Study On Multi-criteria Decision-making Approach With Incomplete Certain Information

In social life or economic activities, there exist a great many multiple criteria decision-making (MCMD) problems, for which many methods such as ELECTRE/PROMETHEE, UTA/UTADIS and MHDIS have been proposed. Among these methods mentioned above, a ranking or classifying of the alternatives is obtained according to the integrated assessing value of each alternative when the decision-making parameters such as the weights or values of the criteria are completely determined. But in the real practice of the decision-making, the provided information of such parameters are fuzzy, even uncertain, or incomplete certain because of the vagueness or uncertainty of the decision-making problems themselves. And the alternatives can't be ranked or classified by using the methods mentioned above. So it is necessary and significant to study the theories or methods for MCMD with incomplete certain information systemically. This paper studies some sorts of MCMD problems as follows.1. The MCDM problems in which the criteria aggregation function is linear or nonlinear (especially the quadric), and the value of the criteria utility or preference is certain or takes the form of fuzzy numbers, intuitionistic fuzzy set, interval intuitionistic fuzzy set, or linguistic variables, and it is also possible that some values of the criteria are not given, are systemically studied. The group decision-making problems in which the importance degree of the decision makers and the weights of the criteria are incomplete certain, and the ordinal numbers or the preference ordering relation on alternatives are provided to express the assessment information of the alternatives, and the values of the criteria take the form of fuzzy numbers, intuitionistic fuzzy sets or linguistic variables, are also systemically studied. By fabricating the optimization tactics and comparison principles of the alternatives, this paper brings forward a series of models or methods to satisfy such decision-making problems mentioned above, and the details are given as follows:(1) The MCDM methods such as TOPSIS, PROMETHEE, Superiority and inferiority ranking, UTA, ELECTRE TRJ, and decision-making based on three tuple AHP and hierarchical discrimination are extended to the MCDM problems with incomplete certain information on weights. And the multi-criteria classification methods on MCDM with incomplete certain information on weights based on optimizing deviation of categories are proposed.(2) The method for MCDM problems with incomplete certain information in which the criteria aggregation function is polynomial is proposed. And also the hierarchical discrimination method for multi-criteria classification problems with incomplete certain information in which criteria aggregation function is quadric is proposed. These methods can react to the relations of the criterion and make the results reasonable and feasible.(3) The TOPSIS, VIKOR and UTA are extended to the fuzzy MCDM problems in which the value of the criterion are given in the form of fuzzy numbers and the weights on criteria are incomplete certain. Meanwhile, the range of the VIKOR and UTA are also developed. And the methods for MCDM problems with incomplete certain information on weights in which the criterion takes the form of intuitionistic fuzzy set or interval intuitionistic fuzzy set are proposed. These provide a theory guide in using the intuitionistic fuzzy set or interval intuitionistic fuzzy set on the problems of MCDM, and broaden the using scope of the fuzzy MCDM.(4) By transforming the assessment information of the alternatives under certain criteria into the belief degree that belonging to the evaluation grade, in which the belief degree is real number or interval number, the ranking or classifying methods are proposed for the MCDM problems in which the information on weights of criteria is incomplete certain and the value of the criteria is incomplete or not given. And the approach on multi-criteria classification decision-making with incomplete certain information and reference set, in which the belief degree of criteria value is uncertain and it is gained by solving the nonlinear programming model, is proposed. These methods solve actual MCDM problems which can't be carried on under incomplete certain information on the weights of criterion and incomplete or missing value of the criteria, then the suitability of the methods have been improved.(5) The optimal assignment approach is proposed for group decision-making problems in which the information of the decision makers' weights is incomplete and the assessment value of the alternatives take the form of ordinal numbers. And such group decision methods are also proposed in which preference ordering relation on alternatives is provided to express the assessment information of the alternatives or different aggregation preference information is provided. The method for group linguistic MCDM problems in which the information of the decision makers' weights and the criteria' weights is incomplete certain and the value of the criterion takes theform of fuzzy numbers, intuitionistic fuzzy set or linguistic variables2.By analyzing the latest researches on optimization theories and optimization algorithms, this paper constructs some algorithms with fast speed for the MCDM models with incomplete information. And the simplex method is exploited when the optimization models can be transformed into linear programming models, or else, the genetic algorithm (GA) is employed. And the details are as follows:(1) For the hierarchical discrimination models with incomplete certain information in which the criteria aggregation function is quadric polynomial, an algorithm is constructed by combining the GA and the simplex method.(2) In the multi-criteria decision-making models on ranking or classifying, the objective function or the constraint terms are obtained according to the recursion algorithm of evidential reasoning under the condition of incomplete information, and it is difficult to figure out such models with the traditional optimization algorithm. So, the GA is introduced to construct an algorithm to solve this kind of model and it works well.(3) For the group decision-making models in which the assessment values of the alternatives are ordinal numbers and the decision makers' weights is incomplete certain, the algorithm is given by combining the GA with the optimal assignment approach.