Abstract: Intuitionistic fuzzy numbers (IFN), characterized by membership, non-membership, and hesitation degree have become pivotal in uncertain decision-making. However, existing ranking methods face critical limitations when hesitation degrees vanish (i.e., degenerate to fuzzy numbers) or when compared with negative-domain IFN. This study addresses these gaps by developing a unified ranking framework that maintains consistency with classical fuzzy number ranking principles while incorporating decision-maker attitudes.
We define subordinate lower fuzzy numbers and subordinate upper fuzzy numbers to bound the membership range of IFN. A preference-weighted centroid (x₀(A~),y₀(A~)) is formulated, where: x₀ integrates geometric centers of subordinate bounds, y₀ combines membership strength and hesitation through an attitude parameter α∈[0,1]. A sign function I_x0 resolves ambiguity in positive/negative IFN comparisons. The ranking index R(A~)=I_x0·x²₀+y²₀ ensures: compatibility with fuzzy number ranking when π_<sub>A~=0; attitudinal flexibility via α-weighting (pessimistic: α<0.5; neutral: α=0.5; optimistic: α>0.5). For trapezoidal/triangular IFN, closed-form centroid formulas prove that R(A~) degenerates to fuzzy centroid index (WANG and LEE, 2008) when π_<sub>A~=0.
Four comparative cases demonstrate the resolution of both counterintuitive rankings for negative IFN and attitude-driven outcome variations while maintaining transitivity. In selecting India's aerospace research center, weighted aggregation of trapezoidal IFN yields robustranking ₅>₁>₂>₄>₃, aligning with benchmark methods still offering explicit preference interpretation.
The proposed method overcomes the three limitations: hesitation-induced ranking failure, sign ignorance in distance metrics, rigidity to decision-maker attitudes. Future work may extend this framework to interval type-2 fuzzy sets and dynamic multi-period decision environments.

Key words: sign center, intuitionistic fuzzy number, ranking

摘要： 在直觉模糊数排序理论中,当犹豫度为零时往往出现排序指标不适用的情况。针对这种情况,本文定义了隶属下限模糊数和隶属上限模糊数,在考虑决策者偏好态度的基础上,构造了直觉模糊数的中心。通过引入符号函数,建立了同时适用于模糊正数和模糊负数的符号中心排序指标,依据排序指标值越大直觉模糊数越大的原则对直觉模糊数排序。排序指标建立的原则是保证直觉模糊数退化为模糊数时,直觉模糊数的排序指标退化为模糊数的排序指标,最后,通过选址实例说明符号中心直觉模糊数排序方法的现实应用价值。

关键词: 符号中心, 直觉模糊数, 排序