CAJ | 학술논문

犹豫模糊信息集结是犹豫模糊集理论中的重要组成部分，近年来由于其越来越受到关注，已成为一个新的研究方向。基于Einstein运算定义了犹豫模糊元间的运算法则，比如：Einstein和、Einstein积以及Einstein幂运算。提出了三种新的Einstein算术平均集结算子，即犹豫模糊Einstein加权平均（HFEWA）算子、犹豫模糊Einstein有序加权平均（HFEOWA）算子以及犹豫模糊Einstein混合平均（HFEHA）算子。基于新的Einstein算术平均集结算子给出一种新的处理犹豫模糊环境下多属性决策问题的方法，并结合实例对决策方法的可行性与有效性进行检验。
유예모호신식집결시유예모호집이론중적중요조성부분，근년래유우기월래월수도관주，이성위일개신적연구방향。기우Einstein운산정의료유예모호원간적운산법칙，비여：Einstein화、Einstein적이급Einstein멱운산。제출료삼충신적Einstein산술평균집결산자，즉유예모호Einstein가권평균（HFEWA）산자、유예모호Einstein유서가권평균（HFEOWA）산자이급유예모호Einstein혼합평균（HFEHA）산자。기우신적Einstein산술평균집결산자급출일충신적처리유예모호배경하다속성결책문제적방법，병결합실례대결책방법적가행성여유효성진행검험。
Hesitant fuzzy information aggregation plays an important part in hesitant fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. Some operations on hesitant fuzzy ele-ments are defined, such as Einstein sum, Einstein product and Einstein exponentiation. Three new kinds of Einstein arith-metic averaging aggregation operators are proposed, such as Hesitant Fuzzy Einstein Weighted Averaging(HFEWA)oper-ator, Hesitant Fuzzy Einstein Ordered Weighted Averaging(HFEOWA)operator and Hesitant Fuzzy Einstein Hybrid Aver-aging(HFEHA)operator. According to these new kinds of Einstein arithmetic average aggregation operators, a new approach for hesitant fuzzy multi-attribute decision-making problems is developed, and an illustrative example is given to verify the developed method and to demonstrate its practicality and effectiveness.