Study On The Methods For Fuzzy Multi-attribute Decision-making

Fuzzy Multi-Attribute Decision-Making(FMADM)problem,whose theory and methods are widely used in the areas of modern economic administration,financial investment,item evaluation,military,etc.is becoming an important research fields of operational research and modern decision science.The theory and methods about FMADM problem are studied in this paper,and the main research works are as follows:1.Ranking problems of several types of fuzzy judgment matrix are studied. Firstly,the mixed least square method based on the concept of the multiplicative consistency of numerical complementary judgment matrix and its corresponding iterative algorithm are proposed.Moreover,its main properties are proven.Secondly, the concepts of interval numbers consistent complementary or reciprocal judgment matrix and their judgment theorem are given.The ranking methods of possibility and the sum of relative superiority degree of alternatives are proposed based on a goal programming model,respectively.Lastly,a new type of hybrid judgment matrix is defined and an optimization model to determine its ranking vector is established.A liner programming method of priority of hybrid judgment matrix is presented.2.Two objective approaches to determine attribute weights based on a quadratic programming model and nonliner programming model are presented with regard to the FMADM problems,in which the information about attribute weights are unknown completely and the attribute values are in the form fuzzy numbers.The ranking methods of alternatives based on the sum of relative superiority degree on every alternative and the projection of the weighted attribute values of every alternative on the fuzzy positive ideal point of alternatives are proposed,respectively.3.Some results are obtained with regard to the FMADM problems that the information about attribute weights is known partly.On the one hand,the two-step optimization method and interactive approach based on the alternative satisfactory degree and similarity degree are presented under the situations which the attribute values are precise and the decision maker has or has no preference information on alternatives respectively.On the other hand,two goal programming models are established to obtain the attribute weights under the situations that the attribute values are fuzzy numbers and the decision maker has or has no preference information on alternatives respectively.The ranking method of alternatives based on the relative membership degree and similarity degree between every alternative and positive ideal point are devloped.Furthermore,the latter method is applied to the project evaluation in the field of venture investment.4.Group decision-making problems based on information aggregated operators are investigated.Firstly,when the preference information about the alternatives are preference orderings,utility values,complementary judgment matrix and reciprocal judgment matrix.The different preference information is uniformed into complementary judgment matrix or reciprocal judgment matrices by using the transformation formulas of each other.Two methods based on Ordered Weighted Geometric(OWG)and Ordered Weighted Arithmetic(OWA)averaging operators for group decision-making problems are proposed.Secondly,When the preference information about the alternatives are fuzzy utility values,fuzzy complementary judgment matrix and fuzzy reciprocal judgment matrix,with some extended operational principles of triangular fuzzy numbers and the transformation formulas of the above different numerical preference information the transformation formulas that fuzzy utility values and fuzzy complementary judgment matrix are uniformed into fuzzy reciprocal judgment matrices are given.A new method based on FOWGA operator for fuzzy group decision-making problems is proposed.Finally,the Continuous Ordered Weighted Geometric Averaging (C-OWGA)operator is extended to accommodate fuzzy environment and the Weighted C-OWGA(WC-OWGA)operator,the Ordered Weighted C-OWGA(OWC-OWGA) operator and the Hybrid C-OWGA(HC-OWGA)operator are presented under the situations which the decision-making information takes the form of interval numbers. By using the operational laws of interval numbers,a novel method based on the HC-OWGA operator for fuzzy multi-attribute group decision-making problem is proposed.5.The corresponding algorithms of the developed models or methods are given, and the corresponding practical examples are illustrated to show their effectivities and feasibilities.