Abstract:  For the intrusion detection model selection problem under the hesitant trapezoidal fuzzy information, an approach based on the hesitant trapezoid fuzzy decision making algorithm is proposed to select the intrusion detection model. First, considering the decision information is hesitant trapezoidal fuzzy number and the attributes are interrelated, based on the hesitant trapezoid fuzzy operational laws, the hesitant trapezoid fuzzy weighted average (HTrFEWA) operator and the hesitant trapezoid fuzzy weighted geometric (HTrFEWG) operator are presented. Then, for the fact that the ordered position of the hesitant trapezoid fuzzy set has different weights, the hesitant trapezoid fuzzy ordered weighted average (HTrFEOWA) operator and the hesitant trapezoid fuzzy ordered weighted geometric (HTrFEOWG) operator are proposed, which is followed by the discussion of their desirable properties. Finally, a new method for multi-attribute decision making is investigated based on the HTrFEWA operator and HTrFEWG operator, and applies the example for the selection of intrusion detection model to demonstrate the method’s practicality and effectiveness.

Key words: Hesitant trapezoid fuzzy set, Einstein operators, aggregation operators; decision making, intrusion detection model

摘要： 针对犹豫梯形模糊信息环境下的入侵检测模型选择问题，构建了一种基于犹豫梯形模糊决策算法的入侵检测模型选择方法。首先，考虑到决策信息为犹豫梯形模糊数且属性间存在相互的关联，基于犹豫梯形模糊数的运算法则，提出了犹豫梯形模糊Einstein加权平均（HTrFEWA）算子和犹豫梯形模糊Einstein加权几何（HTrFEWG）算子；其次，针对犹豫梯形模糊数的有序位置存在具有不同权重的情况，构建了犹豫梯形模糊Einstein有序加权平均（HTrFEOWA）算子和犹豫梯形模糊Einstein有序加权几何（HTrFEOWG）算子，并讨论了其相应的基本性质；最后建立了基于HTrFEWA算子和HTrFEWG算子的多属性决策方法，并通过入侵检测模型的选择实例说明提出的决策方法是合理和有效的。

关键词: 犹豫梯形模糊集, Einstein算子, 集结算子, 决策算法, 入侵检测模型