少数服从多数选择原则的多目标方法

A Multiobjective Method of Selection Principle for the Minority Submitting to the Majority

少数服从多数是实际中广泛采用的一种选择原则．本文通过用效用函数表示集体（委员会）中每一个体的偏好，将少数服从多数选择问题描述成一个多目标决策问题（ＭＭＯＤ）在，在对个体和效用函数只作某种连续性假定下，得到了少数服从多数选择的存在性定理并用集值映射不动点定理给出了证明．通过在不同空间上构造委员会的偏好结构，指出了这种偏好的锥诱导性和这种偏好的有效选择与多目标决策问题（ＭＭＯＤ）的Ｍ－解之间的等价性．

The minority submitting to majority, as a selection princi-ple,is extensively used in actual selection problems.D rawing into utility function exressing the preference of each indidual in a collective(or a com-mittee),this paper describes selection problems for minority submitting to majority as a multiobjctive decision making problem(MMOD).Under only supposed each indidual utility function possessing some continuity, an existence theorem of selection for minority submitting to the majority is got,and proved by the fix point theorem of set-valued map. constructed preference structure of the committee,the cone induced property of the preference and the equivale nce between the effective selection of the pref-erence and M-solution of the multiobjective decision making problem(MMOD)are revealed.