The connected of generalized α-major optimal solution set for multiobjective decison-making

The research on the topological structure of major efficient solution set and optimal solution set is an important research topic in the study of multi-objective optimization. In this paper, the concept and properties of generalized α - major optimal solution of infinite-dimensional multiobjective decisionmaking problem are studied. Under the condition that objective mapping is cone H_α-quasiconvex and cone H_α-bounded, the connectedness theorems of generalized α - major optimal solution set are obtained and proven for infinite-dimensional multi-objective decision-making problems.