On lattice-ordered t_r-norms for type-2 fuzzy sets

2020/04/07 by Xinxing Wu, Guanrong Chen, Wu, Xinxing +1
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy Logic and Control Systems #Fuzzy Systems and Optimization #General Mathematics (math.GM) #Multi-Criteria Decision Making

paper · pdf · doi:10.48550/arxiv.2004.03593

openalex publication_date 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered t_r-norm, which is not the convolution of t-norms on [0, 1], is obtained. These results negatively answer two open problems posed by Walker and Walker in [15].

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