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连续区间数的中位算子及其灵敏度分析

     

摘要

研究决策信息以区间数形式给出的方案决策问题.考虑到区间数非均匀分布的特点,为避免区间极端值在区间数确定中产生较大误差,本文将中位数概念运用到区间数的确定上,提出OIP(Ordered Interval Point)有序中位算子.取单位区间单调函数(BUM函数)为二分之一所表示的值为权重,将区间数确定为一个实数,并研究算子单调性和有界性的初等运算性质.通过比较OIP算子与COWA算子对态度参数和区间长度的反应灵敏度,获得了在一定条件下OIP算子对态度参数反应更稳健,对区间长度反应更灵敏的结论.最后用算例证明该算子的可行性和有效性.%The information of decision making problems is given in the form of interval numbers.Taking into account the characteristics of non-uniform distribution of interval numbers,the OIP(ordered intermediate operator)is proposed to avoid extreme value errors in the determination of interval numbers.This operator will use the concept of median to determine interval numbers.The weight is 1/2 of the value of the basic unit interval monotonic function(BUM function).The interval number is defined as a real number and the properties of the BUM function and the boundedness of the operators are studied.Then the OIP operator is extended to a more general IW-OIP operator.By comparing the response sensitivity of the OIP operator and the COWA operator to the attitude parameters and the interval length,the conclusion is obtained that the OIP operator is more robust to the attitude parameters and is more sensitive to the length of the interval under certain conditions.In the risk preference,the higher sensitivity of the endpoints on the interval is,the greater comprehensive attribute value of the scheme is.In the risk aversion,the higher sensitivity of the lower point of the interval is,the greater comprehensive attribute value of the scheme is.Finally,a numerical example is used to demonstrate the feasibility and effectiveness of the proposed operator.

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