方法对比

	Hamacher T-范数	犹豫模糊TOPSIS（含可选的不完整权重信息）(Xu-Zhang 2013 KBS)	直觉模糊TOPSIS	TOPSIS的毕达哥拉斯扩展
领域	决策	决策	决策	决策
方法族	MCDM	MCDM	MCDM	MCDM
起源年份	1978	2013	1986	2014
提出者	Hamacher, H.	Xu, Z., Zhang, X.	Atanassov, K. T.	Zhang, X., Xu, Z.
类型	Parametric t-norm family — Hamacher (rational generator)	Distance-to-ideal ranking (Hwang-Yoon 1981) extended to Hesitant Fuzzy Elements (HFE ⊂ [0,1]) via the hesitant normalised Euclidean distance d_1 (Xu-Xia 2011b); supports three weight-information modes: fully specified, completely unknown (Eq.(22) maximizing deviation closed-form), and partly known (Model M-2 linear programme).	Distance-based ranking under Intuitionistic Fuzzy uncertainty	Pythagorean outranking/ranking — Pythagorean Fuzzy Number (PFN: μ, ν; μ²+ν² ≤ 1)
开创性文献	Hamacher, H. (1978). Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. Progress in Cybernetics and Systems Research	Xu, Z., Zhang, X. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems	Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems	Zhang, X., Xu, Z. (2014). Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of Intelligent Systems
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相关	4	8	5	8
摘要	TNORM-HAMACHER (Hamacher T-norm — Rational parametric t-norm for fuzzy aggregation) is a t-norm multi-criteria decision-making (MCDM) method introduced by Hamacher, H. in 1978. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.	HF-TOPSIS (Hesitant Fuzzy TOPSIS with optional incomplete weight information (Xu-Zhang 2013 KBS)) is a ranking multi-criteria decision-making (MCDM) method introduced by Xu, Z., Zhang, X. in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.	IF-TOPSIS (Intuitionistic Fuzzy TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Atanassov, K. T. in 1986. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.	PF-TOPSIS (Pythagorean extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Zhang, X., Xu, Z. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.