直觉模糊软集上的新型运算及其在决策问题中的应用
A Novel Necessity Operation on Intuitionistic Fuzzy Soft Sets and Related Application
DOI: 10.12677/pm.2024.1411397, PDF,    国家自然科学基金支持
作者: 陈炎炎, 潘小东*：西南交通大学数学学院，四川 成都
关键词: 直觉模糊软集；正规化运算；模糊决策；Intuitionistic Fuzzy Soft Sets； the Necessity Operation； Fuzzy Decision-Making Problems
摘要: 直觉模糊软集从参数化和程度化两个方面来表述对象，这种表述可以更全面地刻画对象的特征。直觉模糊软集的正规化运算是在保持直觉模糊软集的表达能力的同时，降低其计算复杂度的一种重要手段。本文通过引入犹豫度偏好参数，提出直觉模糊软集正规化运算的一种拓展模型。首先，利用犹豫度偏好参数将犹豫度按照偏好重新分配给隶属函数和非隶属函数，使二者之和为1，得到一种新的正规化运算。其次，讨论这种正规化运算的基本性质。最后，通过一个实际问题验证基于直觉模糊软集正规化运算的模糊决策方法具有合理性和有效性。
Abstract: Intuitionistic fuzzy soft sets characterize objects from the perspective of parameterization and degree, which can describe objects more comprehensively. The normalization operation of intuitionistic fuzzy soft sets is an important means to reduce the complexity of the computation in the process of application while maintaining the expression ability of intuitionistic fuzzy soft sets. In this paper, an improved model of normalization operation of intuitionistic fuzzy soft sets is proposed. Firstly, the hesitation degree is redistributed to membership function and non-membership function according to the preference of decision maker, making the sum of membership value and non-membership value is 1, and a new normalization operation is obtained. Secondly, some elemental properties of this new necessity operation are discussed. Finally, a practical example is used to verify the rationality and effectiveness of the fuzzy decision-making method based on the normalization operation of intuitionistic fuzzy soft sets.
文章引用：陈炎炎, 潘小东. 直觉模糊软集上的新型运算及其在决策问题中的应用[J]. 理论数学, 2024, 14(11): 301-313. https://doi.org/10.12677/pm.2024.1411397

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