Research On Hybrid Multiple Attribute Decision Making

Multiple attribute decision making problems are common in the areas of social, economic,and engineering. With the rapid development of society and economy, as well as thecontinuous progress of science and technology, the applications of multiple attribute decisionmaking problems become more and more diverse and complex. Due to some constraints of thesubjective and objective factors, the evaluation values of alternatives against the attributes indecision matrix are always uncertain, and are expressed in the forms of fuzzy linguistics (orlinguistic variables), Preference orderings, and so on. With respect to this kind of hybridmultiple attribute decision making problems, how to propose valid solution methods is theimportant subject of attentions.With respect to the hybrid multiple attribute decision making problems with unknownattribute weights, this dissertation makes an investigation and study from the followingaspects.Firstly, with respect to the hybrid multiple attribute decision making problems withlinguistic evaluation values, a general method is proposed. The distance functions of triangularfuzzy numbers and trapezoidal fuzzy number are defined to calculate the relative distancesbetween the evaluation values of linguistic variables and the negative ideal point of thecorresponding attribute. Thus, the evaluation values of linguistic variables are uniformed intocrisp values and the decision matrix is uniformed. Based on the uniformed decision matrixwith single-point values, an optimal model is set up to calculate the attribute values. Themaximum possible intervals of the overall values of the alternatives are calculated thereforeand the matrix with superiority possibility degree between the alternatives is obtained. In theend, the rankings of the alternatives with superiority possibility degreeis obtained.Secondly, the hybrid multiple attribute decision making problems with attribute values ofpreference orderings and interval numbers are investigated too, as well as a method isproposed. In order to normalize the hybrid decision matrix, two type of attribute values need tobe transformed into single-point values. A function for transforming preference orderings intosingle-point values is defined. In the meantime, by defining the relative distance between theattribute values of interval numbers and the negative ideal point of the corresponding attribute, this kind of evaluation values are normalized into single-point values too. Then, based on thedecision matrix with single-point values obtained, an optimal model is set up to figure out theattribute weights which make the overall values of every alternatives maximum. The simpleweighted sum method is used to calculate the overall values of the alternatives to rank them orchoose the best one among them.Finally, the hybrid multiple attribute decision making problems with attribute values ofpreference orderings and linguistic variables are investigated, with two methods are proposed,i.e., the method based on transforming preference orderings into utility values, and the onebased on basic linguistic term set. In the former method, a function for transformingpreference orderings into single-point values is used, and the linguistic variables arenormalized into utility values by calculating the grey correlation degree between them andtheir positive ideal attribute values.In the later method, by setting up the membership function between ranking positions andtheir corresponding intervals, preference orderings is transformed into the fuzzy set of thebasic linguistic term set. At the same time, fuzzy operations are used to transform the linguisticvariables into the fuzzy set of the basic linguistic term set too. Thus, the hybrid decision matrixis uniformed into the format of the fuzzy set of the basic linguistic term set, based on which anoptimal model is set up to find the attribute weights as well as the overall values of thealternatives.