广义直觉模糊几何Bonferroni平均及其多属性决策

Generalized intuitionistic fuzzy geometric Bonferroni mean and its applications for multi-attribute decision making

针对直觉模糊环境中的信息集成问题,基于阿基米德T-范数和S-范数,提出新的广义直觉模糊几何Bonferroni平均算子。该算子不仅能够考虑到每种属性的重要性,而且可以有效地捕获属性间的内在联系。首先,基于阿基米德T-范数和S-范数的直觉模糊运算法则,提出一种新的广义直觉模糊几何Bonferroni平均算子,并研究该算子的几种优良性质,包括幂等性、单调性、有界性和置换不变性;其次,探讨了广义直觉模糊几何Bonferroni平均算子的几类特殊形式;最后,基于提出的算子构建一种新的直觉模糊多属性决策方法,并结合区域经济发展研究实例。实验结果表明,提出的决策方法是可行的和有效的,并且使得决策者能够依据其态度进行决策。

Concerning the problem of information aggregation in the intuitionistic fuzzy environment, a new Generalized Intuitionistic Fuzzy Geometric Bonferroni Mean（ GIFGBM） operator was proposed on the basis of the Archimedean T-norm and S-norm. The proposed operator considered the importance of each attribute and could capture the interrelationships among attributes. Firstly, based on the intuitionistic fuzzy operational laws with Archimedean T-norm and S-norm, the GIFGBM was investigated. Then, its desirable properties were studied, including idempotency, monotonicity, boundedness and permutation invariance. Some special cases of the GIFGBM were further discussed in detail. Finally, an approach to intuitionistic fuzzy multi-attribute decision making was developed with the proposed aggregation operator, and the presented method was applied to research on the development of the regional economy. The experimental results show that the proposed decision making method is practical and effective, and the decision makers can make decision by their attitude.