概率区间值直觉犹豫模糊Maclaurin对称平均算子及决策方法

Probabilistic interval-valued intuitionistic hesitant fuzzy Maclaurin symmetric mean operators and decision method

在概率区间值直觉犹豫模糊集(PIVIHFS)的基础上,引入Maclaurin对称平均算子和Archimedean范数,构建一种基于概率区间值直觉犹豫模糊Maclaurin对称平均(PIVIHFMSM)算子的多属性决策模型,用来刻画决策专家输入多个参数值的决策信息,决策者可根据风险偏好等主观意识选择合适的参数值进行决策,同时能保证决策信息的有效性和完整性,避免决策过程中的不确定性和决策信息缺失问题.首先,回顾PIVIHFS的定义和排序方法以及Archimedean范数;其次,提出概率区间值直觉犹豫模糊Maclaurin对称平均(PIVIHFMSM)算子,研究其优良性质及常见形式;最后,提出一种基于PIVIHFWMSM算子的多属性决策方法,并进行比较分析,通过实例验证该方法的可行性和有效性.拓展PIVIHFS理论和应用领域,为决策属性具有相关性和决策信息有可能缺失提供新思路.

Based on the probabilistic interval-valued intuitionistic hesitant fuzzy set(PIVIHFS), this paper introduces the Maclaurin symmetric mean operator and the Archimedean norm, and constructs a multi-attribute decision model based on the PIVIHF Maclaurin symmetric mean(PIVIHFMSM) operator. The model is used to describe the decision information of the decision expert inputting multiple parameter values. The decision maker can select the appropriate parameter value according to subjective consciousness such as risk preference to make decision. The problems of uncertainty and lack of decision information in the decision-making process are avoided. Firstly, the definition and ordering method of the PIVIHFS and the Archimedean norm are reviewed. Then, the PIVIHFMSM operator is proposed, and its excellent properties and common forms are studied. Finally, the decision-making method based on the PIVZHFMSM operator is proposed, comparison analysis of which is conducted to prove its feasibility and effectiveness.This paper expands the PIVIHFS theory and application fields, and provides new ideas for the relevance of decision attributes and the possible lack of decision information.