Intuitionistic fuzzy reducible weighted Maclaurin symmetric means and their application in multiple-attribute decision making

AbstractAs an important information aggregation tool, the Maclaurin symmetric mean (MSM) can capture the correlation between multiple input values and has recently become a hot topic in the field of academic research. Due to the importance of the fact that attribute variables are often different, many weighted MSMs have been designed to deal with various fuzzy information aggregation problems. However, these weighted form operators do not have the properties of idempotency, i.e., the weighted average value of equivalent fuzzy numbers varies with their weights. In addition, when their weights are equal, the weighted MSMs cannot reduce to the MSM, which means they do not have reducibility. To solve these problems, in this paper, we introduce the reducible weighted MSM (RWMSM) and the reducible weighted dual MSM (RWDMSM), and we extend them to aggregate intuitionistic fuzzy information. In order to better analyze and understand the operation mechanism of the proposed weighted MSMs, we discuss several advantageous properties and special related cases of the proposed weighted MSMs. The other objective of this paper is to investigate the practice application of the proposed weighted MSMs in decision making under conditions of an intuitionistic fuzzy environment. A case study shows that the decision-making method based on the intuitionistic fuzzy RWMSM and RWDMSM can flexibly capture the correlation and reflect the decision maker’s risk preference.

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