Pythagorean Fuzzy Symmetric Cross Entropy and Weighted Projection Method for Multi-attribute Decision Making

doi:10.3778/j.issn.1002-8331.2110-0440

Abstract

Abstract: This paper studies the Pythagorean fuzzy multiple attribute decision making problems. On the basis of Euclidean distance isometric measure, the distance between each alternative with positive and negative ideal solutions is calculated, it is possible to have a situation where the alternative which closer to the positive ideal solution is also closer to the negative ideal solution, as a result, the ranking results cannot really reflect the pros and cons of each alternative. In order to effectively overcome the reverse order problem of decision results, first of all, Pythagorean fuzzy symmetric cross entropy satisfying symmetry and boundedness is proposed, furthermore, Pythagorean fuzzy weighted symmetric cross entropy is defined. Secondly, for the canonical Pythagorean fuzzy decision matrix, positive and negative ideal alternatives are determined by score function, by calculating the symmetric cross entropy of each alternative with positive ideal alternative, the weight of each attribute is determined according to the grey correlation contribution degree. Thirdly, the weighted projection values of each alternative to positive and negative ideal alternative are calculated respectively, two kinds of weighted projection values are normalized, through the degree of closeness of each alternative, the alternative’s sequencing result is obtained. Finally, this decision method is applied to R&D project optimization decision problem, and the effectiveness and rationality of this method are verified by comparative analysis.

Key words: Pythagorean fuzzy set, Pythagorean fuzzy symmetric cross entropy, normalized weighted projection, R&, D project optimization decision

摘要： 在Pythagorean模糊多属性决策问题中，以欧式距离等距离测度为基础计算各备选方案与正、负理想解的距离，可能产生与正理想解距离更近的待选方案却与负理想解的距离也更近，导致所得方案排序结果并不能真实反映各备选方案的优劣程度。为有效克服决策结果的逆序问题，提出满足对称性、有界性的Pythagorean模糊对称交叉熵，进而给出Pythagorean模糊加权对称交叉熵的定义；针对规范化的Pythagorean模糊决策矩阵，以得分函数确定正、负理想方案，通过计算各方案与正理想方案的对称交叉熵并依据各属性的灰色关联贡献度确定各属性权重；分别求出各备选方案到正、负理想方案上的加权投影值，将两类加权投影值标准化处理，通过各方案的贴近度实现方案的排序择优。最终将该决策方法应用于R&D项目优选决策问题，并经对比分析验证该决策方法的有效性与合理性。

关键词: Pythagorean模糊集, Pythagorean模糊对称交叉熵, 标准化加权投影, R&, D项目优选决策

HAN Erdong, LI Zhanqiang. Pythagorean Fuzzy Symmetric Cross Entropy and Weighted Projection Method for Multi-attribute Decision Making[J]. Computer Engineering and Applications, 2022, 58(5): 75-84.

韩二东, 李占强. Pythagorean模糊对称交叉熵及加权投影的多属性决策[J]. 计算机工程与应用, 2022, 58(5): 75-84.

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