Weighted Joint Efficient Number Method And Its Research In Group Multi-Orjective Decision-Making

This paper firstly introduces the forming background and research status of multi-objective programming and group multi-objective decision-making. After that, the main content of this dissertation focuses on discussing the properties of multi-objective programming and group multi-objective decision-making. The main contributions are as follows.The first part, the concept and properties about generalized a-major optimal solution of infinite-dimensional multi-objective programming problem are introduced. When objective function meet the condition of cone Hα-quasi-convex and cone Hα-bounded, the connectedness theorems of generalized α-major optimal solution set for infinite-dimensional multi-objective programming problems are obtained.The second part, the concept of the αk-major efficient number with double parameters a and k of alternatives is given, and a class of αk-major joint efficient solutions in group multi-objective decision-making is founded. Then the existence characterizations of αk-major joint efficient solutions in multi-objective decision-making it discussed. Meanwhile some necessary conditions and sufficient conditions of the solution are obtained, and the geometric characterizations of αk-major joint efficient solution are proven in group multi-objective decision-making.The third part, the weighted joint efficient number and weighted joint efficient mapping in group multi-objective decision-making are bulided. And many important properties of weighted joint efficient mapping in group multi-objective decision-making are studied. Based on this, the weighted joint efficient number method of group multi-objective decision-making is obtained, which laids a solid foundation for further researching efficiency theory and practical application of group multi-objective decision-making.