On the admissibility of the alpha-order for fuzzy numbers

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-08-23 DOI:10.1007/s40314-024-02885-2

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

引用次数: 0

Abstract

The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose \(\beta \)-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.

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论模糊数α阶的可接受性

α-阶的概念是最近引入的一种二元关系，它允许对有界支持的模糊集进行排序，并且其 \(beta \)-切点是具有有限数量连接成分的封闭子集。本文将探讨这种 α 阶的一些关键属性。具体来说，我们将重点讨论可接受性，这是为模糊数定义的任何排序方法的一个基本属性，因为它保证了这种排序方法与实线上的通常阶一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.