关键词: 符号中心, 直觉模糊数, 排序

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