多指标区间数关联决策模型的研究

根据区间数的特性，定义了区间数的距离，并证明了当区间数为实数时，区间数距离就是实数距离的推广；在此基础上，根据灰色关联度的理论，提出了区间数关联度的计算方法，从而把灰色关联分析理论由实数序列拓广到区间数序列；进一步研究了具有区间数的多目标决策问题，建立了多指标区间数关联决策模型。该模型不仅避免了寻求虚拟理想方案和负理想方案的困难，而且它把整个评价方案看作一个整体来寻求最优决策方案，还具有易于在计算机上实现的特点。最后，以实例验证了该模型的有效性与实用性。此方法为解决具有区间数多指标决策问题提供了一种科学、实用的决策新途径。

Study on Incidence Decision Making Model of Multi-Attribute Interval Number

Based on the characteristic of interval number, the distance of interval number is defined. The distance of interval number is proved to be the extent of real number distance when the interval number is real number. Based on the grey incidence degree theories, the computing method for the degree of interval number incidence is developed. The grey incidence analysis theory is extened from the real number sequence to the interval number sequence and the development of the grey incidence theories is promoted. This paper studies the incidence decision making problems of multi-attribute interval number and models the incidence decision making model of multi-attribute interval number. The model gets rid of the difficulty to seek dummy ideal scheme and negative ideal scheme, and seek the optimum decision making scheme in the whole system. Meanwhile, the model is easy to be implemented in computer program. Finally, its validity and its practicability are examined with examples. The method offers a new scientific and practical decision making approach for solving the decision problem with multi-attribute interval number.