On the admissibility of the alpha-order for fuzzy numbers

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发表日期：

2024年8月23日

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Diego García-Zamora,
Anderson Cruz,
Fernando Neres,
Antonio Francisco Roldán López de Hierro,
Regivan H. N. Santiago,
Humberto Bustince

摘要

The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose $\beta $ $β$ -cuts are closed subsets with a finite number of connected components. This paper explores some key properties of such alpha-order. Specifically, we will focus on admissibility, a fundamental property for any ranking method defined for fuzzy numbers since it guarantees that such a ranking method is consistent with the usual order on the real line.