(2) The entropy method to determine interval attribute weights based on the relativedominance is proposed, and the objective weighting method based on the possible degree ofinterval index difference is proposed, which reflects interval defuzzification ideas. Theobjective weighting method based on the decision makers prefer coefficient of intervalindex difference is proposed. The introduction of decision-makers’subjective preferences toweight the value which is the distance between decision-making numerical coefficientindex and positive or negative ideal point. And it represents the interval numbers’differenceof decision policy under the properties of various indexes. Planning weighting methodexpressing decision makers prefer based on the prospect theory is proposed. Through usingthe value function of prospect theory and processing the interval numbers of decisionmatrix, the loss and gain value function matrix function are established. And theprogramming model is established to get the weight. The three combination weightingmethod of interval number based on prospect theory expressing the decision makers’preferences is proposed, and the impact of three types of decisions makers about decisionsresult is considered. This method not only considers the objective difference amongdecision index, but also considers the decision makers’ preferences. The accuracy andscientificity of weight method are improved.(3) This dissertation also researches a new interval multiple attribute decision makingmethods which is based on decision makers’preference which is used in the power industry.Introducing income loss ratio and interval number distance formula, the TOPSIS improvedmethods of interval multiple attribute decision based on the prospect theory is proposed.The improved method of gray correlation based on the prospect theory is proposed, and theVIKOR method based on improved interval multiple attribute decision making is proposed.(4) When the reference point of proposed property is chosen, the average of attributeindex can be taken as a reference point. Grey set pair analysis method is proposed forinterval Numbers in calculating the prospect value function and the prospect weightingfunction. This application of processing method expands the researchment of prospecttheory in multiple attribute decision making problems and has a high research value.The decision theory and the results of research are re-classified. Due to the differentrational levels of decision-makers, decision theory is divided into classical and moderndecision theory, the finite rational decision theory and behavioral decision theory areclassified as modern decision theory. This new classified method can define the past and now decision theory so clearly that the theory is easily retrospected. The mappingrelationship between the generation of evaluation index system and the object system ofevaluation is proposed. And for the generation of evaluation index system the directionalguidance is given from the prospect of theoretical evaluation.