基于公理化模糊集合的投影相似度多属性决策方法
Projection Similarity Multi-Attribute Decision-Making Method Based on Axiomatic Fuzzy Sets
DOI: 10.12677/PM.2021.115086, PDF,    国家自然科学基金支持
作者: 王 虎*, 潘小东：西南交通大学，数学学院，四川 成都
关键词: 多属性决策；语言值；公理化模糊集；投影相似度；Multi-Attribute Decision-Making； Linguistic Value； Axiomatic Fuzzy Set； Projection Similarity
摘要: 针对属性值为语言值的模糊多属性决策问题，本文提出了一种以公理化模糊集合为基础的投影相似度多属性决策方法，将评价自然语言转化为相对应的由模糊划分生成的公理化模糊集；将已知备选方案看作向量，基于公理化模糊集合向量的模长与余弦值，提出了投影相似度；并由此构建了相应的多属性决策模型。最后，通过算例的比较来说明该模型的有效性和实用性。
Abstract: Aiming at the problem of fuzzy multi-attribute decision-making in which the attribute value is a linguistic value, this paper proposes a projection similarity multi-attribute decision-making method based on axiomatic fuzzy sets, which transforms the evaluation natural language into corresponding axiomization generated by fuzzy division Fuzzy set: Regarding the known alternatives as a vector, based on the modulus length and cosine value of the axiomatic fuzzy set vector, the projection similarity is proposed; and the corresponding multi-attribute decision-making model is constructed from this. Finally, the effectiveness and practicability of the model are illustrated by the comparison of calculation examples.
文章引用：王虎, 潘小东. 基于公理化模糊集合的投影相似度多属性决策方法[J]. 理论数学, 2021, 11(5): 709-719. https://doi.org/10.12677/PM.2021.115086

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