直觉模糊幂Heronian平均算子及其在多属性决策中的应用  

Intuitionistic fuzzy power HM operators and their application to multiple attribute decision making

作　　者：施明华 肖庆宪[1,2] SHI Minghua;XIAO Qingxian(Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;Shanghai Research Institute of Systems Science, Shanghai 200093, China;School of Finance and Mathematics, West Anhui University, Lu＇an 237012, China)

机构地区：[1]上海理工大学管理学院,上海200093 [2]上海系统科学研究院,上海200093 [3]皖西学院金融与数学学院,六安237012

出　　处：《系统工程理论与实践》2018年第4期971-982,共12页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(11171221);上海市一流学科项目系统科学(SI201YLXK);上海市高原学科项目管理科学与工程(GYXK1201);安徽省优秀青年人才支持计划项目(gxyq2017058)~~

摘　　要：针对需要同时捕获变量个体间的关联性和整体均衡性的信息融合问题，本文在直觉模糊环境下，将Heronian平均算子和幂平均算子相结合，提出了直觉模糊幂Heronian平均算子和直觉模糊加权幂Heronian平均算子．新算子利用Heronian平均算子的交叉运算来体现变量的关联性，同时引入支撑度系数来挖掘信息的相对贴近度，从而在信息融合过程中体现整体性．此外，还探讨了新算子的一些优良性质和特例，并给出一种多属性决策方法．最后，通过算例验证了该方法的可行性与有效性．In order to capture not only the interrelationship between the input arguments, but also the overall balance of aggregate object in information fusion problem, in this paper, we combine Heronian mean with the power average operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy power Heronian mean operator （IFPHM） and the intuitionistic fuzzy weighted power Heronian mean operator （IFWPHM）. The new operators use the crossover operation of Heronian mean to represent the correlation of variables, and introduce the support degree coefficient to mine the relative closeness degree of information, so as to embody the integrity in the process of information fusion. The desirable properties of these new extensions of Heronian means and their special cases are investigated. Finally, based on the IFWPHM operator, we present an approach to multiple attribute decision making and illustrate its validity and feasibility with a practical example.

关 键 词：直觉模糊数 多属性决策 Heronian平均算子 幂平均算子 

分 类 号：C934[经济管理—管理学]